Earthquake Effect on Underground Structures

(Underground Tunnels)

by

AMIR HOSSEIN JODEIRI

In Partial Fulfillment of the Requirements

For the Degree of subject

Earthquake Engineering

MAPUA Institute of Technology

CIVIL ENGINEERING DEPARTMENT

Professor PILONES

SEMESTER (1) 2011- 2012

Abstract

Due to the increasing development of land and construction costs for

each of these structures are just important in the urban transport and the danger of injury

against the risk of earthquake to be studied. A review on the seismic behavior and design of

underground structures in soft ground is described focusing on the development of equivalent

static seismic design called the seismic deformation method. In the past most of the

underground structures were designed without seismic considerations, because generally the

tunnels had a good performance during the earthquakes compared to aboveground structures

behavior.

INTRODUCTION

BACKGROUND

The first part - of the vulnerability of underground structures in earthquake

Why the tunnel?

1 - Shortening and increase the efficiency of traffic

2 - Improve the geometric profile

3 - More safety against earthquake

Damaging agents:

1- Earthquake vibrations

2- Fault

3- Tectonic Uplift and Subsidence

In a broad sense, earthquake effects on underground tunnel structures can be grouped into two

categories – ground shaking and ground failure.

Ground shaking refers to the vibration of the ground produced by seismic waves propagating

through the earth’s crust. Body waves travel within the earth’s material. They may be either

longitudinal P waves or transverse shear S waves and they can travel in any direction in the

ground. Surface waves travel along the earth’s surface. They may be either Rayleigh waves or

Love waves.

Earthquake vibrations:

1-Volume waves PW and SW

2- Surface waves LW and RW

Factors affecting the behavior of the tunnel:

Site condition, Shape and size of the Tunnel, Tunnel depth, Tunnel lining

Failure modes:

Deformation at the Tunnel, Creation of cracks or open joints, falling from the ceiling or walls.

Reduce losses:

Increase the vulnerability of structures to absorb the deformation applied ,   Appropriate use

of joints at intersections ,   Avoid direct contact with the layers

of rock tunnel, The rigid parts connected to the main structure must be coordinated with the

main structures are vibrating.

The definition section of Tunnel

Features tunnels and how they are affected by the earthquake Effective. The definitions in this

section of the tunnels and the effect of each vulnerability of the tunnels.

Depth of tunnel:

In general, tunnels, earthquake, other than very superficial structures

stable. The land displacement, range of motion, acceleration and velocity of a particle's

generally increasing with depth, is reduced (particularly if the ground is soft), so

in cases where the acceleration of the earthquake at a depth of 50 meters, 40percent

is woven.

Shape and size of the tunnel

The tunnel cross section is larger, the sensitivity It is the most earthquake. One of

the great tunnels being localized at the inter sections and Metro stations . There are usually two

or more together in the tunnel the focus will be tunnels, causing tensions between

the static environments. In this case when seismic waves pass through a tension that is

happening.

How to make a huge impact on the vulnerability of seismic waves, because the method of

excavation, the soil stays completely intact and the other of these tunnels are usually built

where the depth of the tunnel is large. After excavation of the tunnel lining to protect against

loss if used. Of course there are also cases where the rocks have enough strength, the cover is

not used, but otherwise allowing the use of Shotcrete, concrete in situ, or are pre-built

components.

Scope of this Study

The work performed to achieve these goals consisted of:

A summary of observed earthquake effects on underground structures.

A review of current seismic design methodology for both circular mined tunnels.

Overview

Discussions of the earthquake shaking effect on underground tunnels

The response of tunnels to seismic shaking motions may be demonstrated in terms of types of

deformations. (Axial, Curvature).

OBJECTIVE

The main objective of the research is to develop a simplified, though accurate, approach to

estimate the earthquake-induced stress increments on tunnel lining. The purpose of this

research study was to develop a rational and consistent seismic design methodology for tunnels

that would also be applicable to other underground structures.

Methodology

Seismic vibrations of the tunnels

Most tunnel structures were designed and built, however, without regard to seismic effects.

Which are usually stimulated by the earthquake slip, especially in the input - output tunnels are

a lot of damage to underground spaces to enter. Many reports of earthquake damage to

underground spaces, through the tunnels have been a slip of the entries. Liquefaction of the

ground, especially if the sediments have a high percentage of loose sand and silt was

constructed; it can damage a lot of space on the ground.

The importance of earthquake vibrations

Burst damage (such as faulting or landslides) in certain areas that can occur with detailed

studies of geological engineering in these areas are identified and measures can be considered,

but the vibration caused by the fault movement at a distance or close to the underground space

and its severity can vary greatly. If the directions of the waves, with miles of tunnels or tunnel

axis may shift again in other forms of underground space will be created. While the disruption

caused by faulting or landslides are usually transformed to the Site Survey is predictable.

The analysis effect of waves on the underground structure

1- Pressure waves:

PW pressure waves with a horizontal shear waves, PW. HSW vertical component

pressure waves are a central component. PW on underground structures creates a

longitudinal strain and tension. Pw is the fastest seismic waves spread out. So the first

wave of the site will affect the soil structure.

Refer: 2

2- Vertical shear waves :

The main types of vertical shear waves are waves which include approximately two thirds

of energy are released. Structures and systems are the vertical displacement.

Refer: 2

3- Riley waves :

Riley in the waves, the particles at the top of their rotation, the wave is moving in the

opposite direction and movement of particles on the surface of the large diameter of the

ellipse that is perpendicular to wave propagation. Riley as vertical shear waves for large wave

structure function. Undergoing a shift underground system is acting based on their height.

Refer: 2

Axial and Curvature Deformations

Axial and curvature deformations develop in a horizontal or nearly horizontal linear tunnel (such

as most tunnels) when seismic waves propagate either parallel or obliquely to the tunnel. The

tunnel lining design considerations for these types of deformations are basically in the

longitudinal direction along the tunnel axis. Figure A shows the idealized representations of axial

and curvature deformations. The general behavior of the linear tunnel is similar to that of an

elastic beam subject to deformations or strains imposed by the surrounding ground.

Axial deformation a long Tunnel

Fig A.

Refer:1

Curvature deformation a long Tunnel

Deformation of cross-section

Fig A.

Refer: 1

Seismic loads cannot be calculated accurately. Seismic loads are derived with a high degree of

uncertainty, unlike dead loads, live loads, or other effects such as temperature changes. Any

specified seismic effect has a risk (probability of exceedance) associated with it.

Overlying of Tunnel section Racking of Tunnel section

Deformation modes of tunnels due to seismic waves

Refer: 1

Seismic soil deformation

Two types of deformation can be obtained from the earthquake on the underground transport

systems, which include shear deformation and curvature deformation. Direct exposure of the

soil local curvature deformation curve (the earthquake) on underground structures arises.

Underground structures must have the capacity to absorb the resulting strain. Shear

deformation as well as the time delay in response to an acceleration of the incoming base is the

bedrock.

Seismic waves from the shear deformation in soil

Refer: 4

Two types of deformation can be obtained from the earthquake on the tunnel, which include

shear deformation and curvature deformation. Direct exposure of the soil local curvature

deformation curve (the earthquake) on underground structures arise. Underground structures

must have the capacity to absorb the resulting strain. Shear deformation as well as the time

delay in response to an acceleration of the incoming base is the bedrock.

The above approach to design of underground structures may lead to very conservative design

requirements if the structure is very stiff relative to the medium. This is the case for structures

with shear walls, for example. In these circumstances a numerical analysis of the soil/structure

interaction becomes necessary. In general, a relatively simple two-dimensional parametric

analysis of a structure such as the one illustrated in Fig. C is all that is needed.

FIG C. Typical soil deformation profile and racking imposed on an underground structure during

an earthquake.

Refer: 1

Loading Criteria

Maximum Design Earthquake (MDE). Given the performance goals of the MDE the

recommended seismic loading combinations using the load factor design method are as follows:

For Cut-and-Cover Tunnel Structures:

U = D + L + E1+ E2 +EQ (Eq. 1)

Where U = required structural strength capacity

D = effects due to dead loads of structural components

L = effects due to live loads

E1 = effects due to vertical loads of earth and water

E2 = effects due to horizontal loads of earth and water

EQ = effects due to design earthquake (MDE)

For Mined (Circular) Tunnel Lining

Where U, D, L, and EQ are as defined in Equation 1

EX = effects of static loads due to excavation

H = effects due to hydrostatic water pressure

The structure should first be designed with adequate strength capacity under static

Loading conditions.

The structure should then be checked in terms of ductility as well as strength when

Earthquake effects, EQ, are considered. The “EQ” term for conventional surface

Structure design reflects primarily the inertial effect on the structures. For tunnel

Structures, the earthquake effect is governed by the displacements/deformations

Imposed on the tunnels by the ground.

• In checking the strength capacity, the effects of earthquake loading should be

U = D + L + EX +H + EQ (Eq. 2)

For Mined (Circular) Tunnel Lining:

Where D, L, EX, H, EQ, and U are as defined in Equation

b2 = 1.05 if extreme loads with little uncertainty. Otherwise, use b2 = 1.3.

U =1.05D +1.3L +b2 EX +H +1.3EQ (Eq.3)

Refer equation: 2

A Practical Approach to Describing Ground Behavior:

The earthquake source characteristics and the transmission paths of various types of waves

should also be included in the model. The ground strains are calculated by assuming a

harmonic wave of any wave type propagating at an angle (angle of incidence) with respect to

the axis of a planned structure.

Figure B represents free-field ground deformations along a tunnel axis due to a sinusoidal shear

wave with a wavelength, L, displacement amplitude, D, and an angle of incidence, q. A

conservative assumption of using the most critical angle of incidence, and therefore the

maximum values of strain, is often made, because the angle of incidence for the predominant

earthquake waves cannot be determined reliably.

Geometry of a Sinusoidal Shear Wave Oblique to Axis of Tunnel

Figure B

Refer: 2

Using the simplified approach, the free-field axial strains and curvature due to shear waves and

Rayleigh waves (surface waves) can be expressed as a function of angle of incidence, as

shown in Table 1. The most critical angle of incidence and the maximum values of the strains

are also included in the table.

Application of the strain equations presented in Table 1 requires knowledge of:

• The effective wave propagation velocity

• The peak ground particle velocity

• The peak ground particle acceleration

Refer: 2

q = Angle of Incidence with respect to Tunnel Axis

r = Radius of Curvature

VS, VR = Peak Particle Velocity for Shear Wave and Rayleigh Wave, respectively

CS, CR = Effective Propagation Velocity for Shear Wave and Rayleigh Wave, respectively

AS, AR = Peak Particle Acceleration for Shear Wave and Rayleigh Wave, respectively

Table B. MAXIMUM FORCES RESULTING FROM SHEAR WAVES

Refer : 2

Measures for mitigating seismic effect on underground structures :

1- Flexible expansion joints , seismic isolation on underground structures, period shift and

energy dissipation

2- Underground structures isolate underground structures from ground deformation.

3- Ground Deformation during an Earthquake:

Deformation resulted from propagation of waves is Limited

Variation of thickness of subsurface ground

Incoherent ground motion at base rock

Damage Statistics

Overburden Depth (meters)

Effect of overburden depth on damage

Type of surrounding hock

Effect of surrounding rock type on damage

Richter Magnitude

Effects of earthquake magnitude on damage

COMPARISON BETWEEN SEISMIC AND STATIC FORCES AND DEFORMATIONS OF A

CIRCULAR TUNNEL

In these analyses the dimensions and material properties of the lined tunnel are:

M2/m, lining diameter: 6m, El = 24,840,000 KN/m2 and thickness of the overburden = 15m

And l ϑ = 0.2

Earthquake and ground parameters:

Young’s modulus (Em):100000-676,000 KN/m2, Gm = 38461.56-260000 KN/m2, γ max =

0.001626-0.004229, ϑ m = 0.3, γ t = 1.7 KN/m3 and Vs = 0.63 m/s and as = 0.45g.

The result of these analyses were compared and summarized as follows:

1) According to Figures A,B through 9, seismic axial forces and bending moment of longitudinal

deformation are much more than seismic and static axial forces and bending moment of

deformation in both no-slip and full-slip conditions. So that tunnels must be designed for

dynamic loading. Also these figures show that seismic forces of longitudinal deformation

increase by increasing flexibility ratio but seismic bending moment of this deformation

decreases by increasing flexibility ratio.

A

Comparison of seismic and static axial forces in No-slip condition vs. flexibility ratio

B

Comparison of seismic and static axial forces in Full-slip condition vs. flexibility ratio.

Figures C and D show the comparison between seismic and static axial forces and

Bending moment of ova ling deformation in full-slip condition. Static axial forces more

than seismic axial forces but static bending moment lower than seismic bending moment in ova

ling deformation. Seismic and static axial forces and bending moment of ova ling deformation

decrease by increasing flexibility ratio.

C

Comparison of seismic and static bending moment of deformation in full slip

Condition vs. flexibility ratio.

D

comparison of seismic and static axial forces of deformation in full-slip condition vs. flexibility ratio.

Comparison between seismic forces of longitudinal deformation and static forces show

that seismic forces of longitudinal deformation are much more than static forces , thus

lining of tunnels must be designed for dynamic loadings. Also dynamic axial forces and

bending moment are much more than static axial forces and bending moment while

overburden increases.

REFERENCE A, B, C, and D: Comparison between seismic and static analyses of

tunnels. Rock Mechanics, Fuenkajorn & Phien-wej (eds) 2009. ISBN 978 974 533

624 7

CONCLUSION

In the past most of the underground structures were designed without seismic considerations,

because generally the tunnels had a good performance during the earthquakes compared to

aboveground structures behavior.

Performance -based seismic design should be aimed both to maintain in operation the tunnels

during the more frequent events (of lower intensity) and to avoid human life losses for

exceptional earthquakes (of higher intensity), according to the local seismic hazard predictions.

In some cases, and almost always in presence of ground discontinuity, structural discontinuity

or high potential of ground failure, protecting measures need to be carefully designed.

REFERENCE

1- A seismic Design of Underground Structures C. M. St John and T. F. Zahrah

Tunneling and Underground Space Technology, Vol. 2, No. 2, pp. 165-197, 1987.

2- Seismic Design of Tunnels Jaw-Nan (Joe) Wang, Ph.D., P.E. Professional Associate Parsons Brinckerhoff Quade & Douglas, Inc. June 1993.

3-Comparison between seismic and static analyses of tunnels. Rock Mechanics, Fuenkajorn & Phien-wej (eds) 2009. ISBN 978 974 533 624 7

4 - Mirmirani, Shahriar. Effect of earthquakes on the tunnels, the fifth Conference of the tunnel 7

to 9 November 2010 Faculty of Engineering of Iran, Tehran University, pages 201 to 207

Appendix

SHAKE TABLE TESTING TO QUANTIFY SEISMIC SOIL-STRUCTURE-

INTERACTION OF UNDERGROUND STRUCTURES

This research uses shake table testing of scale soil-structure models to mimic the coupled

seismic response of underground structures and surrounding/supporting soil (termed soil-

structural-interaction or SSI). Currently the seismic design of subways and other critical

underground infrastructure rely on little to no empirical data for calibrating numerical

simulations. This research is working towards filling that empirical data gap. The research is

composed of two phases, the first a validation of the free-field response of a flexible wall barrel

filled with model soil, the second a test to measure the “racking” deformations induced in a

model subway cross-section embedded in the model soil.

This research project targets the seismic design of subways and other similar underground

structures. A scale model testing platform has been developed for 1D shake table tests

That mimics the dynamic free-field conditions of a soil column of soft cohesive soil subjected to

seismic loading. In this soil column a model structure is embedded to measure what are

Commonly called “racking” deformations or deformations of the top with respect to the bottom

of the embedded structure the stiffness ratio of the soil to the structure results in the soil-

Structure -interaction. These measured “racking” deformations will be modeled numerically

using equivalent linear (FLUSH) and non-linear (ABAQUS) soil-structure-interaction programs

to expand the applicability of the empirical results.

TESTING PLATFORM

In physical testing, and scale model testing in particular, the testing equipment and physical

model details can demand the bulk of the research efforts. This project is no exception. The first

year of this project was spent acquiring the necessary materials, fabricating and modifying the

testing equipment, and calibrating the testing platform.

The central piece of testing equipment is a flexible wall barrel that mimics free-field seismic site

response when subjected to shaking on the shake table. Validation of the testing platform

involves comparing analytical results with recorded response from the flexible wall barrel.

Figures 1 and 2 show the validation by Meymand (1998) demonstrating the dynamic

performance of the flexible barrel versus other testing containers. As can be seen the flexible

wall barrel provides the most accurate representation of seismic soil response with respect to

the prototype soil column as modeled numerically using QUAD4M (Hudson et al. 1994).

Figure 1. Different model soil containers for SSI shake table testing (after Meymand 1998).

Figure 2. Dynamic analysis of different model soil containers. showing that the flexible wall

barrel provides the most realistic response when compared to prototype field conditions (after

Meymand 1998).

The flexible wall barrel and associated equipment was assembled on the 1D shake table in the

Parsons Earthquake Lab at Cal Poly, and the mixing of an appropriate model soil was carried

out. Figure 3 shows the flexible wall barrel assembled on the shake table awaiting the model

soil. Figure 4 shows the filling of the barrel and Figure 5 shows the full barrel awaiting shake

table testing.

Figure 3. Testing platform showing the shake table with the flexible wall barrel. The flexible wall

barrel is composed of the four corner posts with universal joints at the top and bottom, the top

and bottom rings, and the barrel wall. The wall is composed of a 6.4 mm thick rubber membrane

which is confined by 45 mm wide Kevlar straps spaced on center every 60 mm. The (yellow)

mixer on the left is used to mix the large volumes of model soil (composed of kaolinite,

bentonite, fly ash, and water).

The Parsons Earthquake Lab at Cal Poly has a 1D shake table with a 9000 kg payload capacity.

Under the maximum payload the table can accelerate up to 1g, has a maximum velocity of 97

cm/sec, a maximum peak to peak displacement of 25 cm, and operates in the frequency range

of 0.1 to 50 Hz. A full flexible wall barrel and accompanying equipment is estimated to weigh on

the order of 7000 kg.

Figure 4. Process of filling the barrel with scale model soil Ten accelerometers were placed in

the soil lifts in both vertical and horizontal arrays to record the dynamic response of the soil

during shaking.

Figure 5. Shown is a full barrel being prepared for initial calibration tests. Note the cross bracing

still in place that will be removed prior to testing to allow the flexible wall barrel free movement in

response to the imposed shaking.

Figure 6 shows the plan view layout of the accelerometer array and the T-bar locations. The

accelerometers arrangement is composed of a central array to measure the average model soil

column response, an off center array in anticipation for the second phase of the test when the

model subway cross-section will be embedded in the soil column, and accelerometers near the

edges to measure any boundary effects due to the flexible wall barrel assembly.

Figure 6. Top down plan view of the flexible wall barrel showing the accelerometer array

layout, T-bar locations, and radial dimensions.

PHASE 1 TESTING

The first phase was to perform free-field tests to measure the dynamic response of the soil

column without the influence of the underground structure and provide a baseline for evaluating

the effects of the soil on the structure. The ground motions selected for table input are;

1. 1979 Imperial Valley, El Centro motion

2. 1992 Landers, Joshua Tree motion

3. 1999 Chi Chi, TCU075 motion

These motions were selected specifically to impose large adverse loads on an underground

structure. These were also the same motions selected and peer reviewed for a tunnel related

consulting project similar to the subway prototype.

PHASE 2 TESTING

An underground section of the BART (Bay Area Rapid Transit) light rail was chosen as the

prototype tunnel cross-section for the SSI tests. This structure is also similar to light rail tunnels

being considered in the Jiangsu province of China. A scale model structure adhering to the

similitude scaling of the structural stiffness of the BART tunnel cross section was assembled.

Figure 7. Shear wave velocity profile from Phase 1 tests. Shear wave velocity was

measured using top down hammer blows and correlated estimates from bottom up T-bar

tests.

Figure 8. Comparison of the free-field flexible barrel recording at the model soil surface

versus SHAKE results of the prototype soil profile. The input motion here is the 1979

Imperial Valley El Centro 180 recording.

This manuscript presents research delving into the seismic soil-structure-interaction

(SSI) of a subway in soft clayey soil. The goal of this research is to provide an empirical

basis for the “racking” deformations that are a design reality of underground SSI

projects. A 1g tenth scale model testing platform was developed for dynamic testing on

the shake table. The platform is composed of a flexible wall barrel, scale model soil, and

associated testing hardware. The first phase of the research, free-field testing, was

completed by the time of manuscript submission. The response of the flexible wall barrel

testing platform is shown in Figure 8 to adequately mimic the prototype soil column as

validated using 1D equivalent linear (SHAKE) numerical analysis.