Thermo-Mechanical Analysis of RCC Dams

Thermo-Mechanical Analysis of Roller Compacted Concrete Dams

Year: 2011

NABEEL AHMED KHAN 2007-MS-STRU-08

DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF ENGINEERING AND TECHNOLOGY

LAHORE, PAKISTAN

Thermo-Mechanical Analysis of Roller Compacted Concrete Dams

Year: 2011

NABEEL AHMED KHAN

2007-MS-STRU-08

(Assistant Prof. Dr. Kafeel Ahmad) SUPERVISOR

(Prof. (R) Dr. Zia-ud-din Mian) EXTERNAL EXAMINER

Civil Engineering Department CHAIRMAN

Faculty of Civil Engineering DEAN

Thesis submitted in partial fulfillment of the requirements for the Degree of Master of Science in Civil Engineering

DEPARTMENT OF CIVIL ENGINEERING, UNIVERSITY OF ENGINEERING AND TECHNOLOGY

LAHORE, PAKISTAN

Dedication

To Parents and Teachers for

leading me into intellectual

persuade and who inspired

me towards the sacred task

of learning.

Acknowledgements

The author would not have been able to finish this project without the support of family and friends who have always been there, the encouragement they give to keep moving and their love to empower, that never fails at any time. Thank you.

The author would like to thank Dr. Kafeel Ahmad, Research Supervisor, who has given a chance to prove that everything is possible. His deep insight and supervision gave a lot of positive perspective, and taught things far more than understanding. To you sir, the author gives lots of thanks and respect. Thank you.

The author would also thank Mr.Mumtaz J. Shabbir (late), the Ex- Head of SED NESPAK who was a true leader and visionary and always inspired everyone towards living purposefully and attaining something with marvel and dedication. He will always live in the hearts for what he taught was the sheer sense of honour and love for the field. Thank you Sir.

And In the end, the author would like to thank Almighty Allah, He who was, is and will always be; Him who is giving high hopes; for giving us strength and hope towards achieving goals; for being true to what He promised. All praises to Him, thank you our Creator and Savior. To God be the glory.

Nabeel A. Khan

ABSTRACT

Roller Compacted Concrete (RCC) has emerged as an excellent material to replace the

costly conventional mass concrete in the construction of large dams worldwide. RCC

dams are built by placing concrete lifts and compacting them with external vibratory

rollers and dozers. The principal advantage of the use of RCC is reduced cost and time in

dam construction. But it has a tendency of excessive thermal cracking which needs to be

controlled during its design and construction.

Concrete setting is an exothermic reaction which produces considerable amount of heat

due to hydration of cement. The low thermal conductivity of concrete and the great

volume of massive concrete structure, such as gravity dam, contribute to a low

dissipation of the hydration heat. The rapid method of construction associated with RCC

dams creates an adiabatic environment inside the dam, as there is no time to dissipate the

heat generated before placing the next layer. This transient thermal gradient results in

volumetric changes which may be restrained by previously set concrete in the vicinity of

the newly placed lift, thus causing tensile stresses. If concrete tensile strain capacity is

exceeded, cracking will occur. Excessive concrete cracking may cause excessive seepage,

with the resulting damaging effects on durability and even structural stability of dam.

Experience shows that thermal cracking is a major concern for RCC dams and a realistic

evaluation of this phenomenon beforehand is mandatory.

In this research, steps involved in thermo-mechanical analysis of large RCC dams have

been presented. Detailed construction-stage thermo-mechanical analysis of Dasu Dam

which is a part of WAPDA’s Future vision 2025 has been carried out as case study

emphasizing on actual site conditions prevalent during the construction of this dam.

TABLE OF CONTENTS ACKNOWLEDGEMENTS ABSTRACT 1.0 INTRODUCTION 1 1.1 Development of RCC 1 1.2 Advent of RCC in Pakistan 2 1.3 Structural Analyses of RCC Dams 3 1.4 Why Thermal Analysis? 3 1.5 Thesis Organization 4 2.0 LITERATURE REVIEW 5 2.1 Introduction 5 2.2 Discussion & Underlying Principles 5 2.3 Numerical Models for Thermo-Mechanical Analysis of RCC 11 2.4 Further Research 26 3.0 COMPUTATIONAL STRATEGY & ALGORITHM 29 3.1 Introduction 29 3.2 Algorithm for Thermo-Mechanical Analysis of RCC Dam 29 3.3 Numerical Modeling and Material Properties 32 3.3.1 Mix Design of RCC 32 3.3.2 RCC Properties Adopted in this Analysis 34 3.3.3 Climatic Variations 38 3.3.4 Placement Temperature 38 3.3.5 Construction Schedule 39 3.4 Computer Modeling 41 3.4.1 Introduction to ANSYS 41 3.4.2 Numerical Discretization and Analysis Procedure 42 3.4.3 Analysis Assumptions 47 4.0 RESULTS & DISCUSSIONS 48 4.1 Introduction 48 4.2 Thermal Gradient Analysis 48 4.3 Thermal Stress Analysis 52 4.4 Thermal Crack Analysis 56 4.5 Fracture Mechanics Parameters 60

4.5.1 Linear Elastic Fracture Mechanics (LEFM) 60 4.5.2 Non Linear Fracture Mechanics 61 4.5.3 Fictitious Crack Model 62 4.5.4 Application of Fracture Mechanics 63 4.6 Validation of Results 66 5.0 CONCLUSIONS & RECOMMENDATIONS 68 5.1 Introduction 68 5.2 Conclusions 68 5.3 Recommendations 71 REFERENCES

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INTRODUCTION Roller Compacted Concrete (RCC) has emerged as an excellent material to replace the

costly conventional mass concrete in the construction of large dams worldwide over the

past forty years. The use of RCC has allowed many new dams to become financially

viable due to the reduced economies realized from the rapid construction method.

In physical appearance, RCC is relatively dry, lean and has zero slump, containing coarse

and fine aggregates that are consolidated by external vibration using vibratory rollers,

dozers and other heavy equipment. In principle, RCC dam is a concrete dam constructed

by using earth/rockfill dam construction equipment. In the hardened condition, RCC has

similar properties to conventional concrete. For effective compaction, RCC must be dry

enough to support the weight of the construction equipment, but have a consistency wet

enough to permit adequate distribution of the paste binder throughout the mass during the

mixing and vibration process.

ACI 116 and ACI 207.5R defines RCC as concrete compacted by roller compaction; and

which will support a (vibratory) roller while being compacted. RCC is usually mixed

using high-capacity continuous mixing or batching equipment. The mix is then delivered

with trucks or conveyors, and spread with bulldozers in layers prior to compaction.

1.1 DEVELOPMENT OF RCC

Roller compacted concrete has been in regular use since 1920s, mostly as a base for

highways and airfield pavements. The rapid worldwide acceptance of RCC was a result of

its economics and successful performance in the recent history. The first use of RCC in

Chapter

1

Chapter 1 Introduction

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large volumes (2.66 million cubic metres) was at Tarbela Dam in 1974 where it was used

to replace rock in the collapsed stilling basins and plunge pools. Shimajigawa Dam, Japan

(completed in 1981) and Willow Creek Dam, USA (completed in 1982) are considered

the principal structures that initiated the global acceptance of RCC dams and up till today,

over 500 RCC dams have been completed worldwide. It has become virtually the

standard method of constructing concrete gravity dams.

Rapid advances in RCC construction have occurred in developing nations to meet

increased water and power needs. Faster concrete placement rates and low heat of

hydration have primarily been key factors for the construction of large RCC dams. The

highest RCC dam built to date is the 216m high Longtan dam, currently nearing

completion in China. The 220 m high Nam Ngum dam in Lao PDR is also at initial

stages. The behaviour of RCC gravity dams is essentially the same as for conventional

concrete gravity dams from structural, operational and maintenance points of view.

1.2 ADVENT OF RCC IN PAKISTAN

Water and Power Development Authority (WAPDA) launched an elaborate plan to meet

the country’s growing energy needs namely “Water Resources and Hydropower

Development -Vision 2025” according to which several large dams have been proposed

throughout Pakistan with Diamer Basha Dam (283m high), Dasu Dam (233m high) and

Bunji Dam (180m high) to name a few being RCC dams specifically. These three large

dams will add approximately 12000 Megawatts to the national grid. Construction of

Diamer Basha Dam will initiate in 2011, Dasu Dam is in tender design stage whereas

prefeasibility studies of Bunji Dam have been completed. Once completed, these dams

will certainly be a landmark for Northern Areas of Pakistan making it a potential hub of

extreme engineering achievements in the field of RCC dam construction.

The design of an RCC dam balances the use of available materials, the selection of

structural features and the proposed methods of construction. Faster concrete placement

rates and low heat of hydration have been key factors for the construction of large RCC

dams. By maintaining good quality control during construction, RCC offers an attractive

option for building large dams especially gravity dams where the concrete volume is


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substantial. Sound rock foundations as encountered at these dam sites are considered the

most suitable for RCC gravity dams. In addition, good quality coarse and fine aggregates

are available abundantly in these localities which add to the advantages of RCC. All these

factors governed the selection of RCC as the ultimate choice for construction of large

dams in Pakistan.

1.3 STRUCTURAL ANALYSES OF RCC DAMS

In general, structural design studies of a concrete dam comprise of stability analysis,

stress analysis and thermal analysis. Stability and stress analyses are based on principles

of statics and dynamics using either the rigid body mechanics or the discretization such as

Finite elements etc. Thermal analysis, on the contrary, is quiet rigorous particularly due to

lengthy algorithms involved because of its non-linear incremental transient nature. Above

that, definition of accurate concrete model incorporating all important properties to

simulate the actual construction scenario of a dam makes the problem even more

complicated.

1.4 WHY THERMAL ANALYSIS?

Concrete setting is an exothermic reaction that produces considerable amount of heat due

to hydration of cement. The low thermal conductivity of concrete and the great volume of

massive concrete structure, such as gravity dam, contribute to a low dissipation of this

heat. The rapid method of construction associated with RCC dams creates an almost

adiabatic behaviour of material in the centre of dam, as there is no time to dissipate the

heat generated before placing the next layer. This transient thermal gradient results in

volumetric changes which may be restrained by previously set concrete, thus causing

tensile stresses. If concrete tensile strain capacity is exceeded, cracking may occur.

Excessive concrete cracking may cause excessive seepage, with the resulting damaging

effects on durability and even structural stability. Experience shows that thermal cracking

is a major concern for RCC dams and a realistic evaluation of this phenomenon

beforehand is mandatory.


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In this research, steps involved in thermo-mechanical analysis of large RCC dams will be

presented. Detailed construction-stage thermo-mechanical analysis of Dasu Dam will be

carried out as case study emphasizing on actual site conditions prevalent at the

construction site.

1.5 THESIS ORGANIZATION

The current research has been presented in different chapters described as under, along

with a brief summary of works carried out.

Chapter 1 focuses on introducing the concept of RCC and how it has developed over the

years replacing the conventional concrete practices in the construction of large dams.

In Chapter 2, a detailed review of literature including the underlying principles of thermo-

mechanical analysis and description of analytical models put forth by various researchers

and some comments on these models have been presented.

In Chapter 3, the computational strategy and modeling of roller compacted concrete has

been discussed. Detailed description of the adopted parameters, various assumptions and

algorithms used in the computer aided modeling and solution of the thermal analysis

problem has been presented. Emphasis has been laid on selection of the most appropriate

mathematical model that would simulate the actual on-site conditions of the proposed

dam.

Chapter 4 presents the results of thermo-mechanical analysis as obtained from the

software. Both tabular data and graphical displays have been provided to give a better

picture and to develop understanding of the actual problem. Sensitivity of the assumed

parameters on the obtained results has also been discussed. A brief discussion on fracture

mechanics parameters has also been presented in this chapter.

Finally, Chapter 5 concludes the main results obtained from this study and some

important recommendations for future research oriented works.

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1LITERATURE REVIEW 2.1 INTRODUCTION This chapter lays emphasis on the basics of thermal stresses in large concrete dams with

detailed description of thermo-mechanical properties of Roller Compacted Concrete

which will be used in detailed analysis afterwards. A number of numerical models

presented by various researchers to depict inherent properties of RCC will also be

provided with particular merits and demerits.

2.2 DISCUSSION & UNDERLYING PRINCIPLES During construction, the placement temperature is somewhat higher than the ambient

temperature prevalent at that instant. As RCC hydrates, its temperature rises and due to

restraint by adjacent material, it experiences compression as it attempts to expand. Once

hydration is essentially complete, the RCC slowly cools decreasing the level of the

compression till a steady state temperature is reached. The temperature which then causes

a stage of no stress is called “zero stress temperature” (ZST). Further decrease of

temperature can cause tensile stresses which can exceed tensile capacity and thus lead to

crack development.

The following figure describes the various parameters relevant to the thermal studies

prepared by Deutsches Talsperren komitee [1].

Chapter

2

Chapter 2 Literature Review

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Figure 2.1: General temperature and stress profile of RCC A = Concrete Temperature

B = Time

C = Concrete Stresses

D = Zero Stress temperature

E = Cracking Temperature

F = Compressive prestressing

G = Tensile stresses

H = Tensile strength

Heat transfer is a complex phenomenon involving conduction, convection, radiation and

heat generation as a result of hydration, all occurring side by side. Due to rapidity of RCC

placement, hydration heat becomes entrapped and this heat is conducted radially to the

layers above and below the one being considered. Coefficient of conductivity governs this

behaviour. Convection occurs as a result of heat loss to the environment depending upon

heat transfer mechanism. Convection takes place in two phases:

a) Immediately after a layer is placed taking some portion of the early heat of

hydration. The setting time of RCC is about five to seven hours during which

much of the heat is dissipated through convection.


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b) Surface heat transfer taking place from the dam face. Heat generated due to

hydration moves towards the dam face due to conduction from where it is lost to

air.

Though the thermal effects of conventional concrete and roller compacted concrete do not

differ much, still a significant difference between the two is the slower placement rate for

conventional concrete which allows for an early dissipation of hydration heat. The rapid

placement inherent to RCC implies that increased insulation due to successive layers is

present by the time peak hydration temperatures are reached. On the other hand, lower

cementitious materials content of RCC implies a lower total adiabatic hydration

temperature rise than an equivalent conventionally vibrated concrete (CVC).

The actual temperature rise in mass concrete depends on the dynamics of exothermic

reaction between cement and water which in turn is time and temperature dependent.

Ambient environmental conditions, thermal properties of the mix, geometry of structure

and construction conditions influence the process of heat development. Uncontrolled

increase in the temperature of mass concrete is detrimental to the integrity of structure.

Increase in volume of concrete equal to the product of temperature rise and co-efficient of

thermal expansions occurs and this process continues till the peak temperatures are

achieved. Over a period of several months or even years, temperature of mass concrete

slowly cools to a stable temperature, or a stable temperature cycle. If concrete is

unrestrained, it is free to contract as a result of cooling from peak temperatures and no

tensile stresses will thus be produced. However, mass concrete structures are always

restrained to certain degrees either due to foundation or previously placed concrete lifts,

tensile stresses are thus obligatory. If these stresses exceed tensile strain capacity of mass

concrete, thermal cracks are formed either on the surface called ‘surface gradient

cracking’ or inside the mass called ‘mass gradient cracking’. Seepage is the principal

problem if magnitude of these cracks is extensive which causes additional hydraulic

gradients inside the dam body, combined with the fact that RCC is somewhat weaker

along the lift joints, creates a major risk for structural stability and weakens the dam in

sliding.


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The following set of figures describes various parameters/processes involved in the

thermal analysis problem of concrete dam. a) during construction and b) after completion

of construction

Figure 2.2 (a): Process of Heat Transfer in Concrete Dams during Construction

Figure 2.2 (b): Process of Heat Transfer in Concrete Dams after Completion of Construction


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Over the last three decades, efforts have been implanted to establish true numerical

simulation of thermal cracking so that potential property and life risk in the event of dam

failures may be avoided. Several models were put forth by renowned researchers to

evaluate thermal properties of roller compacted concrete as will be presented in the

subsequent sections. But before that, a brief description of thermal and mechanical

properties of roller compacted concrete is given below [14]:

Adiabatic Temperature Rise (Tad): An adiabatic system is one in which heat is neither

allowed to enter or leave. Adiabatic temperature rise is therefore, a rise in temperature of

concrete due to heat of hydration of cement in adiabatic conditions. In mass concrete,

temperatures near the centre of mass will be sum of placement temperatures and adiabatic

temperature rise. Near the surface, peak temperatures will be numerically close to

ambient temperatures. Total temperature rise depends on the cement content in the

concrete mix. Traditionally, almost half of the cement quantity had been replaced with

other cementitious compounds just to reduce the total heat of hydration. Typical values of

adiabatic temperature rise in mass concrete ranges from 11 to 19 °C at 5 days to 17 to 25

°C at 28 days. ACI 207.1R also gives typical curves for adiabatic temperature rise to be

used in case of unavailability of laboratory data.

Specific Heat (c): Specific heat is the amount of heat required for unit rise in

temperature in a unit mass. Its value is affected by temperature changes however, it is

assumed constant for mass concrete calculations. Typical values range from 0.75 to 1.25

kJ/kg-K.

Thermal Conductivity (K): It is the rate at which heat is transmitted through a material

of unit area and thickness when there is a unit difference in temperature between the two

faces. It is the product of thermal diffusivity, specific heat and density. It is also assumed

to be independent of temperature for the purpose of thermal analysis. Typical values of

thermal conductivity for mass concrete range from 1.7 to 3.5 W/m-K.

Thermal diffusivity (h2): Thermal diffusivity is the rate at which temperature change

can occur in a material. It is obtained by dividing thermal conductivity with the product of


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specific heat and unit weight (= K/γc). It is also assumed to be independent of time and

temperature. Typical values range from 0.003 to 0.006 m2/hr.

Modulus of Elasticity (Ec): It is defined as the ratio of normal stress to corresponding

normal strain below proportional limit. For concrete, modulus of elasticity depends on the

degree of hydration and hence it is time and temperature dependent. However, its

temperature dependency is neglected for mass concretes. Laboratory tests should be

performed to determine elasticity values at various ages to represent the ‘aging’ effects.

Typically, its value range from 21 to 38 GPa at 28 days. Sustained modulus of elasticity

(Esus) includes creep effects and can be obtained directly from creep tests.

Co-efficient of Thermal Expansion (Cth): It is the change in linear dimension per unit

length divided by temperature change. The value of this coefficient depends on the type

and quantity of coarse aggregates and is considered independent of time and strength.

Typical values are 5 to 14 × 10-6 per °C.

Tensile Strain Capacity (εsc): It is the change in length/volume per unit length/volume

that can be accommodated in concrete prior to cracking. It depends on time and strength

of concrete and also upon the rate of loading.

Creep: Creep is defined as time dependent deformation due to loads applied for

longer periods. It results in an increase in strain, but at a continuously decreasing rate

keeping the stress constant. It depends on modulus of elasticity and hence is time and

strength dependent. Specific creep is the creep under unit stress or strain per MPa.

Shrinkage: Drying shrinkage occurs due to loss of moisture from concrete structures

which are relatively thin than mass concrete. Autogenous shrinkage is a decrease in

volume of concrete due to hydration of the cementitious materials. For mass concrete

structures, only autogenous shrinkage is considered. It occurs over longer time periods

and is dependent on time and strength of concrete.


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2.3 NUMERICAL MODELS FOR THERMO-MECHANICAL ANALYSIS OF RCC

Thermo-mechanical analysis is a complex problem due to involvement of plenty of

variables. Aging of concrete is the most important aspect in this regard as almost all

properties of concrete vary with age of concrete. Furthermore, changing environmental

conditions adds to the complexity of this problem. Research is still underway to develop

the most accurate numerical and analytical model of roller compacted concrete in the

construction of dam representing the actual on-site scenarios.

Some of the most prominent works carried out by researchers and practicing engineers at

various mega projects are presented below. Each is followed by a brief note of author’s

observations:

Cervera and Goltz (2004) [7] presented a modified 1-D thermo-chemo-mechanical model

for analyzing roller compacted concrete dam. The idea behind this 1-D model was to

reduce the computational efforts and CPU time cost in analyzing 2-D or 3-D models. The

model presented by these authors was implemented in computer program named COMET

developed by International Centre for Numerical Methods in Engineering (CIMNE) in

Barcelona, Spain.

The following hydration model based on the principles of thermodynamics was presented

by the authors:

Thermal field equation is given by: 𝐶 − (𝜉) = 𝑅𝑒𝑥𝑡 + 𝑘𝑇 ∇. (∇T) … 2.1 where, T = temperature (°C)

C = heat capacity per unit volume

Q = velocity of liberated heat per unit volume

Rext = heat production of the external volume of heat source

kT = thermal conductivity

ξ = hydration degree = Q/Q∞

Q∞ = final amount of liberated heat in ideal conditions


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The final degree of hydration depends on the water-cement ratio and is calculated by:

𝜉∞ = 1.031𝑤/𝑐0.194+𝑤/𝑐

… 2.2

This is equivalent to assuming a linear dependency of the form Q(ξ) = Qξ ξ where Qξ is

the latent heat, assumed to be constant. To incorporate aging effects on material

properties, an internal variable k was defined which is calculated as:

𝑘 = (𝐴𝑓𝜉 + 𝐵𝑓) 𝑇𝑇−𝑇𝑇𝑇−𝑇𝑟𝑒𝑓

𝑛𝑇𝜉 … 2.3

where, Af, Bf = material constants

Tref = reference temperature

TT = maximum temperature at which hardening of concrete will occur

nT = material property controlling sensibility to the curing temperature

Thus, compressive strength is given as:

𝑓−(𝑘) = 𝑘𝑓∞− … 2.4 where, 𝑓− is the compressive strength and 𝑓∞− is its final value. On a similar pattern,

tensile strength and elastic modulus can be given as:

𝑓+(𝑘) = 𝑘2/3𝑓∞+ and 𝐸(𝑘) = 𝑘2/3𝐸∞ … 2.5 The creep effects were modeled via a visco-elastic damage model based on the

framework of Continuum Damage Mechanics Theory considering short and long term

behaviours involving creep and relaxation phenomenon. Detailed description of this

model is given in [7].

Results from software COMET which is based on the above mathematical model were

compared with temperature data obtained from thermometers installed in Rialb RCC

Dam, Spain.


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Observations and Comments:

This 1-D strip model is able to calculate temperature gradients and thermal stresses quiet

accurately. ‘Slide lines’ were placed on both sides of the strip model to simulate the

horizontal heat flux. However, calculation of these slide lines is quiet problematic as heat

can flow in any diagonal direction as well which cannot be modeled with these slide lines.

In addition, transverse crack pattern is difficult to judge from this model due to its 1-D

behaviour.

Calmon et-al (2004) [6] presented a numerical model for thermal stresses of RCC dams

using 2-D finite element method. According to them, the general 2-D partial differential

equation governing the heat flow in a solid is given as:

𝜕𝜕𝑥𝑘(𝑥) 𝜕𝑇

𝜕𝑥 + 𝜕

𝜕𝑦𝑘(𝑦) 𝜕𝑇

𝜕𝑦 + = 𝜌𝑐 𝜕𝑇

𝜕𝑡 … 2.6

where q = rate of internal heat generation due to hydration per unit of volume and time (W/m3)

ρ = density of material (kg/m3)

c = specific heat capacity of concrete (J/kg°C)

k = thermal conductivity of the material (W/m°C)

ρc = thermal capacity of concrete, and

T = temperature function depending on the location and time

Boundary conditions for this heat flow problem are Neumann conditions given as:

𝑘𝑥𝜕𝑇𝜕𝑥𝑛𝑥 + 𝑘𝑦

𝜕𝑇𝜕𝑦𝑛𝑦 + 𝑞(𝑥,𝑦, 𝑡) = 0 … 2.7

where nx and ny are the Cartesian co-ordinates of the vector of directional cosines of the

normal to the surface and q(x,y,t) is the heat flow gained/lost by unity area. To simulate

environmental conditions, Calmon et-al used the following equation based on Newton’s

law:

qc (x,y,t) = hc [T(x,y,t) – Ta(t)] … 2.8


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Here hc is the convection heat transfer coefficient (also called film coefficient, W/m2) and

for concrete surfaces, it is approximated as:

hc = 3.8w + 4.7 … 2.9 Authors used the following relation originally given by Polivka & Wilson (1976) and

modified by Silva (2002) to portray heat transfer by radiation between two surfaces:

𝑞𝑟(𝑥,𝑦, 𝑡) = 𝑉𝜎 11∈𝑟+ 1∈𝑠−1 (𝑇𝑟4 − 𝑇𝑠4) … 2.10

where V = radiation factor (o ≥ V ≥ 1)

σ = Stefan-Boltzmann constant [5.6705 x 10-8 W/(m2.K4)]

εs = emissivity of the surface

εr = emissivity of the external source of radiation

Ts = absolute temperature of the surface (Kelvin)

Tr = absolute temperature of the source (Kelvin)

Now heat gained due to solar radiations was expressed by the following relation: qs(x,y,t) = a.I (x,y,t) … 2.11 Here α is the coefficient of absorptivity of solar radiation and I (x,y,t) is the total incident

solar radiation at any point at time t. These values can be obtained from local

meteorological data. To model the heat of hydration of concrete, following equation

based on experimental works of Rastrup (1954) was used.

𝑄 = 𝑞 + 𝐸. 𝑒𝑏.(𝑡𝑒)−𝑛 … 2.12 where Q is the heat of hydration (J/g) and E, b, n, q are constants depending on

composition of concrete mix. The variable te is an equivalent time for the process in real

time t and is obtained as:


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𝑡𝑒 = ∑ 20.1(𝑇𝑡−𝑇𝑟)𝑡0

3600 … 2.13

Here Tt is the temperature of the process during time Δt in seconds and Tr is the reference

temperature. Heat generation rate per unit volume and unit time is

= 𝐶.𝑛. 𝑏. (𝑡𝑒)−𝑛−1𝐸. 𝑒−𝑏.𝑡𝑒−𝑛 . 20.1(𝑇𝑡−𝑇𝑟)

3600 … 2.14

where, = heat generation rate per unit volume (W/m3)

C = cement content per unit volume of concrete (kg/m3)

N, b and E are constants and their values are determined from experimental data

For defining material model in the computer program, authors utilized previously

published data. Variation of modulus of elasticity with time was calculated from the

following equation:

𝐸 = 𝑡𝑎+𝑏.𝑡

… 2.15

Here, t is the age of concrete while a and b are constants. Creep of concrete was also

considered and following equation developed by United States Bureau of Reclamation

(USBR, 1956) was implanted in the computer program

𝐽(𝑡,𝑡0) = 1

𝐸𝑡0+ 𝐹𝑡0 . log (𝑡 − 𝑡0 + 1) … 2.16

𝐹𝑡0 = 𝑐 + 𝑑/𝑡0 … 2.17 where, 𝐸𝑡0 = modulus of elasticity at initial age to

𝐹𝑡0 = coefficient depending on time to, calculated from above equation

c and d are co-efficient of creep function


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Authors developed two computer programs PFEM_2D T and PFEM_2D AT based on

above presented equations in collaboration with Furnas Centrais Electricas S.A. Brazil.

This software was applied for thermal stress analysis of the gravity dam at Cana Brava

hydroelectric plant in Goias, Brazil.

Observations and Comments: The model presented by Calmon et-al (2004) is restricted to two dimensional heat transfer

problems. Furthermore, un-coupled thermo mechanical analysis is performed i.e. first

temperature distributions for all time increments is calculated and later, these values are

used in the second software to judge thermal stresses. This uncoupling is cumbersome in

terms of data handling within the software.

In addition, this model does not give any method for determining the placement

temperatures of concrete which is a major participant in early thermal stresses. Most of

the material properties like thermal conductivity, diffusivity, specific heat etc were

considered independent of time and temperature. No emphasis was laid on tensile

properties of concrete and hence thermal crack propagation was not determined.

Zhang, Zhu and Guo (2004) [28] presented thermal stress simulation and possible crack

pattern of 111 m high Mianhuatan RCC dam, China. The authors considered the

following equations to simulate material properties of concrete.

𝐸(𝜏) = 𝐸0(1.0 − 𝑒−𝛼𝜏𝛽) … 2.18 where, τ = concrete age, E(τ) = elastic modulus at age τ, E0 = ultimate elastic modulus, α

and β are test parameters.

𝜃(𝜏) = 𝜃0(1.0 − 𝑒−𝛼𝜏𝛽) … 2.19 where, θ(τ) = insulated temperature rise at age τ, θ0 = ultimate insulated temperature

rising. To simulate creep of concrete, authors suggested the following equation:


Page | 17

𝐶(𝑡,𝑇) = (𝐴1 + 𝐴2𝜏−𝑎1)1 − 𝑒−𝑘1(𝑡−𝑇) + (𝐵1 + 𝐵2𝜏−𝑎2)1 − 𝑒−𝑘2(𝑡−𝑇) +𝐷𝑒−𝑘3𝜏1 − 𝑒−𝑘3(𝑡−𝑇) … 2.20 In this equation, A1, A2, B1, B2, α1, α2, k1, k2 and k3 are parameters depending on

experimental data. Authors used compound layer method along with variable time

increments in different regions while modeling Mianhuatan dam on a program developed

by IWHR.

Observations and Comments: The creep model suggested by authors is very complex involving lots of variables and no

indication has been given to determine these variables from lab testing. Compound layer

method adopted in this study is a powerful tool to reduce number of calculation steps

while assuring accuracy. In this method finer mesh is used at early ages of concrete to

account for minute thermal changes. As time progresses and temperatures attain

somewhat constant values, these fine meshes are merged into larger sized meshes. On

similar pattern, time steps are also changed from smaller time steps at early ages to larger

ones at later. This method is very efficient and reduces calculation time dramatically.

Noorzaei, Ghafouri and Amini (2006) [23] investigated the influence of placement

schedule on thermal stresses of RCC dam. A finite element based computer code named

STARD was developed and following relationships were postulated to determine

temperature gradient and corresponding stresses. These were later applied to calculate

thermal stresses for 169m high Roodbar RCC dam, Iran.

Fourier equation governing thermal generation and temperature distribution for isotropic

2-D environment is

𝜕2𝑇𝜕𝑥2

+ 𝜕2𝑇

𝜕𝑦2+ 𝑄

𝐾= 𝜌𝐶

𝐾𝜕𝑇𝜕𝑡

… 2.21

where, ρ = density

C = concrete specific heat


Page | 18

T = concrete temperature

K = concrete conductivity co-efficient

Q = rate of heat introducing per unit volume

α = thermal diffusing

Two main boundary conditions for this problem are Drichlet and Couchy boundary as

shown below:

T = Tp … 2.22

𝐾𝑥𝜕𝑇𝜕𝑥𝑙𝑥 + 𝐾𝑦

𝜕𝑇𝜕𝑦𝑙𝑦 + 𝑞 + ℎ(𝑇𝑠 − 𝑇𝑓) = 0 … 2.23

where Tp is the known value of temperatures on nodal points at boundaries, q is the heat

flowing from surface, h is the film co-efficient, Ts is unknown temperature at the

boundary nodal points, Tf is ambient temperature, lx and ly are direction cosines.

Authors used the following numerical model originally developed by Taylor and Galerkin

for solving these equations.

[𝐴𝐺∗ ]∆T = 𝐹𝐺∗ … 2.24 Here [𝐴𝐺∗ ] is the load matrix and 𝐹𝐺∗ is the force matrix. Relations for determination of

these matrices are given in Ref [5]. For determination of hydration heat, equation given

by M. Ishikawa (1991) for RCC was used

Q = ρcTad … 2.25

where Tad is the adiabatic rise in concrete temperature and is given by: Tad = Kt (1-e-αt) … 2.26 Here Kt is the maximum temperature of concrete under adiabatic conditions and α is a

parameter representing heat generation rate. This yields the following equation:

Q = ρc Kt αe-αt … 2.27


Page | 19

Temperature of RCC while placing is another key factor and authors postulated the

following equation for its determination

Tcasting = Tanu -2/3(Tanu-Tmon) + Crush Add + Mixing Add + Transporting Add … 2.28 Adding temperature of aggregate crushing and concrete mixing is generally assumed

equal to 1.1 °C. The effect of radiations of newly placed concrete was considered by

adding 1°C to the computer model. To account for temperature distribution in rock, it was

suggested that heat transfer should be analyzed for temperature data of 2-3 years before

starting of construction.

The influence of placing schedules was checked by performing thermal analysis for two

different conditions: placement starting on 1 November and placement starting on 1 July.

Based on their research, authors concluded that concrete placement starting in summer

season will increase tensile stresses near the dam foundations.

Observations and Comments: The numerical model used by Noorzaei et-al is very elaborate and comprehensive.

However, more exact calculations have been put forth by other researchers as will be

discussed in the subsequent sections.

Nehrin and Fuji (2001) [21] carried out 3-D finite element thermal analysis using

ANSYS/Thermal software for 56.5 m high Hinata Dam, Japan. Mathematical formulation

adopted by the authors for this purpose is presented below:

The governing partial differential equation used for 3-D transient thermal conditions in

Cartesian coordinates is given by:

𝜌𝑐 𝜕𝑇𝜕𝑡

= [𝑘]∇2𝑇 + 𝑞𝑘 … 2.29

Initial conditions adopted for this problem were lim𝑡→0 𝑇(𝑃, 𝑡) = 𝑇0(𝑃) … 2.30


Page | 20

where P = P(x,y,z) at any point. The boundary conditions prevalent for this problem are stated below: Prescribed temperature = T(P, t ≠ 0) = T’

Prescribed heat flux over the surface, 𝑞𝑘 = 𝑞𝑇𝑛 … 2.31

Heat transfer by convection, expressed by Newton’s Cooling law,

𝑞𝑇𝑛 = −ℎ𝑐𝑇𝑏 − 𝑇 … 2.32

where Tb is the bulk temperature of the atmosphere, T is the surface temperature and hc is

the film coefficient and its value given by Froli [1993] for concrete-air interface is:

ℎ𝑐 = 5.6 + 4.0 𝑉 for V< 5m/s = 7.15 𝑉0.78 for V ≥ 5m/s … 2.33 Solar radiation absorbed by the dam surface was expressed as: 𝑞𝑇𝑛 = 𝑎[𝐼𝑑 + 𝐼𝑖] … 2.34 Here a is the absorptivity of the concrete surface, Id is the direct solar radiation and Ii is

indirect (diffused) solar radiation. Determination of absorbed solar radiation is very

complex and so a suitable fictitious temperature Tb* called “equivalent atmospheric

temperature” was introduced because it included the effects of both heat from sun and

effects of air temperature. Hence,

𝑞𝑇𝑛 = −ℎ𝑐𝑇𝑏∗ − 𝑇′ where 𝑇𝑏∗ = 𝑇𝑏 + 𝑎

ℎ𝑐[𝐼𝑑 + 𝐼𝑖] … 2.35

Heat generation due to hydration was given as: 𝑞" = 𝜌𝑐 𝜕Ω𝜕𝑡

with Ω(t) being obtained from

curve fitting on experimental data (Tu and Niu, 1998) and was expressed as :

Ω(t) = 28.96(1 − e−0.38t) °C … 2.36 For determination of thermal stresses and strains, authors cited the work of Lewis,

Morgan and Zeinkiewicz (1981).


Page | 21

Computer model of the dam section developed on ANSYS/Thermal consisted of 5625 8-

noded, 3-D hexahedral elements with temperature and structural displacements assigned

as DOF for these elements. All initial and boundary conditions were applied to this model

except thermal radiations for which another layer of specialized elements provided in the

software database was superimposed on the previous model. To determine the

requirements of pre-cooling of concrete, three cases were investigated i) Tp = Tamb + 3°C

(no pre-cooling), ii) Tp = Tamb (mild pre-cooling) and iii) Tp = Tamb - 3°C (intense pre-

cooling).


Results obtained from this thermal study were similar to data obtained from

thermocouples installed at various levels of the dam. Simulation of thermal field by

software ANSYS/Thermal was quiet realistic and comprehensive. Flexibility of modeling

different boundary conditions of the problem is the primary advantage of ANSYS.

However, a few discrepancies in the authors’ work were exclusion of creep effects from

the problem and ignoring material non-linearity which would have returned more precise

results.

One of the most remarkable research works in this subject is carried out by Giesecke, Qin

and Marx (2002) [16] from University of Stuttgart, Germany. They presented a realistic

and computational efficient method to solve temperature and thermal stress problems for

large RCC dams. Numerical model developed by the authors is presented below:

The Fourier differential equation for changing temperature field is given as:

𝑐𝜌 𝜕𝑇(𝑥,𝑡)𝜕𝑡

− ∑ 𝜕𝜕𝑥𝑖

𝑑𝑖=1 𝑘𝑖

𝜕𝑇(𝑥,𝑡)𝜕𝑥𝑖

= 𝑞 for x Є Ω, t > 0 … 2.37

Here, T = temperature [°C]

c = specific heat [J/(kg.K)]

ρ = density [kg/m3]

d = dimension of domain Ω

ki = thermal conductivity [W/(m.K)]


Page | 22

q = rate of heat generation [W/m3]

Heat transfer from the surface of concrete is given by: qn = qH + qL - Rn … 2.38 qn = heat flux normal to the surface of structure [W/m2]

qH = sensible heat flux through conduction and convection [W/m2] = αc.(To - Ta)

Here αc is the convective heat transfer co-efficient [W/(m2.K)], Ta is temperature of the

fluid and To is temperature of the structure surface

qL = latent heat flux through evaporation and condensation [W/m2] based on Penman-

Brutsaert Model

Rn = net radiation [W/m2] = qG - qE

qG = net incoming short-wave radiation = (1.0 – αG).G

Here αG is the albedo (reflection coefficient) of the structure surface with respect to global

radiations and G is the global radiation incident upon the structure surface.

qE = net outgoing long-wave radiation = αr .(To-Ta)

αr = ε. σ. (To2 + Ta

2)( To + Ta)

where,

αr = radiative heat transfer coefficient [W/(m2.K)]

ε = radiation exchange coefficient [-]

σ = Stefan-Boltzmann constant = 5.67035 x 10-8 [W / (m2.K4)]

To = temperature of the surface [K]

Ta = temperature of the atmosphere [K]

Summarizing these equations, qn =(ac +ar)(To-Ta) + qL –qG = a(To-Ta) + qL -qG … 2.39 To represent the adiabatic rise in temperature due to hydration heat, authors derived the

following expressions:


Page | 23

𝑞 = = 𝑐𝜌𝑇𝑎𝑑 = 𝑐𝜌𝑇𝑎𝑑∞ … 2.40 Q = rate of hydration heat

Tad = adiabatic temperature rise measured in adiabatic test

𝑇𝑎𝑑∞ = final value of Tad

ξ = hydration degree = 𝑇𝑎𝑑/𝑇𝑎𝑑∞

For a temperature regime different from that under which Tad is measured, ξ can be calculated as

𝜉 = exp (− 𝑏𝑡𝑒𝑛

) … 2.41

Here b and n are material constants and te is the maturity or equivalent age and is calculated as: 𝑡𝑒 = ∫ exp [𝐵𝑡

𝑜 (𝑇(𝜏) − 𝑇𝑟𝑒𝑓)]𝑑𝜏 … 2.42 Where B is a material constant called temperature sensitivity factor, Tref is the reference

temperature for which maturity equals the real time values. So hydration degree under a

variable temperature regime can be calculated as:

= 𝑑𝜉𝑑𝑡𝑒

𝑑𝑡𝑒𝑑𝑡

= 𝑏𝑛exp (− 𝑏

𝑡𝑒𝑛)

𝑡𝑒𝑛+1exp [𝐵(𝑇(𝑡) − 𝑇𝑟𝑒𝑓)] … 2.43

Authors used the work of Cervera et-al [7] for simulating aging effect on mechanical

properties of concrete. Total strain in concrete was assumed to be a sum of stress related

part 𝜀𝜎 (comprising of elastic strain 𝜀𝑒 and creep strain 𝜀𝑐) and stress unrelated part 𝜀⋉𝜎

(comprising of shrinkage strain 𝜀𝑠 and thermal strain 𝜀𝑇 . This is shown below:

𝜀 = 𝜀 + 𝜀⋉𝜎 = 𝜀 + 𝜀 + 𝜀 + 𝜀 … 2.44 Stress related strain was determined using a rheological model consisting of springs,

Kelvin chains and a single dashpot representing stiffnesses, viscosities and transitional

thermal creep respectively.


Page | 24

The above described model was incorporated in a finite element program TESAR which

was used for calculating temperature field development of Longtan RCC dam in China.

To improve the computing efficiencies, authors used adaptive compound layer method

and adaptive time step method to control the discretization in space and time respectively.

This means that in the regions of freshly placed concrete, temperature and stresses are

calculated layer by layer but as time passes, thermal and mechanical properties of

concrete in lower regions become somewhat stationary and hence these individual layers

can be combined into one thicker layer having coarser mesh.

Due to unavailability of solar radiations data at the site, effects of solar radiation and

evaporation were not considered in the analysis. However a parametric study was carried

out on 1-D strip model to explore the influence of solar radiation and evaporation on RCC

dams. Environmental data was taken from Web Service of National Technical University

of Athens. Based on these studies, it was concluded that influence of solar radiation and

evaporation on temperature development of RCC is significant. Also the magnitude and

distribution of the wind speed have significant effects on the temperature evaluation of

early age concrete.


The mathematical model presented herein is very elaborate and quiet realistic. Almost all

primary factors involved in the transient temperature problem have been incorporated in

this model. However, due to missing site data, effects of solar radiations and evaporation

were ignored which has introduced a marginal error of up to 2% in the final results. Many

of these equations will be used in the current research also because of the resemblance of

environmental and structural features of Longtan Dam China and the proposed Dasu

Dam, Pakistan.

Thermal Studies at Diamer Basha Dam: Diamer Basha dam is located about 60 kms upstream of Dasu dam and as per WAPDA’s

vision 2025; it will be constructed prior to Dasu dam. So the preliminary thermal studies

carried out during the detail design of Diamer Basha dam are of principal importance in

the current research.


Page | 25

Material testing was not carried out during this study, therefore material properties

assumed for the preliminary thermal analysis were based on experience with other

projects. Seven trial mixes were assumed having different proportions of cementitious

materials (cement, fly ash, slag etc). Heat of hydration and modulus of elasticity were

assumed independent of temperature. Following expressions were used in this study [3]:

Initial elastic modulus: 𝐸𝑐 = −1.6(𝑓𝑐′)3 + 45(𝑓𝑐′)2 + 989.4𝑓𝑐′ … 2.45

Splitting strength: 𝑓𝑠𝑝𝑙𝑖𝑡 = 0.1329𝑓𝑐′ … 2.46

Tensile strength: 𝑓𝑡′ = 0.3 log(10𝑓𝑐′) .𝑓𝑠𝑝𝑙𝑖𝑡 = 0.03987.𝑓𝑐′. log (10𝑓𝑐′) … 2.47

Creep function: 𝐹(𝑘) = 33.216 (𝑓𝑐′)−0.7128 … 2.48

Sustained elastic modulus defined as the equivalent elastic modulus for calculating an

elastic quantity (stress or strain) at time tj, due to a disturbance (stress or strain) applied

between the time increment from ti to ti+1 was used to calculate varying stresses in the

long term. Following formulae was used:

𝐸𝑠𝑢𝑠𝑡𝑗 , 𝑡𝑖,𝑖+1 = 12

𝐸𝑒,𝑖+𝐸𝑒,𝑖+1+0.5(𝐹(𝑘)𝑖+𝐹(𝑘)𝑖+1).ln (𝑡𝑗− 0.5(𝑡𝑖+ 𝑡𝑖+1)+1.0)

… 2.49

A two stage analyses comprising short time phase (during construction) and long term

phase (after completion of construction) was carried out for the project. Simplified 1-D

strip model was made for the ‘construction line’ analysis taking account of the time-

dependent construction sequence of lifts, placement temperatures, adiabatic rise in

temperature, heat exchange between concrete surface and environment only in one

direction. For long term phase, 2-D finite element model was built in program EFESYS to

analyze effects of temperature dissipation following construction and hydration process

until steady state is achieved inside the concrete mass.

Based on these expressions, surface and mass gradient cracking of RCC were estimated

and it was concluded that some surface cracking is expected at the upstream and

downstream faces. To encounter upstream cracking, special crack control measures will

be adopted. Results from this thermal analysis were passed to stability analysis to account

for some strength loss within near surface lift zones.


Page | 26

2.4 FURTHER RESEARCH Researchers and scientists have utilized modern tools and experimentation to further

investigate the influence of physical and chemical properties of RCC on its thermal

behavior. Many expressions and graphs have been developed to represent these time

dependent properties as will be discussed in the proceeding sections:

Eirele (1999) presented a simplified expression for temporal development of static modulus of elasticity in compression of normal weight concrete based on CEB-FIP 1993.

𝐸𝑐(𝑡) = 𝐸𝑐,28 𝑡

17.6+0.37𝑡

1735 … 2.50

where, Ec(t), time dependent modulus [GPa]

Ec,28, modulus at age of 28 days [GPa]

t, concrete age [days]

This expression is only suitable for rough estimation as the model parameters are just

valid for standard concrete and not for low cement roller compacted concretes. To cope

with this matter, Conrad, M. et-al (2004) [10] investigated the effects of modulus of

elasticity of young RCC via experimentation. They tested an RCC mix of 85 + 0 (85

kg/m3 OPC and 0 kg/m3 Pozzolan) at ages of 3h, 6h,… up to 365 days. The best

experimental fit of the curve based on the results of these tests is shown below:

𝐸𝑐(𝑡) = 𝐸𝑐,∞. exp(𝑎. 𝑡𝑏) … 2.51 Applying 𝐸𝑐,∞ = 𝐸𝑐,365 = 24.4 GPa, a = -5.0, b = -0.63, the best fitting of test results could

be achieved by which elastic modulus at early age as well as higher ages could easily be

represented.

Bazant (1988) presented a mathematical model for simulation of heat evolution,

shrinkage and creep of concrete. “Shrinkage Core Model” as normally called, gives the

formulation of heat source in terms of concrete maturity.


Page | 27

𝐻(𝑡,𝑇) = 𝐻∞𝛼𝑀

1+𝛼𝑀 … 2.51

The maturity M, is a function of time t and absolute temperature T as:

𝑀(𝑡,𝑇) = ∫ 𝑒𝑥𝑝𝑡𝑡𝑑 𝑄

𝑅 1𝑇1− 1

𝑇 𝑑𝑇 … 2.52

where,

H∞ = Total value of concrete hydration heat per unit volume [kJ/m3]

α = Heat source parameter [1/day]

Q/R = Activation energy / universal gas constant [°K]

T1 = Reference temperature, normally 20°C = 293 °K

td = Dormant period [day]

Yang and King (2003) presented experimental measurement of thermal expansion of

concrete for six samples with different mix designs. The principal conclusions of their

research were that thermal expansion is strongly dependent on the type of coarse

aggregate. Cycles of heating and cooling have negligible impact on thermal expansion

coefficient values. These values are also dependent on shape of specimen and rate of

loading in laboratory.

Table 2.1 gives a tabular summary of different properties of RCC adopted in the design of

various RCC dam projects worldwide.

Page | 28

Table

2.1:

Prop

erties

of R

CC m

ateria

l ado

pted o

n diffe

rent d

ams Un

it we

ight

Ultim

ate

Stre

ngth

Modu

lus of

El

astic

ityPl

acem

ent

Temp

eratu

re

Adiab

atic

Teme

p Ri

se

Spec

ific

Heat

Ther

mal

Cond

uctiv

ityTh

erma

l Di

ffusiv

ity

Co-ef

ficien

t of

Ther

mal

expa

nsion

Tens

ile

Stra

in Ca

pacit

y

Co-ef

ficien

t of

Hea

t Tr

ansfe

r

Ceme

ntFly

ash

kg/m

3MP

aGP

a° C

° CkJ

/kg-°C

W/m

-°Cm

2 /hrpe

r °C

W/m

2 -°C

1Cin

dere

Dam,

Turke

y60

3013

10 x

10-6

60 x

10-6

2Ca

na B

rava D

am, B

razil

2441

-9 (90

days

)28

300.8

368

1.890

911

.7 x 1

0-613

.9467

3Ri

alb D

am, S

pain

2550

-42 (U

lt.)23

7.17.8

x 10

-610

018

024

00+1

.1222

.4(90

day)

151.0

192.4

180.0

0375

5.6 x

10-6

150

180

2400

+1.58

26.6(

90da

y)16

.70.9

82.3

860.0

0375

6.6 x

10-6

200

180

2400

+1.87

27.7(

90da

y)18

5Sa

lto C

axias

Dam

, Braz

il23

88-10

.2Te

/(2.12

e-3+

Te*0

.162e

-3)1.1

051.7

905

7.07 x

10-6

13.95

33

6Ro

odba

r Dam

, Iran

2400

150.9

205

2.105

11.63

7Mi

yaga

se D

am, J

apan

9139

2450

201.0

461.7

096

8 x 10

-611

.638

Hina

ta Da

m, Ja

pan

9034

2350

250.2

10.8

81 x

10-5

25.8

9Mi

lltown

Hill

Dam,

USA

6666

16.7

181.0

473.3

0.005

1.8 x

10-6

104

025

29-18

.3(90

day)

16.5

12.7

200.9

211.8

0.003

2.2 x

10-6

104

4725

31-27

.3(90

day)

1711

.120

0.921

1.80.0

032.2

x 10

-647

1925

20-11

.9(90

day)

1211

.712

.20.9

211.8

0.003

2.2 x

10-6

187

8024

38-30

.8(90

day)

11.7

29.4

0.921

1.80.0

032.2

x 10

-611

Portu

gues

e Dam

, Port

ugal

25.6

91.0

040.0

022

9.5 x

10-5

RCC

Comp

ositio

n

200

Mian

huata

n Dam

, Chin

a

Willo

w Cr

eek D

am, U

SA104

Proje

ct Na

meSr

. No.

Page | 29

COMPUTATIONAL STRATEGY & MODELING

3.1 INTRODUCTION

In this chapter, methodology for carrying out detailed thermo-mechanical ‘TM’ analysis

of RCC dams will be presented. All pertinent parameters adopted for this analysis will

also be described. Algorithms will be finalized for carrying out 2-D thermal analyses with

particular emphasis on selected software. Structural features of Dasu Dam will be

described in brief and relevant thermal analysis aspects of this dam will be discussed.

3.2 ALGORITHM FOR THERMO-MECHANICAL ANALYSIS OF RCC DAM

Fig 3.1 represents a flow chart that describes the steps involved in carrying out detailed

thermal analysis of dam. Primarily this study incorporates the following steps for carrying

out thermo-mechanical analysis.

i. Data Collection and assumptions

ii. Finite Element Modeling

iii. Thermal gradient analysis

iv. Thermal stress analysis

v. Crack Analysis

Chapter

3

Chapter 3 Computational Strategy & Modeling

Page | 30

Illustrative Example; Dasu Dam

For elaboration of detailed thermo-mechanical analysis, an illustrative example of Dasu

Dam will be presented in this section. Dasu dam is part of ‘Vision 2025’ by Water and

Power Development Authority Pakistan to meet the ever-increasing energy needs of the

country. Under this project, several small and large dams have been planned across the

country. Dasu dam has been placed in the final phase of this project to be commissioned

by the year 2025. Feasibility Studies of Dasu Hydropower Project were completed by

Joint venture of world renowned consultants including NESPAK, MWH, Colenco, ACE

and Binnie in February 2009.

Dasu dam is essentially a roller compacted concrete gravity dam 233m high and having a

maximum base width of 213m. Approximate crest length of the dam is 518m. Being a

massive structure, having 4.6 million cubic meters of RCC, it was deemed necessary to

evaluate the thermal cracking potential of Dasu dam so as to avoid any perilous effects on

overall structural stability.

During the feasibility studies, preliminary level thermal analysis of Dasu dam was carried

out by the author. This analysis was focused on post-construction thermal behaviour to

evaluate any sustained thermal stresses that would have been detrimental for overall

stability of the dam. Software MSC.MARC was used to calculate thermal stresses.

Uniform material properties were assumed in computer modeling and all these properties

were assumed to be time and temperature independent. Results of this analysis were later

input in the structural analysis of dam to evaluate factors of safety against stress and

stability.

Following are some of the main characteristics of Dasu Dam [18]:

Dam Crest Level 957 m

Crest Width 13 m

Crest Length 518 m

Maximum Dam base width 213.5 m

Lowest Foundation Level 724 m

Upstream Dam Slope 0.15H: 1V, 0.2H: 1V

Downstream Dam Slope 0.75H: 1V


Page | 31

Fig 3.1: Flowchart for Thermo-mechanical Analysis

Start

Data Collection & Literature Review

Selection of Appropriate Material properties for Illustrative Example

Ambient Environmental Conditions

Roller Compacted Concrete Properties

Foundation Properties

Determination of Construction Schedule

Numerical Modeling & Discretization in ANSYS® MultiPhysics

Comparison of Results with Dasu HPP Feasibility Studies

Conclusions

Non-linear Incremental Structural Analysis (NISA)


Page | 32

A typical section of the proposed RCC gravity dam at spillway section is given in Fig 3.2:

Fig 3.2: Cross-section of Dasu Dam [18]

3.3 NUMERICAL MODELING AND MATERIAL PROPERTIES

Based on extensive research and data collected from similar projects having synonymous

ambient conditions, material properties of RCC have been assumed for this study so as to

simulate the actual on-site conditions that will be encountered during construction. Efforts

were diverted to select such material properties that have been based on reliable research

and can be applied efficiently to a computer model as well. It is worth mentioning that no

material testing has been carried out for confirmation of the selected material properties.

3.3.1 Mix Design of RCC

The advent of RCC Dam construction can be traced to the 1980s. The first RCC dam was

constructed in Japan. It was conceived along the lines of a conventional concrete dam but

with the concrete compacted by roller. Cementitious contents for Japanese RCC Dams

have generally been about 130 kg/m3, with a 30% fly ash replacement of cement. This

dam was closely followed by the Willow Creek and Upper Stillwater dams in the USA.

The former featured a dry-lean, low paste, RCC mix with a cement content of less than


Page | 33

100 kg/m3. The Upper Stillwater dam featured high paste mixes and approximately 60%

of cement replacement by fly ash. The intention was to form impermeable mixes with

high tensile strengths.

The two approaches of low paste RCC coupled with a waterproof facing and medium to

high paste RCC mixes which are themselves sufficiently impermeable, have subsequently

dominated RCC dam construction. They are also sometimes considered as representing a

soils or geotechnical philosophy versus a concrete philosophy. The soils philosophy

considers RCC as a cement-enriched processed soil, or aggregate, whose mix design is

based on moisture-density relationships. For the concrete philosophy, the RCC mix is

considered to be a true concrete whose strength and other properties follow the water-

cement relationship with strength being inversely proportional to its water-cement ratio.

The RCC mix should not, however, contain so much paste that a measurable slump is

produced or excess paste is brought to the surface with only a few passes of a vibratory

roller. Recent trends in RCC mix design have tended towards the concrete philosophy

approach.

The fresh and hardened properties of RCC are sensitive to variations in cement and

pozzolan properties. A single and consistent source of cement and pozzolan is commonly

used. The selection of a pozzolan suitable for RCC should be based on its conformance

with ASTM C 618. Some variations beyond the ASTM limits can be allowed provided

the pozzolan is consistent in its proportion. Pozzolans meeting the specifications of

ASTM C 618 for Class C, Class F, and Class N have been successfully used in RCC

mixtures. Class F and Class N pozzolans are usually preferred, since they normally

contribute less heat of hydration than Class C and have greater sulphate resistance. The

use of pozzolan will depend on required material performance as well as on its cost and

availability at the project.

This analysis assumes a cementitious material content of 170kg/m3, comprising 100kg

cement and 70kg pozzolanic material which represents 40% replacement of cement. This

analogy of 40% cement replacement has already been adopted in Ghazi-Barotha

hydropower project and remarkable results have been achieved.


Page | 34

3.3.2 RCC Properties Adopted in this Analysis

Following are the mechanical and thermal properties of RCC adopted in this TM analysis:

a) Modulus of Elasticity (Ec)

The temporal growth of stiffness and the initial release of the hydration heat in

conjunction with the temperature rise of the concrete mass and the present restraint

(internal and external) result in moderate compressive temperature stresses. These

stresses may be caused by high relaxation of stresses and creep effects in the early age.

However, when the hydration process nearly stabilizes and the rate of heat release retards,

the temperature of the mass begins to drop. In this phase, the concrete mass has gained a

much higher stiffness, so only a small drop of temperature may compensate for the

initially built up compressive stresses. Further cooling affects tensile stresses which may

exceed the tensile strength and in turn lead to thermal cracking.

For the prediction of thermal cracking in RCC, a better understanding of the temporal

development of the Young’s Modulus of Elasticity is required especially in the very early

state of curing. In most publications, RCC properties and their temporal evolution are

considered to be equal to those of conventional mass concrete. A very well known

expression stipulated in literature and experimentally investigated by Conrad, M. et-al [10]

has been used in the current TM analysis.

𝐸𝑐(𝑡) = 𝐸𝑐,∞. exp(𝑎. 𝑡𝑏) … 3.1

where,

Ec (t) = time dependent modulus [GPa]

Ec,∞ = final modulus of Elasticity at 365 days [GPa]

t = concrete age [days]

α & b are Constants

Based on experimentation, the value of α and b is -5.0 and -0.63. Following is the

graphical representation of temporal growth of RCC Modulus.


Page | 35

Fig 3.3: Variation of RCC modulus with Age

b) Adiabatic Heat of Hydration

Heat generation within the concrete mass is an adiabatic phenomenon occurring as a

result of hydration process. Amount of heat generated is directly related to the cement

content in the concrete mix. In very large concrete mass, temperature near the center of

mass will be approximate sum of placement temperature and adiabatic rise due to

hydration. Near the surface, peak temperatures will be lower and will be near ambient

temperatures.

The adiabatic temperature rise due to hydration heat is based on the following expression

published by ASCE (1986) [26].

T(t) = K (1-e-αt) … 3.2

where

T = temperature (°C)

t = time (Days)

α and K are constants based on unit cement content and placement temperature


Page | 36

Values of these constants are obtained from charts developed by Radovanic (1998) from

experiments on several small and medium sized samples. Based on this expression, the

rate of heat generation R(t) is calculated as [26]:

R(t) = K Cp γ α e-αt … 3.3

where

Cp = Specific heat capacity of RCC (J/g°C)

γ = Density of concrete (g/m3)

t = Time (Days)

c) Surface Heat Transfer Co-efficient (Film Co-efficient)

The surface heat transfer coefficient “h” (film coefficient) is applied to all exposed

surfaces to represent the convection heat transfer effect between the surrounding air and

the concrete surface. The following approximate equation is used to calculate the surface

heat transfer coefficient [14]:

h = hc + hw … 3.4

where, for a concrete surface, the average value of hc is taken to be 6.0 W/m2-°C, and hw

is approximately related to the wind speed “v” as hw = 3.7v (with v in m/s).

d) Compressive Strength

Values of compressive strength fc’ has a direct influence on the modulus of elasticity of

concrete so it is imperative that sufficient compressive strength is assigned to RCC.

Tensile strength is also taken as a percentage of compressive strength and hence adds to

the need for sufficient strength. For the current studies, value of fc’ has been taken equal

to 20 MPa.

e) Tensile Strength

ACI 207.1R-96 states that mass concrete has sufficient tensile strength and hence the

assumption of ‘Zero tensile strength’ as in reinforced concrete of smaller sized members


Page | 37

may be violated to utilize the benefits inherent to mass concrete. For this reason, different

codes present different relations in terms of modulus of rupture of concrete for

determining tensile strength. For this analysis, tensile strength value equal to 5% of the

ultimate compressive strength has been assumed.

f) Tensile Strain Capacity

For thermal analysis, value of tensile strain capacity is of much more concern than the

tensile strength because this particular value will decide the specific location and pattern

of thermal cracks in mass concrete. This value depends on the ultimate strength and also

on the rate of loading. For conservative approach, value of tensile strain capacity ‘TCS’

has been taken equal to 20 microns or 2 × 10-5.

Apart from above stated properties, following are some other properties that were used to

calculate thermal stresses in Dasu RCC dam.

Table 3.1: RCC and Rock Foundation Properties Used in the Analysis

Sr. No Properties RCC Foundation

1 Modulus of Elasticity, (MPa) Varies

with Age 20,000

2 Poisson’s Ratio 0.2 0.25

3 Unit Weight, (kg/m3) 2600 2900

4 Co-efficient of Thermal Expansion, (per °C) 7 ×10-6 3.5 ×10-6

5 Thermal Conductivity, (W/m.°C) 2.0 1.1

6 Specific Heat, (kJ/kg°C) 1.05 0.8

7 Film Co-efficient (W/m2.°C) 19.36 19.36

8 Heat of Hydration Rate (W/m3) Varies

with Age -

9 Tensile Strain Capacity 2 × 10-5 -


Page | 38

3.3.3 Climatic Variations

For Dasu dam, mean monthly average temperatures data for the past 30 years has been

used. Following are the main climatological parameters observed at Besham Qila located

about 85 km downstream of Dasu dam site which have been adopted for this analysis:

Table 3.2: Ambient Temperatures [3,18]

Month

Precipitation Temperature (°C)

(mm) Maximu

m Minimum Average

January 88.8 21.7 3.3 12.5

February 140.1 27.8 2.2 15.0

March 164.4 35 8.9 22.0

April 110.7 38.3 10 24.2

May 65.1 43.4 11.7 27.6

June 67.6 45.6 17.8 31.7

July 123.1 44.5 18.9 31.7

August 125.2 40 18.3 29.2

September 71.3 39.5 17.2 28.4

October 52.4 34.5 10 22.3

November 35.6 28.9 6.7 17.8

December 54.4 25.6 4.4 15.0

Annual 1098.7 45.6 2.2 23.9

3.3.4 Placement Temperature

Placement temperature of mass concrete is another important parameter that has a direct

influence on the peak temperatures and hence on thermal stresses. A simplified equation

postulated by Noorzaei, Ghafoori and Amini (2006) [23] has been used in this analysis

Tplacement = Tanu - 2/3(Tanu - Tmon) + Crush Add + Mixing Add + Transporting Add


Page | 39

Adding temperature of aggregate crushing and concrete mixing has been assumed equal

to 1°C while the effect of radiations on newly placed concrete has been considered by

adding 1°C to the placement temperature. It is worth mentioning here that due to higher

peak temperatures and probability of flood overflows, no concreting activity was assumed

from May to September.

Following is the placement temperature adopted for this study:

Months Jan Feb Mar April May June July Aug Sept Oct Nov Dec

Temp (°C) 14 15 15 17 x x x x x 17 15 14

3.3.5 Construction Schedule

Rapid and continuous delivery of RCC is important to mass concrete applications. As a

general guide, the average sustained placing rate does not exceed 65% of the nominal

plant capacity when haul vehicles are used for delivery to the dam, and 75% when an all-

conveyor delivery system is used. Typically the designed nominal plant capacity should

include a factor of 1.20 to 1.30 over the sustained rate requirement to allow for the RCC

manufacturing plant breakdown/maintenance. These values tend to be lower on smaller

projects and higher on larger projects [3].

For Dasu dam, the construction schedule is established by considering the geometry of

the dam and climatological conditions. Total quantity of RCC in the dam body is

approximately 4.6 million cubic meters [18]. RCC placing rate is assumed to be

approximately 325m3/hr with a 16 hour working day and 26 days a month. There is a

break in concreting operations from May to September each year due to extreme high

temperatures and the probability of floods in summer. No loss of days due to rains,

floods, strikes etc. have been considered. Two 500 m3/hr batching plants will be required

for this construction schedule with one to be used in case of breakdown. Construction has

been assumed to start in October. This is because experience shows that if concreting is

started just before summer months, temperature gradients are much higher near the base

of dam. This results in severe cracking around this zone and the chances of large crack at

the dam-foundation interface are high. Table 3.3 shows the assumed construction

schedule.


Page | 40

Table 3.3: Construction Sequence and Schedule of Dasu dam

Dam

Elevations

Construction Schedule

Year 1 Year 2 Year 3 Year 4 Year 5

724 1 Oct.

730 9 Oct.

740 5 Nov.

750 5 Dec.

760 7 Jan.

770 9 Feb.

780 20 Mar.

790 5-May 1 Oct.

800

18 Nov.

810

15 Jan.

823

15-May 1 Oct.

830

10-Dec

840

10-Feb

854

5-May 1-Oct

860

5-Nov

870

5-Jan

880

28-Feb

890

15-Apr 1-Oct

900

20-Nov

910

31-Dec

This schedule has been developed based on the following assumed placement rates:

o 325m3/hr from base to El. 810

o 200m3/hr from El. 810 to El. 830

o 325m3/hr from El. 830 to El. 910


Page | 41

3.4 COMPUTER MODELING

3.4.1 Introduction to ANSYS

Thermo-mechanical analysis is a very complex problem involving extreme non-linearities

in geometry and material of a structure. Geometry and material properties of dam change

at every instant and this time and temperature dependency adds to this greatly non-linear

problem. Such an analysis is named as Non-linear Incremental Structural Analysis

(NISA) by structural engineers. ANSYS® MultiPhysics version 11.0 has been used to

carry out this TM analysis. ANSYS is general purpose software with extensive

capabilities to model complex structures and is commercially used in mechanical, civil,

automobile and aviation sectors to analyze and design wide range of structures. This

software is equipped with an extremely efficient solver that can simulate and analyze all

kinds of engineering models in shortest possible times. ANSYS has built-in algorithms to

solve heat transfer, fluid mechanics and structural problems in a user friendly

environment and for this reason ANSYS was used in the present research.

Apart from basic software capabilities, ANSYS has been equipped with many modern

tools to solve variety of problems in minimum computing time. Amongst these are

‘Coupled-Field Solver’ and ‘Birth & Death of Elements’ which have been used in this

TM analysis. The Elements library provided within ANSYS database is also quiet

extensive and user friendly.

a) Coupled Field Solver

A coupled-field analysis is a combination of analyses from different engineering

disciplines that interact to solve a global engineering problem, hence we often refer to a

coupled-field analysis as a multiphysics analysis. In principle, when the input of one field

analysis depends on the results from another analysis, the analyses are coupled. This

coupling can either be one way or two way based on the problem requirement.

In a thermal stress problem temperature field introduces thermal strains in the structural

field, but the structural strains generally do not affect the temperature distribution. The

coupled field solver embedded in ANSYS results in the reduction of analysis time

drastically and hence results in saving of time and cost. Many coupled field solvers like


Page | 42

thermal-structural, electrostatic-structural, electrostatic-structural-fluidic, electro-thermal-

structural-magnetic and many other combination of analysis can be efficiently carried out.

b) Birth & Death of Elements

Using a specialized command provided in the software, incremental construction of dam

can be easily modeled by introducing EKILL and EALIVE commands in the ANSYS

command interface. This command simulates the exact construction sequence of structure

with properly introduced boundary conditions by activating new RCC lifts (layers) with

time in the computer model. The new layer has boundary conditions and material

properties corresponding to younger concrete while the layers present beneath this fresh

layer have different properties and boundary conditions depending on their particular age.

This cycle continues until the construction is completed. This command is very efficient

in carrying out non-linear incremental structural analysis.

3.4.2 Numerical Discretization and Analysis Procedure

With reference to the illustrative example i.e Dasu Dam, following is the procedure for

carrying out the complete thermo-mechanical analysis using computer aided modeling in

software ANSYS® MultiPhysics.

a) Finite Element Modeling

The main body of the dam was modeled using 1240 plane strain elements. A standard lift

height of 3 m as proposed in the construction schedule was adopted which resulted in a

total of 62 lifts to reach to the top of roller compacted concrete portion of dam. Each lift

was modeled as one layer of elements divided equally along the length. Foundation rock

was also modeled to a depth of 50 m and 50 m on both upstream and downstream of dam

body to include its thermal effects. Figure 3.4 shows the FE model used in this analysis.

b) Element Type

The type of element selected for the analysis is very important for these types of problems

as all pre and post-processing as well as the numerical algorithms depend on this element

type. For the current analysis, PLANE 223; a 2-D 8 noded quadratic coupled field solid

with four degrees of freedom at each node was used. This element can perform a wide


Page | 43

variety of coupled field analyses. Advanced analysis features such as Birth and death,

large deflection, joule heat generation and solution control required for TM analysis; are

inherent to this element type. This coupled field solid eliminates the need for reanalyzing

the whole structure again and all necessary outputs are obtained from a single analysis

run.

c) Material Models

Material properties for RCC and rock as described in the previous sections were

introduced using material models. A special add-on to ANSYS named CivilFEM was also

utilized to model the most accurate properties for roller compacted concrete. One

limitation associated to the software was that material properties cannot change with time

automatically. For this reason, several material models with different modulus of

elasticity values of concrete were defined so that temporal growth of material modulus

can be defined exclusively. Material non-linearities were defined using this technique.

d) Time

The time for analysis corresponds to the actual chronological time of construction. All

material properties, boundary conditions and birth of elements were based on this time

and so this had to be dealt with attention.

Time unit for this analysis was assumed to be one day. The non-linear incremental

structural analysis was performed on monthly basis starting from one year before the start

of dam construction and continued to 2500 days from this start point. Analysis before

construction start was carried out to apply average temperature gradients on the

underlying rock so that the foundation effects can be represented properly. Analysis time

was divided into 25 steps with a maximum of 20 sub-steps for each step.

e) Nonlinear Options

As the TM analysis problem is both non-linear and time varying, so non-linear options of

ANSYS were activated. Full Newton Raphson method was adopted for incremental non-

linearities. Number of iterations for each subset were limited to 25 while convergence

limits were set to calculate sufficiently accurate results. Advanced features such as ‘line


Page | 44

search; and ‘solution predictor’ were also activated so that results could be achieved in

minimal time but not at the expense of any loss of accuracy.

f) Boundary Conditions

For each time step, boundary conditions were applied to all the active elements based on

their age (i.e. age of concrete). ANSYS classifies all loads into two broad categories

namely Surface loads and Body loads. All loads are however, applied to the finite

elements within the software.

As soon as the cement mixes with water, exothermic reaction produces considerable heat

of hydration. This adiabatic heat of hydration, calculated by the formulae given in Section

3.3.2 (b) was applied to all the active elements in the FE model. As an initial condition,

each element was subjected to the placement temperatures stipulated in Section 3.3.4.

Annual average air temperatures were assigned as boundary conditions on u/s and d/s

faces of dam representing external heat radiations from sun. Surface heat transfer

coefficients (film coefficients) as given in Section 3.3.2 (c) were also assigned as

boundary conditions. As the analysis progressed, all of these boundary conditions were

re-assigned to particular element layers depending on the age of that layer/lift. This

procedure continued till the completion of analysis time. Figure 3.5 represents a graphical

display of all boundary conditions applied to the FE model.

A flowchart of complete TM analysis algorithm adopted in this research is presented in

Fig 3.6.


Page | 45

Fig 3.4: FE Model used in TM Analysis

Fig 3.5: Boundary Conditions in TM Analysis


Page | 46

Fig 3.6: Algorithm for TM analysis

Thermo-Mechanical Analysis

Pre-Processing

Finite Element Modeling

Define Geometric & Material Properties

Birth and Death of Elements Technique

Apply Initial & Boundary Conditions to

all Active Elements

Modify RCC Properties based on time for all

Active Elements

Post-Processing

End of Stage Placement

Last Stage

Save Results for Further Processing

YES

NO

Take a New Stage


Page | 47

3.4.3 Analysis Assumptions

For this detailed 2-D TM analysis, various assumptions were made to obtain reliable and

accurate stress and strain states of the dam body. The highest section of the dam with the

corresponding maximum base width was used in the analysis. Some other assumptions

adopted are:

• Self weight and any superimposed loads on the dam were not activated in the

analysis to obtain stresses due to thermal loads only.

• No material testing was carried out and all material properties were derived from

literature based on the specified mix design.

• RCC and rock were considered isotropic.

• RCC material properties such as modulus of elasticity, specific heat, co-efficient

of thermal expansion, thermal conductivity and convection co-efficient were

considered independent of temperature effects.

• Creep and shrinkage effects of concrete were ignored.

• Mean monthly average temperatures based on the average of past 30 years were

considered for temperature loads. Daily peaks were ignored due to unavailability

of daily temperature variations.

• Placement temperature was not allowed to exceed 17°C.

• Grout enriched vibrated RCC as proposed on the u/s and d/s faces of dam were

not considered in thermal analysis.

• Construction was assumed to start on 1st October and placement of RCC was

assumed to be discontinued from May to September each year due to high

ambient temperatures unsuitable for placing mass concrete.

Page | 48

RESULTS & DISCUSSIONS

4.1 INTRODUCTION

Results obtained from the detailed TM analysis will be presented and discussed in detail

in this chapter. ANSYS postprocessor has been utilized to obtain relevant output data and

spreadsheets have been configured to apply more rigorous analytical procedures so as to

achieve accurate results. Results will be presented in both graphical and tabular formats

and contours of temperature and stress profiles will also be shown. Fracture mechanics

parameters used to obtain the probable crack lengths in concrete mass will also be

discussed in this chapter.

Broadly classifying, following types of analyses were carried out for this detailed TM

analysis

I. Thermal Gradient Analysis

II. Thermal Stress Analysis

III. Mass and Surface Cracking Analysis

All of them will be discussed in the subsequent sections.

4.2 THERMAL GRADIENT ANALYSIS

The non-linear incremental structural analysis (NISA) technique adopted in TM analysis

and the inherent transient nature of the problem resulted in bulk of output data. Post

processing is an intensive job in ANSYS. Results are obtained both at nodal points,

termed as integration points, as well as element centroids. Which result to be used for

Chapter

4

Chapter 4 Results & Discussions

Page | 49

which analysis, depends on the user’s know-how of the problem. Although the coupled

field solver embedded in ANSYS displays all analysis results in a single run, however for

simplicity, we will discuss each of the so-called ‘thermal’ and ‘mechanical’ analyses

results separately.

Thermal gradients mean the variations in temperature values inside the body of dam.

Since the temperature profiles are variable along the dam cross-section and it is

unfeasible to analyze every finite element for variations in temperature values throughout

the analysis time, so few critical positions were selected along u/s and d/s faces of dam as

well as along the exact centerline of dam section. Results obtained at these positions, in

the shape of time history curves were studied. These were transferred to excel

spreadsheets for further post-processing.

Following are the contour plots of temperature profiles inside the dam body at different

time instants during the construction of dam:

Fig 4.1: Temperature at 130 days from Start of Construction



Page | 50




Page | 51

Fig 4.5: Temperature at the end of analysis time (i.e. Day 2500)

These contour plots show variations in temperatures encountered during the construction

and hence can be used for deciding the provision of temperature control measures to be

adopted by the contractor.

Fig 4.2 shows temperature values after 14 months from the construction start (taken as 1st

October). A maximum temperature of 30 °C occurs at approximately 60 m above the base

of dam. It is worth mentioning that this is the same elevation at which the construction

process was stopped in May (of the successive year of start) due to higher summer

temperatures reaching up to 40°C. During this time, concreting was assumed to

discontinue as such high temperatures are detrimental for concrete and the probability of

delayed ettringite formation is high which renders roller compacted concrete completely

useless. Actually, delayed ettringite formation (DEF) is an internal sulphate attack in

concrete. Ettringite is a by-product of cement hydration in normal conditions. But in case

of high heat and temperatures, water becomes a redundant and is not readily available for

the complete hydration process. Due to this, formation of ettringite in concrete matrix is

delayed. On the other hand, such high temperatures are also inappropriate because it will

be impossible for construction labour to work under such heat and humidity.


Page | 52

Maximum temperature of 32 °C was observed after 22 months from the construction start

(Fig. 4.3) while maximum temperature value of 44°C was observed at 5 years after the

construction start (Fig 4.5). This higher value was observed at El. 890 m. At this

elevation, spillway has been constructed using conventional concrete. Its cement content

is 300 kg/m3 in comparison to 100 kg/m3 for RCC. Further investigation revealed that at

this elevation, dam width reduces significantly near the top and ambient temperatures

which are the prime heat source, accumulate and result in enhanced thermal effects at this

elevation. Although this maximum temperature may still be acceptable as the concrete

properties will not be hampered by much, yet some measures will have to be taken up as

precautions. Cooling pipes may be inserted at this location which will help in controlling

the inside temperatures of concrete.

4.3 THERMAL STRESS ANALYSIS

Results of thermal gradient analysis obtained from the one way coupling of TM analysis

were used to calculate thermal stresses. These are more meaningful in terms of the

required concrete strength as any excessive tensile stresses should have to be restricted

primarily by the material properties. All other temperature control measures will only

help in reducing tensions for certain time period. Results of this stress analysis will be

utilized for further crack analysis. Compressive stresses also developed due to

temperature gradients but these are of no importance in crack analysis. In fact these

compressive stresses tend to heal some minor cracks developed earlier but this effect will

be ignored in the analysis. Table 4.1 gives the maximum thermal stress values obtained at

different locations. This table has been derived from ‘Time History Post-processor’ of

ANSYS. Time histories of different elements were obtained and the peaks were read from

these plots.


Page | 53

Table 4.1: Maximum Thermal Stresses along Dam Height

Elevation

(m)

Thermal Stresses (MPa)

U/S Face Along Centerline D/S Face

Tensile Compressive Tensile Compressive Tensile Compressive

740 0.410 0.222 0.127 0.000 0.399 0.285

750 0.494 0.188 0.190 0.000 0.501 0.188

760 0.726 0.459 0.380 0.000 0.726 0.000

770 0.520 0.459 0.380 0.000 0.722 0.000

780 0.494 0.188 0.190 0.000 0.501 0.190

790 0.000 1.537 0.000 0.792 0.000 1.543

800 0.061 0.570 0.000 0.190 0.057 0.634

810 0.726 0.459 0.380 0.000 0.726 0.000

823 0.027 1.537 0.000 0.684 0.027 1.600

830 0.278 0.903 0.000 0.000 0.278 0.412

840 0.716 0.459 0.380 0.000 0.716 0.000

854 0.007 1.598 0.000 0.684 0.007 1.598

860 0.000 0.631 0.000 0.190 0.000 0.493

870 0.716 0.459 0.380 0.000 0.716 0.000

880 0.494 0.681 0.187 0.000 0.494 0.184

890 0.000 3.528 0.000 2.949 0.000 3.783

900 0.045 1.125 0.000 0.190 0.045 0.397

910 0.384 0.681 0.190 0.000 0.384 0.045


Page | 54

Fig 4.6: Maximum Stresses at U/S face of Dam (-ve Compressive, +ve Tensile)

Fig 4.7: Maximum Stresses at D/S face of Dam (-ve Compressive, +ve Tensile)

724

744

764

784

804

824

844

864

884

904

924

-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Dam

Hei

ght (

m)

Stress (MPa)

724

744

764

784

804

824

844

864

884

904

924

-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Dam

Hei

ght (

m)

Stress (MPa)


Page | 55

Fig 4.8: Maximum Stresses at Dam Centerline (-ve Compressive, +ve Tensile)

Form Table 4.1 and Figures 4.6 to 4.8, it is clear that the maximum tensile stress at u/s

and d/s faces of dam is 0.73 N/mm2 while along the centerline, maximum tensile stress is

0.38 N/mm2. Tensile strength equal to 5% of the compressive strength (equal to 1.0

N/mm2 for 20 N/mm2 compressive strength) for mass concrete as directed by ACI and

various other researchers could be used here. Using this allowable strength, possibility of

tensile cracks will be eliminated altogether for the results obtained. But this analogy is

correct only for exterior loads like the hydrostatic, superimposed and seismic loads etc.

For thermal loads which act from within the body of dam, this criterion for allowable

tensile strength does not seem justified and cracks will definitely appear in the concrete

mass. For this reason, instead of tensile strength, tensile strain capacity has been defined

and will be discussed in the subsequent sections.

The above charts also show a sudden rise in the compressive stress values near the top of

dam. At this location, conventional concrete has been used for the construction of

spillway which has higher cement content than RCC. Due to the presence of this high

cement content conventional concrete, higher heat of hydration will release and higher

724

744

764

784

804

824

844

864

884

904

924

-3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0

Dam

Hei

ght (

m)

Stress (MPa)


Page | 56

compressive stresses will hence appear. But as discussed earlier, such compressive

stresses are hardly a concern in assessing the crack potential of dam.

4.4 THERMAL CRACK ANALYSIS

Tensile strain capacity ‘TSC’ has been discussed in Section 2.2 and 3.3.2(f). It is the

allowable strain which will occur before the onset of any cracking. But as soon as the

tensile strains exceed TSC, cracking will initiate. Crack analysis addressed herein

comprises of surface cracking and mass cracking potential. Surface cracks are those

which will appear on the u/s and d/s face of dam due to applied boundary conditions.

Mass cracks will appear inside the body of dam and as discussed earlier, these have been

estimated by extracting the analysis results along the centerline of dam cross section.

Since a 2-D TM analysis was carried out which only depicts the tensile and cracking

strains at one section, whereas, cracks will appear throughout the crest length. For this

reason, following analytical procedure has been implemented to extrapolate the results of

2-D analysis into the third dimension so that the number of cracks and crack spacing may

be determined along the crest length [11]:

Cracking strain = Sc = Thermal Strain – Tensile Strain Capacity

Dam length considered = L

Total cracking width = Cw (total) = Sc × L

Assumed cracking width = Cw

No. of cracks = N = Cw (total) / Cw

Crack spacing = S = L / N

Following values were used for this crack analysis:

Tensile strain capacity = 2 × 10-5

Assumed Crack Width = 2 mm [12, 14]

This assumption for 2 mm crack width is required to calculate the number of cracks each

having a width of 2 mm. In actual every crack will have different widths but for

simplicity and ease in calculation, this uniform width will be used here. Using the above

calculation steps, transverse and longitudinal crack spacing has been calculated from


Page | 57

surface cracking and mass cracking strains respectively. Following tables will depict the

results of surface and mass cracking analysis.

Table 4.2: Transverse Crack Potential along the Dam Crest

Elevation

(m)

Surface Gradient Cracking

U/S Face D/S Face

Cracking

Strain

No. of

Cracks

Crack

Spacing

(m)

Cracking

Strain

No. of

Cracks

Crack

Spacing (m)

736 1.474E-05 1 135.66 1.474E-05 1 135.66

778 9.050E-06 1 220.99 9.493E-06 1 210.68

781 1.124E-05 1 177.89 1.124E-05 1 177.89

784 5.499E-05 4 36.37 5.499E-05 4 36.37

787 5.674E-05 4 35.25 5.674E-05 4 35.25

790 1.474E-05 1 135.66 1.474E-05 1 135.66

793 1.474E-05 1 135.66 1.474E-05 1 135.66

796 1.474E-05 1 135.66 1.430E-05 1 139.86

799 9.050E-06 1 220.99 9.493E-06 1 210.68

808 7.743E-06 1 258.30 7.743E-06 1 258.30

811 1.124E-05 1 177.89 1.124E-05 1 177.89

814 1.124E-05 1 177.89 1.124E-05 1 177.89

817 1.124E-05 1 177.89 1.124E-05 1 177.89

820 5.499E-05 6 36.37 5.499E-05 6 36.37

823 5.499E-05 6 36.37 5.499E-05 6 36.37

826 1.124E-05 1 177.89 1.124E-05 1 177.89

829 7.743E-06 1 258.30 6.600E-06 1 303.03

832 3.100E-06 0 645.16 4.243E-06 1 471.36

835 4.243E-06 1 471.36 4.243E-06 1 471.36

838 7.743E-06 1 258.30 7.743E-06 1 258.30

841 1.124E-05 1 177.89 1.124E-05 1 177.89

844 1.124E-05 2 177.89 1.124E-05 2 177.89

847 1.124E-05 2 177.89 1.124E-05 2 177.89

850 5.499E-05 8 36.37 5.499E-05 8 36.37

853 5.560E-05 8 35.97 5.560E-05 8 35.97

856 1.360E-05 2 147.06 1.360E-05 2 147.06

859 8.350E-06 1 239.52 8.350E-06 1 239.52

865 3.100E-06 1 645.16 3.100E-06 1 645.16


Page | 58

868 4.850E-06 1 412.37 4.850E-06 1 412.37

871 6.600E-06 1 303.03 6.600E-06 1 303.03

874 6.600E-06 1 303.03

877 2.030E-05 4 98.55 4.335E-05 8 46.14

880 8.010E-05 14 24.97 8.010E-05 14 24.97

883 8.010E-05 15 24.97 8.010E-05 15 24.97

886 1.239E-04 23 16.15 1.239E-04 23 16.15

889 9.060E-05 17 22.08 9.060E-05 17 22.08

892 1.360E-05 3 147.06 1.360E-05 3 147.06

895 1.360E-05 3 147.06 1.360E-05 3 147.06

898 1.360E-05 3 147.06 1.360E-05 3 147.06

901 1.010E-05 2 198.02 1.010E-05 2 198.02

904 6.600E-06 1 303.03 6.600E-06 1 303.03

907 6.600E-06 1 303.03 6.600E-06 1 303.03

910 6.600E-06 1 303.03 6.600E-06 1 303.03

In general, RCC dams are divided into blocks by way of self induced joints which are

materialized by means of conventional formwork or by inductors. In the first case, blocks

permit the use of formwork on the dam face in one of the monoliths, while other is being

concreted. Its inconvenience is that the passage of machines from one block to the other is

restricted but this can be solved by many ways. For the case of driven joints or inductors,

blocks are made wider or continuous from one side to other depending upon the crest

length, and a synthetic/galvanized sheet is inserted by special equipment like a vibrating

blade machine. These joints continue throughout the dam cross section at certain

intervals. Next to upstream face, transverse joints are water proofed by the use of water

stops.

From the above table, minimum crack spacing for transverse cracks is calculated to be 16

m at El. 886 m. This shows that at every 16 m, a transverse joint will have to be inserted

along the dam crest length. With the block method of construction, as envisaged in the

Feasibility Studies of Dasu Hydropower Project [18], this induced crack spacing can be

altered so as to treat the vertical joints between the construction blocks equivalent to

transverse crack inducers.


Page | 59

Placement of vertical contraction joints in RCC is mainly governed by hydraulics and

thermal-construction considerations. Visible cracking in transverse (upstream-

downstream) direction usually is not a structural concern in gravity dams, but it is

unsightly and sometimes alarming to the public. It also results in water loss and a need to

collect and remove the leakage from galleries built for this purpose.

Table 4.3 shows the longitudinal crack spacing obtained from the mass gradient cracking

analysis carried out along the dam centerline.

Minimum crack spacing observed inside the dam body is 11 m at El. 886 showing that

vertical crack inducers need to be provided at this distance. These are not surface cracks

and hence are not visible and detectable easily. These unseen cracks can extend parallel to

the dam axis literally dividing the dam into two or more sections and hence create serious

stability and structural concerns. The dam will probably be safe and stable for normal

load conditions, especially if the crack is closed and does not contain water. But if

seepage continues to occur through foundation, lift joints or monolith joints, water filled

longitudinal cracks will jeopardize the sliding and overturning stability of the dam.

Table 4.3: Longitudinal Crack Potential along the Dam Section

Elevation

(m)

Mass Gradient Cracking

Cracking Strain No. of Cracks Crack Spacing

(m)

784 3.750E-05 2 53.33

787 4.100E-05 3 48.78

820 3.750E-05 4 53.33

823 3.750E-05 4 53.33

850 3.750E-05 5 53.33

853 4.100E-05 6 48.78

877 1.650E-05 3 121.21

880 9.000E-05 16 22.22

883 9.000E-05 17 22.22

886 1.775E-04 34 11.27

889 1.110E-04 21 18.02


Page | 60

Since the table shows that probability of occurrence of a longitudinal crack exists

between El.784 and El. 890, an induced longitudinal contraction joint needs to be

provided between these elevations at the centerline of dam. This can be achieved by

constructing longitudinal galleries at each of these elevations. A longitudinal joint can be

constructed between these galleries by impressing a slot vertically through RCC lifts

using pneumatically driven steel plates and a geo-grid inserted at the bottom of the

respective lifts. These galleries can also provide access for the purpose of monitoring,

drainage and future grouting. At locations where transverse and longitudinal joints meet,

drain holes are to be provided which deliver drained water to galleries.

4.5 FRACTURE MECHANICS PARAMETERS

Results discussed until now, depict the numbers and spacing of longitudinal and

transverse cracks anticipated inside the body of dam. Although longitudinal joint will be

provided throughout the crest length, depth of transverse cracks which will appear on the

dam surface remains a serious concern. Cracks ranging from few millimeters to several

meters have been observed in different dams worldwide. To assess the depth of these

cracks, detailed implementation of fracture mechanics of concrete is required. Concrete

fracture parameters are not yet defined completely and a lot of research is underway to

investigate the mechanism of fracture inside the reinforced and mass concretes. For the

present scope of study in this detailed TM analysis, several simple fracture mechanics

models were studied and efforts were made to reach at a rational solution. A brief

discussion on these parameters is presented in the following section after which the

selected parameters will be applied to the results of illustrative example.

4.5.1 Linear Elastic Fracture Mechanics (LEFM)

The first explanation of the mechanism of fracture in brittle materials was given by

Griffith (1920). Based on the analysis of a sharp crack in a sheet of brittle material, with a

constant remotely applied stress, it was demonstrated that the stresses near the crack tip

tend to approach infinity. Thus, the stress state in the vicinity of the crack tip proved to be

crucial for the load carrying capacity of the sheet. It was shown that in order for the crack


Page | 61

to advance, a certain amount of potential energy must be accumulated in the system,

which will release as a result of movement/deformation along the crack tips. Analysis of

this energy balance condition resulted in a formula for the maximum applicable remote

tensile stress as [15]:

𝜎𝑐 = 𝐸𝐺𝑐𝜋𝛼

… 4.1

where,

E is the modulus of elasticity, Gc is the critical energy release rate and α is the crack

length. Gc is the amount of energy needed to fully separate a unit area of crack surface. If

σ < σc, no cracking will occur. Irwin (1957) utilized the same theory and stress intensity

factors ‘SIF’ for fundamental crack opening modes were derived for various materials.

SIF is an important parameter for structural integrity assessment of structures containing

cracks. SIF gives a measure of the intensity of the stress field in the crack tip region. This

parameter gives the possibility to analyze crack growth or the possible catastrophic failure

if a given load is applied to the structure. The stress intensity factors can be calculated

using stress and strain analyses and energy released during the crack growth can be

estimated. The estimation of stress intensity factors can be done by analytical or

numerical techniques.

For the loading conditions assumed by Griffith (1920) [20], the critical stress intensity

factor at any crack tip will be equal to

𝐾𝐼𝐶 = 𝜎 √𝜋𝛼 … 4.2

Using eq 4.1 and 4.2, following equation is obtained

𝐺𝑐 = 𝐾𝐼𝐶2

𝐸 … 4.3

4.5.2 Non linear Fracture Mechanics

LEFM can be used to estimate important fracture parameters for linear elastic materials

however, concrete shows neither linear nor elastic behaviour and for this reason, non-

linear fracture mechanics parameters were utilized. Various models have been put forth


Page | 62

by the researchers for investigating fracture in concrete. Following is a broad

classification of these models:

A detailed description and application of each of these models is available in literature.

For the purpose of TM analysis, only the Fictitious Crack Model ‘FCM’ presented by

Hillerborg (1976) will be discussed here.

4.5.3 Fictitious Crack Model

Crack formation in concrete is caused due to several reasons. The fictitious crack model

(FCM) as developed originally by Hillerborg et al (1976) is an efficient tool to predict the

formation of cracks in a composite material such as concrete. Fracture energy and strain

softening modulus of the material are required in this model. The concept of fictitious

crack is energy-based according to the model of concrete fracture. In FCM the zone of

micro-cracking and debonding ahead of the crack front is modeled as a cohesive stress

that acts to close the crack. The magnitude of cohesive stresses on the crack surface is

Non linear Fracture Models

Cohesive Crack Models Equivalent Elastic Crack Models

Fictitious Crack Model

(Hillerborg 1976)

Crack Band Model (Bazant

& Oh 1983)

Two Parameters Model (Shah

1995)

Size Effect Law (Bazant 1984)

Effective Crack Model (Karihaloo

1998)


Page | 63

determined by a softening law that relates stress to the relative displacement of the crack

surfaces through fracture energy [15].

Being heterogeneous in nature, concrete has a complex microstructure. Whenever load is

applied, microcracks will appear in concrete and these cracks grow with time. Fig 4.9

shows a macrocrack (continuous traction-free crack) with its surrounding zone in a

cementitious material. The damage zone ahead of this traction-free crack is referred to as

the fracture process zone ‘FPZ’. This zone plays a vital role in the growth of crack.

Within the FPZ, many micro-failure mechanisms including matrix microcracking,

debonding of interfacial transition zones ‘ITZ’, crack deviation and branching take place [27]. All these mechanisms contribute to the Fracture Energy which is defined as the

specific work of fracture necessary to cause any cracking. It can be obtained from area

under the stress-displacement curve of a uniaxial tension test. In the FPZ, the Young’s

modulus is smaller than that of the undamaged material and stress relaxation takes place.

Fig 4.9: Fracture Process Zone ahead of a crack [27]

In order to illustrate the size dependence in a simple and dimensionless way, Hillerborg

introduced the concept of a characteristic length, lch, as a unique material property.

𝑙𝑐ℎ = 𝐸 𝐺𝐹𝑓𝑡2 … 4.4

4.5.4 Application of Fracture Mechanics

The proper fracture mechanics theory to be applied for a crack growth problem, as is the

case with thermo-mechanical analysis, depends on the relative size of the FPZ ‘l’’ with

respect to the smallest critical dimension ‘D’ of the structure under consideration. In


Page | 64

general, linear elastic fracture mechanics applies for D/ l > 100, while nonlinear quasi

brittle fracture mechanics is applied for structures having 5 < D/ l < 100. For D/ l < 5

non-local damage models, particle models or lattice models are applied [15]. Since for the

case of concrete gravity dam, critical dimension is much larger than the anticipated FPZ,

so LEFM can be applied to evaluate fracture parameters. However, in the following

section, non-linear fracture parameters in addition to LEFM have been calculated for

accuracy.

Choi et-al (2006) [9] performed series of 3-point bending tests on reinforced concrete

beams in order to evaluate the most suitable fracture parameters. Notches were crafted on

the beam specimens as a standard test procedure stated by the RILEM committee [9].

Various samples with varying notch lengths and widths were tested and results were

interpreted using linear elastic fracture mechanics parameters defined for brittle materials.

From the results obtained from these tests, following average values of fracture

parameters were obtained.

KIC = Critical Stress Intensity Factor = 0.7 MPa (m)1/2

GIC = Energy release rate i.e. potential energy per unit area = 19 J/m2

GF = Fracture energy = 150 J/m2

Now, using the Griffith’s theory of LEFM, SIF for a plate with remotely applied uniform

stress which creates an edge crack as shown in the Fig. 4.10 is given by the following

equation [15]:

𝐾𝐼 = 1.12 𝜎 √𝜋𝛼 … 4.5

Based on the above equation and normal principal stresses obtained

from the TM analysis, crack length α was calculated at different

elevations along the u/s face of dam. Table 4.4 shows the calculated

crack lengths:

α Fig 4.10: Edge Crack for uniform stress [15]


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Table 4.4: Crack lengths along dam Height

Elevation

(m)

Crack Length at

U/S Face Elevation

(m)

Crack Length

at U/S Face

α (mm) α (mm)

740 205.9 830 94.7

750 299.9 840 629.4

760 647.7 854 0.1

770 331.4 860

780 299.9 870 629.4

790 880 299.9

800 4.6 890

810 647.7 900 2.5

823 0.9 910 181.2

The above table shows that a maximum crack length of approximately 650 mm appears at

El.810. This crack length will govern the provision of water stops that should be provided

near the u/s face of dam so as to create a barrier in the path of water accumulated in these

cracks.

Now proceeding further into the non linear fracture parameters which have been based on

Hillerborg’s theory. Influence of maximum aggregate size Фmax on specific fracture

energy GF of concrete was investigated by Trunk & Wittmann (1998) [27]. They obtained

the following relation:

𝐺𝐹 = 𝛼 . Ф𝑚𝑎𝑥𝑛 … 4.6

where the values of α and n are calculated to 80.6 and 0.32 respectively. For Dasu dam,

maximum aggregate size was assumed to be 75 mm inside the concrete mix. Using this

size and the constant values given above, specific fracture energy of roller compacted

concrete is equal to 320 J/m2.

Value of characteristic length as calculated by eq 4.4 with tensile strength being kept

equal to 800 kN/m2 comes out to be 12.3 m. This characteristic length is a measure of

brittleness of the material and it is specific for any specific type of material [15]. Length of

the fully developed fracture process zone is roughly defined as 1.8 times lch, which comes


Page | 66

out to be 22.1 m. From the results of LEFM, approximate traction-free crack length

comes out to be less than 1.0 m while the fracture process zone which extends ahead of

the traction free crack is approximately 22 m for the roller compacted concrete adopted in

this analysis.

4.6 VALIDATION OF RESULTS

Results of thermo-mechanical analysis using computer aided modeling are generally

verified using thermocouples installed in mass concrete samples. In fact, at times, small

scale models of entire RCC dams are created by following the techniques and procedures

to be followed by contractors so as to investigate all important conditions that can occur

during actual construction.

Validation of thermo-mechanical results is quiet expensive and cost intensive practice and

it involves installation of thermocouples or distributed fibre optic temperature

measurement device which transmit inside temperatures of concrete mass to computers

and the data for temperature variations is recorded continuously. This data is then

compared with the thermal analysis results and validation is hence accomplished.

Due to limitation of resources, validation of results of this TM analysis using

thermocouples and material testing was not possible. Hence a comparison of results of

this TM analysis and several other RCC dams under similar ambient conditions is hereby

made so as to validate the correctness of results.

Table 4.5: Maximum Thermal Stress Values of Different Dams

Sr. No. Project Name

Maximum Thermal Stress

(MPa)

Tension Compression

1 Rialb Dam, Spain 0.6 1.6

2 Salto Caxias Dam, Brazil 0.2 0.8

3 Roodbar Dam, Iran 1.5 3.8

4 Hinata Dam, Japan 1.0


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5 Portuguese Dam, Portugal 0.6

6 Tha Dan Dam 0.2 1.5

7 Sarraire Dam, Switzerland 0.5 0.6

8 Mianhuatan Dam, China 2.0 2.2

9 Dasu Dam, Pakistan 0.8 3.8

The above values clearly depict that the results obtained from this TM analysis are close

to those obtained at other dams worldwide. This shows that the procedures adopted for

this study are quiet precise and give results in the acceptable range.

Page | 68

CONCLUSIONS & RECOMMENDATIONS

5.1 INTRODUCTION

The results achieved during this detailed thermo-mechanical analysis of Dasu RCC dam

are very helpful for deciding the required strength parameters of concrete mix as well as

for finalizing the construction schedule. In this chapter several conclusions drawn from

this analysis will be presented and suggestions for future research works will be

highlighted.

5.2 CONCLUSIONS

Following are the conclusions drawn from this research:

• Thermal Gradient Analysis shows that a maximum temperature of 44°C will

prevail inside the dam body at El. 890m. Near the base of dam, temperature varies

from 20 to 35 °C. Temperature time histories of the surface elements follow a

cyclic variation due to the fact that these elements are more influenced by ambient

temperatures. Elements near the center of dam are less affected by solar radiations

incident on the surfaces and hence time histories of these central elements are

more influenced by adiabatic temperature rise.

• Strict temperature control measures during batching and placement operations

involving pre-cooling of aggregates before mixing, liquid nitrogen cooling during

mixing and effective curing during construction is required. Post cooling of dam is

Chapter

5


Page | 69

practically very difficult and expensive for such a massive structure. So efforts

need to be focused on temperature controlling at earlier stages.

• Results of thermal stress analysis indicated that a maximum tensile stress of 800

kPa appears at several locations in the dam body and particularly at those

locations where the concreting operations were stopped in summer due to high

ambient temperatures. It is worth mentioning here that during summers, when the

concreting will be halted, peak flows and even floods will be anticipated and these

would be allowed to overtop the already constructed RCC dam. This would

naturally help in cooling down of temperatures inside the already constructed

portion of dam.

• Surface gradient crack analysis shows that cracks due to thermal strains will

appear at about 50m above the base of dam. Maximum number of surface cracks

appear at El.886 and here the probable crack spacing is about 16 m. These cracks

are not a structural concern in gravity dams, but these are unsightly and sometimes

alarming for the public. Water will accumulate inside these cracks and create

increased pressure which will intensify the crack propagation phenomenon. To

avoid this water stoppers must be installed near the u/s face of dam.

• To control transverse cracking, vertical contraction joints will be provided at 16 m

interval throughout the crest length of dam. This spacing will be adjusted with

respect to the width of monolith block adopted for construction of RCC dam.

Contraction joints will preferably be synthetic or galvanized sheets which will be

inserted into the concrete lifts by special equipment like a vibrating blade machine

• Mass Cracking Analysis shows several cracks within the body of dam. Thus,

probability of appearance of longitudinal crack inside the dam body at mid

distance of base width is high. These unseen cracks can extend parallel to the dam

axis and can divide the dam into two or more sections and hence create serious

stability and structural concerns. To avoid this, a possible solution is to provide

two longitudinal galleries throughout the dam length at El. 790 and El. 890. A pre-

defined crack (i.e. longitudinal joint) can be constructed between these two

galleries by impressing a slot vertically through RCC lifts using pneumatically

driven steel plates.


Page | 70

In the light of analysis assumptions discussed earlier, the following comments are due:

• The 2-D RCC model used in this study is considered acceptable because RCC

placement is usually continuous along the third dimension i.e. along the length of

the dam. In addition, the thermal conductivity of concrete is very less as compared

to its convective co-efficient. Heat generated inside the dam body will naturally

tend to escape using the shortest route i.e. from u/s and d/s faces of dam.

• RCC material properties and heat of hydration values used in this study were

based on the available literature. Creep and shrinkage effects of RCC which cause

relaxation of stresses were not considered.

• The majority of induced cracking due to tensile stresses were related to

temperature drop from peak temperatures in summers to somewhat stable

temperature conditions in winters.

• The construction schedule is the most important parameter for thermal behaviour

of RCC dam.

• Large monolith widths without contraction joints are inappropriate as they cause

an increased axial tensile stress on the upstream face of the dam which may result

into vertical cracking. In actual when interior temperature of the dam body is high

and environmental temperature is low, temperature gradient will be much higher

which will create greater axial stresses on the dam surface. Based on experience,

monolith widths for RCC dam construction must be within 20-30 m.

• The current analysis was based on the construction schedule prepared for the

conventional Block Method of construction in which concrete dam is constructed

in blocks of specified widths. For this type of construction, 2-D thermal analysis

provides proper simulation of thermal stresses. However, a new method of

construction named Sloped Layer Method is also being currently used worldwide.

In this method, dam construction is carried out as a single block rather than

several monoliths. The choice of construction method depends on the contractor’s

ability and experience. If Sloped Layer method is adopted, a full 3-D TM analysis

of the entire dam body will have to be carried out to simulate the proper thermal

stresses prevalent inside the concrete dam.


Page | 71

• Thermal analysis of concrete dams is carried out in parallel to structural analysis

(i.e. stability and stress analyses). Results from thermal analysis in terms of

temperatures or stresses are combined with structural analysis results in order to

evaluate the behaviour of dam body against all loads. Crack lengths and spacing

as obtained from this TM analysis will vary when other structural loads are

combined with thermal loads.

5.3 RECOMMENDATIONS

Based on the procedures followed and results obtained from this thermo-mechanical

analysis, following are a few recommendations for carrying out any future research

works.

• Although 2-D TM analysis provides all necessary information for thermal stability

of dam, a full 3-D TM analysis must be carried out in case Sloped layer method of

construction is adopted.

• Thermal analysis results should be incorporated in the structural analysis so as to

obtain the exact behaviour of dam against anticipated loads.

• Fracture mechanics parameters used in this study were calculated for static

thermal analysis. However, the actual thermal loads vary with time and hence

dynamic fracture analysis will be required to ascertain the exact fracture

mechanics parameters such as transient crack lengths.

• As indicated earlier, intense material testing is required to obtain all thermal and

structural properties of roller compacted concrete. This requires sampling of

materials from the site as these materials will represent the actual on-ground

scenario for concrete that will be used in dam construction. Tests on this concrete

should be carried out for obtaining all necessary material properties and the results

from these tests should be used in detailed TM analysis.

• Creep and shrinkage effects of mass concrete should also be considered for a full

3-D thermo-mechanical analysis.

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Thermo-Mechanical Analysis of RCC Dams

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