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Blast Effects on Underground Pipes

Akinola J. Olarewaju e-mail: akinolajolarewaju@yahoo.com

N.S.V. Kameswara Rao e-mail: nsv@ums.edu.my

Md. A. Mannan e-mail: mannan@ums.edu.my

Civil Engineering Program, School of Engineering and Information Technology, SKTM; Universiti Malaysia Sabah, 88999, Kota Kinabalu, Malaysia

ABSTRACT This paper has outlined the static and dynamic responses between the various components of blast which are blast load, ground media, pipes, and the intervening layer. Response of linear models of buried pipes due to surface static load was studied using ABAQUS code and results compared with that of SAP code. In addition, using UFC (2008), blast wave parameters for 50kg TNT in different pipes were obtained. Furthermore, response of buried pipes due internal explosion for the same explosive was equally studied. Equivalent earthquake parameters on ground surface for the same explosive were obtained and compared with San Fernando earthquake of 1971. Analytical method cannot provide accurate result owing to its limitations. However, numerical methods considered by modeling for solving linear and non-linear as well as dynamic equilibrium equation are Newton and central difference methods. The solutions to the dynamic equations using these numerical methods are achieved using ABAQUS and Sap codes. KEYWORDS: Blast, Underground Pipes, Analytical, Numerical, Overpressure, Blast, Response.

INTRODUCTION In our day-to-day activities, we come across underground structures like pipes, shafts, tunnels, etc which are

used for services like water supply, transportation, dewatering and drainage, sewerage, oil and gas supply, storage facilities, piling for jetties berths and foundations, caissons, surface and underground main lines for irrigation, penstocks for hydro-electric projects, etc. Due to huge investment in the construction of underground structures especially pipes, there is need to study the responses of these installations due to blast most especially where it is laid across the road or directly underneath multistory buildings. Underground pipes are made of different materials such as steel, concrete, clay, etc.

It is important to consider the severity of destruction of explosion due to blast. Blast can create sufficient tremors to damage sub-structures over a large area. It has been reported that at 138kpa of blast wave, reinforced concrete structures will be leveled (James, 2008). Consequent upon these phenomena are loss of lives and property. In the manufacturing industry, it leads to disruption in production, land degradation, etc. As a result of

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these, there is need to mitigate the consequences of blasts in underground pipes. This is by designing protective pipes, suggesting possible mitigation measures or providing alternatives which will necessitate thorough understanding of the interaction and responses of the constituents of the blast. The constituents are the explosive, ground media, intervening layer, structural components (pipes), and blast characteristics (Robert, 2002). In studying soil-pipe interaction through modeling, some experimental data are needed to simulate the prevailing situations between all the constituent materials (Ganesan, 2000). These data could be obtained from field tests, laboratory tests, theoretical studies, work done in related fields, and extension of work done in related fields (Newmark and Haltiwanger, 1962).

A lot of works have been done on dynamic soil-structure interaction majorly for linear, homogeneous, and semi-infinite half space. The response of elastic half space was first carried out by Lamb (Lamb, 1904). Newcomb (1951) and Converse (1953) derived empirical relation for the determination of resonance frequency in vibrated soil. It was established that softer soils have lower natural frequency. Hard clays have less natural frequency than sand stones. Ronanki (1997) obtain the responses of buried circular pipes under three-dimensional seismic loading. Method used is the finite element based software package, SAP-80. George, et al (2007) analytically examined the blast-induced strains to buried pipelines. According to them, comparisons of result showed improved accuracy as well as the advantage of accounting for the effect of soil conditions. In this paper, through modeling, surface static load and internal explosion effects in buried pipes were studied.

METHODOLOGY In buried pipes, the constituents of the blast comprises of the rock media, soils, intervening medium and the

pipes.

Rock and Soil Media

The rock media depends on the geotechnical properties of the ground medium. It ranges from intact rocks like schist to average quality to poor quality rocks. Rocks are formed as a result of various natural processes like cooling of molten magma, the precipitation of inorganic materials, the deposition of shells of various organisms, etc. Rocks are classified into three. These are igneous rocks, e.g. granite, volcanic-basalt, etc, sedimentary rocks, e.g. sandstone, limestone, shale, conglomerate, or metamorphic rocks, e.g. schist, slate. Rocks undergo geologic action namely denudation, deposition, and earth movement. These processes lead to the formation of soil. Soil is a material which disintegrates into individual grains by mechanical means. Examples of mechanical means are agitation in water, application of flow pressure, etc. Soils are identified by various methods; Bureau of Soils (1890-1895), Atterberg 1905, and MIT 1931. It also includes USDA 1938, AASHO 1970, and Unified Soil Classification System 1952. Others are: ASTM 1967, etc (Peck, et al, 1974). The three major types of soils encountered in buried pipes are frictional soils, cohesive soils, and frictional-cohesive soils. Cohesive soils contain clay minerals comprising of montmorillonite, kaolinite and illite as major group of minerals. The minor groups are allophone, chlorite, vermiculite, attapulgite, palygorkite, and sepiolite (Grim, 1953; Ola, 1983). It must be noted that most natural soils are anisotropic. These are soils that have different geotechnical properties in different direction. Isotropic soils are those having geotechnical properties that do not vary with direction while homogeneous soils have the same kind of constituent elements, same uniform composition or structure. Two layers of soils can be considered as a single homogeneous anisotropic layer. This depends on the equivalent isotropic coefficients for the two layers. To determine geotechnical properties of soils and rocks, the following procedural steps are identified: surface exploration, geological survey, subsurface exploratory, field classification, laboratory investigation, miscellaneous laboratory tests, rock cores, etc. Typically adopted constitutive relations of soils are elastic, elasto-plastic, or visco-plastic. Under blast load the initial response of

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the constituents is the most important. It involves some plastic deformation that takes place within the vicinity of the explosion. As a result of this one could take the ground media to be an elasto-plastic material. Beyond this, soil can be considered as elastic material at distance from the explosion. Visco-elastic soils exhibit elastic behavior upon loading followed by slow and continuous strain increase at decreasing rate (Boh, et al, 2007; Greg, 2008). In this study, soils and pipes were modeled as elastic materials.

Surface waves and body waves are generated when there is explosion. This can take place on the ground surface or underground. Consequently there are isotropic component and deviatory component of the stress pulse. Transient stress pulse causes compression and dilation of soil or rock. This is accompanied by particle motion which is known as compression or P-waves. The deviatory component causes shearing stress. These are known as shear or S-wave. On the surface of the ground, the particles adopt circular motion. This is known as Rayleigh or R-wave. Compression, P-waves and shear, S-waves happens in underground explosions. They move within short range due to intervening medium which is soil or rock. On the other hand, Rayleigh, R-waves dominates above-ground explosions. As a result they have long range (Kameswara, 200). Energy impulse from explosion decreases as it travels for two reasons, firstly, due to geometric effect i.e. by three dimensional dispersion of blast energy. Secondly, due to energy dissipation i.e. result of work done in plastically deforming the soil matrix.

Pipes

Basically there are two types of cylindrical shells (pipes), namely, thin cylindrical shells, and thick cylindrical shells. If the thickness of the wall is less than between 0.10 to 0.067 of its diameter, it is known as thin shell. Walls of such vessels are thin compared to their diameter. If otherwise, it is known as thick shell (Khurmi, 2002). In thin cylindrical shell, stresses are assumed to be uniformly distributed while in thick shell, stresses are no longer uniformly distributed, in that case it becomes complex. When thin cylindrical shell is subjected to pressure, there are two modes of failure; is either it split into two troughs (failure due to hoop stress), or it split into two cylinders (failure due to longitudinal stress). In analytical solution, one approach is the stress function concept. This was first proposed by Sir George B. Airy, later generalized for three-dimensional case by Clerk Maxwell. The equation is

( +

)2 = 0 or 4 = 0 (1)

This equation is referred to as the biharmonic equation. is known as Airy stress function. In more complicated problems like blast, the analytical approach may not provide accurate solution owing to its limitation despite the improved accuracy put forward by George, et al (2007). In that case numerical methods must be employed if acceptable accuracy is to be obtained. In the analysis of dynamic soil-pipe interaction, it involves determination of displacement, pressures, stresses, etc around the pipe (Fig. 1). The soil density, modulus of elasticity, Poisson ratio and friction coefficient obtained from soil tests are used. For the elastic materials, where no data are available, the following friction coefficient can be used, Silt = 0.3, Sand = 0.4, and Gravel = 0.5 (Lester, 2008).

Blast Energy

The majority of explosives are formed from Carbon, Hydrogen, Nitrogen and Oxygen. The general chemical formula is Cx Hy Nw Oz. Explosion can occur below, beside or above a structure. The categories of blast in this context are: free-air blast, air burst, surface burst and underground blast. A comparison of the parameters from surface burst with those of free-air explosions indicate that, at a given distance from a detonation of the same weight of explosive, all of the parameters of the surface burst environment are larger than those for the free-air environment. For a conservative design, surface burst is considered being the worst of all the types of blast. UFC

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(2008) allows for an increase of 20% of the actual weight of the explosive material under consideration. Energy imparted to the ground by the explosion is the main source of ground shock (Ngo, et al, 2007). For a sufficiently deep underground explosion, there is no blast wave. The detonation of a high explosive generates hot gases under pressure. Consequently, a layer of compressed air known as blast wave is formed. Blast wave instantaneously increases to a value of pressure above the ambient pressure. This is referred to as the side-on overpressure. It decays as the shock wave expands outward from the explosion source. After a short time, the pressure behind the front may drop below the ambient pressure (Fig. 2). TNT (trinitrotoluene) equivalent values are used to relate the performance of different explosives. This is the mass of TNT that would give the same blast performance as the mass of the explosive compound in question (Longinow and Mniszewski, 1996). Conversion factors obtained from Remennikov (2003) for various explosives are as follows; TNT (trinitrotoluene) - 1.000, RDX (Cyclonite) - 1.185, PETN - 1.282, Compound B (60% RDX 40% TNT) - 1.148, Pentolite 50/50 - 1.129, Dynamite - 1.300, and Semtex - 1.250. There are three methods available for predicting blast loads on structures. These are Empirical methods using Unified Facilities Criteria, UFC (2008) as shown in Figure 2, TM 5-855-1, etc), CONWEP, etc. Semi-empirical methods based on simplified models of physical phenomena. These methods attempt to model the underlying important physical processes in a simplified way. Numerical methods based on mathematical equations that describe the basic laws of physics governing a problem. There is universal normalized description of blast effects known as blast wave scaling laws. It is general practice to express the charge weight, W as an equivalent mass of TNT. Results are given as a function of the dimensional distance parameter (scaled distance),

Z (2)

R is the actual effective distance from the explosion. W is the weight of the explosion generally expressed in kilograms.

Ground Movement Parameters

Overpressure and dynamic pressure pulse are considered in above ground portions of structures. Only overpressure pulse (pressure which acts on the structure) is considered in the design of underground structures. For isotropic compression of soil (P-waves), the velocity Cp or seismic velocity, c is computed as,

Cp or c E = (3)

E is the bulk modulus obtained from uniaxial unconfined compression test which produces conservative values. is the density of soil. v is the Poissons ration of soil. Poissons ratio fluctuates for different materials over a narrow range. Generally it is in the order of 0.2 to 0.5, averagely, 0.3 (for cohesionless soil), and 0.4 (for cohesive soil). The largest possible value is 0.5 and is normally attained during plastic flow and signifies constancy of volume (Chen, 1995). c vary

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Figure 1: Cross-section of pipe in different soil layers

Figure 2: Peak incident and reflected pressures for surface blast for different explosives

from values less than 200m/s for loose, dry sands to values in excess of 1500m/s for saturated clays. Commonly used value for soils is 300 m/s. It can be calculated from the elastic constants of soil (Chi-Yuen, et al, 2006). Ground shock parameters are equally known as the soil movement parameters. These translate into loading which the soil delivers to the buried structures. These parameters are peak particle displacement caused by a buried explosive at a location a distance from the structure and peak particle velocity which depends on both the seismic velocity and peak particle velocity (Husabei, 2009; Kameswara, 2000). For a totally or partially buried charge located at distance R from the structure, peak particle displacement, x caused is estimated by,

x = 60 (1n) , (4)

Peak particle velocity, u, is given by

u = 48.8 Fc (-n) (5) x is measured in meters and W is the charge mass in kg. Fc is a dimensionless coupling factor for the

explosive charge which depends on explosive charge burial depth (usually taken as = 1). c is the soil seismic

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velocity in m/s and, n, is the dimensionless attenuation coefficient (usually taken to be = 2.75). R is the radial distance (m) measured from the center of the charge weight, W. The value of the loading wave velocity, Cp (m/s) shown in Figure 3 is given by seismic velocity, c and peak particle velocity, u as,

Cp (fully saturated clays) = 0.6 c + u,

Cp (sands) = c + u, (6)

Figure 3: Loading wave velocity in underground blast for saturated clay and sand

The specific impulse is then evaluated using this,

io = Cp x (7)

is the density in kg/m3 and io is measured in Ns/m2 (UFC, 2008; Zhengweng, 1997).

METHODS OF ANALYSIS There are several numerical methods for assessing the response of structures due to dynamic (blast) loadings.

These are iteration, series methods, weighted residuals (least square methods), finite increment techniques (step by step or time integration procedure) usually referred to as finite difference, Newmark, Wilson, Houbolt, Eular, Runge-Kuta and Theta methods. Finite difference is popularly used to solve ordinary and partial differential equations, in particular, dynamic problems. Using this method, solution domain is replaced by a number of discrete points called mesh points or nodes. Solution to the problem is obtained at these points by converting the differential equation into an algebraic equation approximately satisfying the differential equation and the boundary conditions. The algebraic equations can be obtained in terms of forward, backward or central difference formulae but central difference formulae are preferred due to their higher accuracy (Kameswara,

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1998). Most of the numerical methods in dynamic analysis are based on finite difference approach. The equation of motion is given as

[m] [ ] + [c] [ ] + [k] [U] = [P] (8)

for U (t = 0) = Uo (9)

(t = 0) = o = vo (10)

Where m, c, k are element mass, damping and stiffness matrices, t is the time, U and P are displacement and load vectors and dot indicate their time derivatives. The time duration (period) for the numerical solution can be divided into n intervals of time t (h). It should be noted that with no damping

t

for stable and satisfactory solution

or with damping

t (

is the maximum natural frequency, is the critical damping factor. Damping may be specified as part of a material definition that is assigned to a model. Elements such as dashpots, springs and connectors could be used which serve as dampers, all with viscous (Rayleigh damping) and structural damping factors. One can choose to model the viscous damping matrix by using material damping properties and/or damping elements (such as dashpot or mass element). Stability limit is the largest time increment that can be taken without the method generating large rapid growing errors. The accuracy of the solution depends on the time step t = h. However, there are some conditionally stable methods where any time step can be chosen on consideration of accuracy only and need not consider stability aspect. Accordingly, the unconditionally stable methods allow a much larger step for any given accuracy. The recurrence formula which gives the value of Ui+1 in terms of Ui, Ui 1 and Pi is given as

m + c kUi = P (11)

where Ui = U(ti) and Ui+1 can be written as

Ui+1 (12)

Repeated use of the recurrence equation gives the response of U of the system in the entire domain of interest. This is also called an explicit integration method since Ui+1 is obtained by using the dynamic equilibrium of the system at ti as given in Eq. 11. The solution can not start by itself, because to obtain Ui (i = 0) from Eq 12, there is need to get the values Uo and U-1. Uo is given by the initial condition in Eq. 9, U-1 has to be generated using the other initial conditions o given by Eq. 10 and the governing equation of motion (Eq. 8) is given by

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o = (m)-1 (Po c o kUo) (13)

From the difference equations, we obtained

U -1 = Uo - h o + o (14)

where o is known from the given initial conditions as expressed by Eq. 13, i is increment number of an explicit dynamic step, and dots indicate their time derivatives (Kameswara, 1998). This is better solved using Abaqus dynamic explicit which uses explicit central difference operator that satisfies the dynamic equilibrium equations at the beginning of the increment, t, the acceleration calculated at time, t are used to advance the velocity solution to time, t + and

displacement solution to time, t + t. In direct-integration dynamics of time integration in the Abaqus Explicit, the equation of motion (Eq. 8) of the system is integrated through out time. This makes it unnecessary for the formation and inversion of the global mass and stiffness matrices [M], [K]. It also simplifies the treatment of contact and requires no iteration. This means that each increment is relatively inexpensive compared to the increments in an implicit integration scheme. It performs a large number of small increments efficiently. Explicit are used for the analysis of large models with relative short dynamic response times and extremely discontinuous events or processes like blast (ABAQUS Users manual, 2008).

FINITE ELEMENT MODELING Methods of structural analysis and design are broadly divided into three, firstly, theoretical methods which carrying out

analysis and the use of design codes, secondly, by testing full size structure using experimental method and thirdly the use of models (Ganesan, 2000). In finite element model, real continuous structure is idealized into assemblage of discrete elements. Force-displacement relations and stress distributions are determined or assumed. The complete solution is obtained for the entire structure by combining the individual elements into an idealized structure. Conditions of equilibrium and compatibility are satisfied at the junctions of these elements. One-dimensional, two-dimensional and three-dimensional finite elements can be used. Advantages of this method are; much greater flexibility both in fitting boundary shapes, in arranging internal distributions of nodal points to suit particular problems, and lastly it provides a great deal of information concerning the variations of unknowns at points within the region of interest. The disadvantage is the expertise required and substantially increased storage requirement for equation coefficients.

a b Figure 4: Finite Element Models (a, at H/D = 1; b, at H/D = 2)

Under the impact of surface static load (linear response), the model of buried pipe was studied and result compared with the work by Ronanki (1997). Range of soil thickness and displacement continuity with the rest of soil layers was considered. The choice of material model is based primarily on the purpose of analysis, in this

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case, soil and pipes were modeled as elastic materials. An homogeneous soil with smooth and rigid boundaries having a width of 7.30m, depth of 4.8m and 10m long contained a 0.96m diameter pipe embedded initially at H/D = 1. Pipe is assumed to be horizontal with no slip between the pipe and the soil. Surface static pressure load of 10Pa is applied to the surface of the soil. The Youngs modulus of soil, Es is 1 x 104Pa, Poissons ratio, v, is 0.3 while the Youngs modulus of pipe Ep is 1 x 106Pa and Poissons ratio, v, is 0.2 (Figure 1). The plane stress/strain thickness is 1. Different depths of embedment were considered. Using Newton method in Abaqus numerical program, the analysis step is general static and period is 1. Maximum number of increments is 100 with initial, minimum and maximum increment size of 0.1, 1E-005, and 1 respectively using direct equation solver method. With an approximate global size of 1.75 is the formation of C3D8I, an 8-noded linear brick, incompatible nodes with 258 hexahedron elements generated for the model. In the work of Ronanki (1997) on response of underground pipes, 256 elements were generated for the same model using SAP-80 numerical program. Large finite element model was used in other to have clear picture of the three-dimensional response of the pipe as shown in Figure 4. The boundary conditions of the finite element model for displacements were fixed at the base and roller on all the four sides. Zero initial conditions were used in all calculations.

Under the impact of internal explosion (non-linear response), the finite element model of all the soils (undrained clay, lose sand and dense sand) is 21.04m width, 8.04m depth and 20m long. Steel and concrete pipes are 1.0m diameter and 20m long. 0.010m and 0.020m thicknesses were considered. Pipes were laid horizontally each at 3.04m and 6.04m depths in other to consider various embedments with no slip assumption. The impulse pressure was assumed to be the normally reflected pressure using Unified Facilities Criteria (2008). A 50kg TNT explosives was used to study the response of buried steel and concrete pipes. The explosion was assumed to occur at the centre right inside pipe. The explosion is represented by a pressure load applied on the circumference of a circle with radius whose center coincides with that of the explosive charge. The magnitude is 30MPa which decreases linearly to zero in a time interval of 0.025 second. The initial stress state before explosion was obtained in the first step and dynamic non-linear response under the blast loading was obtained using Dynamic Explicit during the second step analysis. The boundary conditions of the finite element model for displacements were fixed at the base and roller on all the four sides. This is to simulate infinity of the soil medium despite the short duration of the blast problem, to allow the energy to dissipate away without reflecting back into the soil and buried pipes. Contrary to our usual engineering intuition, introducing damping to the solution reduces the stable time increment. Raleigh damping is meant to reflect physical damping in the actual material. A small amount of numerical damping is introduced in the form of bulk viscosity to control high frequency oscillations.

RESULTS AND DISCUSSIONS The results of effects of different depth embedment depth on the pipe is graphically shown in Figure 5 while

the pressure generated in different diameter pipes for different charge weight are shown in Figure 6. Time history of external work and total energy by 50kg TNT in buried pipes at different depth in different soil media is presented in Figures 7 and 8. The consequence of ground shaking (earthquake) on the ground surface is acceleration.

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Figure 5: Effects of different depth of embedment on the pipe: (a) pressure; (b) displacement; (c) max principal strain

(d) maximum principal stress

Accelerographs are used to measure the maximum ground horizontal acceleration (m/s2) of the ground surface over time (s). This acceleration can be converted to a fraction of earths gravity by dividing by (g) 9.81 m/s2. By integrating the horizontal ground acceleration, the horizontal velocity (m/s) of the ground surface over time was obtained. Further integrating the velocity, the horizontal displacement (m) at the ground surface against time (s) was obtained. A 50kg TNT blast in underground pipes produces equivalent earthquake parameters on ground surface. These parameters (velocity and displacement) are compared with San Fernando Earthquake of 1971 as shown in Table 1.

Figure 6: Pressure generated in different diameter pipes for the three charge weights: (a) peak reflected pressure;

(b) side-on overpressure

Under the impact of surface static pressure loading (linear response), at H/D = 1, for no slip condition, the spring-line of the pipe has the highest pressure and mises values while the crown and the invert has the least values of the parameters. It shows that as the spring-line is bulging out as a result of the overburden and static pressures, it compresses the soil and soil itself excerting pressure on it. This interactions result in the increase in the values of the above mentioed parameters. The crown pressure at H/D=1 is 0.99 (approximately 1.0) times that of crown pressure at H/D=2 and it further reduces to 0.74 times that of crown pressure at H/D=3.The crown mises at H/D=1 is 0.844 times that of the crown mises at H/D=2, while the crwon maximum prinicipal strain at H/D=1 is 0.688 times that of the crown maximum principal strain at H/D=2. In addition to this, the crown has the highest displacement while the invert has the least. This value reduces as the depth of embedment increases as shown in Fig 5 (a-d). This is due to the effects of overburden pressure and that of static load resting directly on the soil. The crown displacement at H/D=1 is 1.307 times that of crown displacement at H/D=2. The maximum horizontal spring-line response in terms of pressure, displacement, maximum principal strain and mises for H/D=1 is 1.2385 times that of maximum horizontal spring-line response for H/D=2. This is in line with the submissions of Roanaki (1997) using SAP program that Embedment depth has significant effect on both the crown and spring-line response. With increase of depth of embedment of pipes, the response decreases. The maximum crown response for H/D=1 is about 1.3 times that of the maximum crown response of H/D=2. In case

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of spring-line response, the maximum horizontal spring-line deflection for H/D=1 is about 1.2 times that of maximum horizontal spring-line deflection of H/D=2.

Figure 7: Time history of external work by 50kg TNT in underground steel and concrete pipes buried in different soil media (a = Loose sand; b = Dense sand; c = Undrained clay)

Figure 8: Time history of total energy by 50kg TNT in underground steel and concrete pipes buried in different soil media (a = Loose sand; b = Dense sand; c = Undrained clay)

Table 1: Equivalent earthquake parameters on ground surface for 50kg TNT blast in buried pipes Parameters a b c d e f g h I J k l m

Pressure (kPa) 28.780 80.827 39.236 223.440 7129.12 9341.75 54.398 144.566 13335.8 14709.5 13264.3 13181 -

Mises (kPa) 34.075 101.649 36.368 167.195 12.273 19.94 61.282 168.053 18.629 79.422 3.830 5.418 - Velocity (m/s) 0.279 1.104 0.1993 0.4843 0.2463 0.8778 0.5968 1.90391 0.37013 1.463 0.11863 0.463 0.030

Displacement (m) 0.0014 0.0068 0.0029 0.01167 0.0071 0.0299 0.0033 0.00114 0.01417 0.05593 0.00419 0.0139 0.149 Period (s) 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 13

Note:- a = Loose Sand20mm Steel Pipe (3.04m); b = Loose Sand20mm Concrete Pipe (3.04m); c = Dense Sand20mm Steel Pipe (3.04m); d = Dense Sand20mm Concrete Pipe (3.04m); e = Undrained Clay20mm Steel Pipe (3.04m); f = Undrained Clay-20mm Concrete Pipe (3.04m); g = Loose Sand10mm Steel Pipe (3.04m); h = Loose Sand10mm Concrete Pipe (3.04m); i = Undrained Clay10mm Steel Pipe (3.04m); j = Undrained Clay10mm Concrete Pipe (3.04m depth); k =

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Undrained 20mm ClaySteel Pipe 6.04m); l = Undrained Clay20mm Concrete Pipe (6.04m depth); m = San Fernando Earthquake of February 9, 1971 (Robert., 2001).

Considering the non-linear response, as the diameter of pipe increases, peak reflected pressure and side-on overpressure as a result of blast in the pipe reduces (Fig 6). As the thickness of steel and concrete pipes reduce, external work and energies as a result of blast increases in the same proportion (Figs. 7 & 8). Soil properties and depth of burial of pipes showed no significant changes in the external work and energies due to internal explosion as shown in the time history (Figs. 7 & 8). However, due to arching effects, stress components on the ground surface reduce more in loose sand as the depth of embedment of pipes increases (Table 1). This validates the non-inclusion of the intervening medium in the model. Unlike concrete pipes, given the same cross-section, steel pipe has the capacity to absorb energies generated as a result of the blast. Pressure changes from negative to positive within the soil medium due to dilations and compressions caused by transient stress pulse of compression wave while velocity, displacement and stresses reduces as it approaches the ground surface (Table 1). Equivalent earthquake parameters on ground surface as a result of explosion in concrete pipes are higher than that of steel pipes, but both are higher than San Fernando earthquake of Feb. 9, 1971 as shown in Table 1. This shows that blast can create sufficient tremor to damage pipes and sub-structures over a large area (Olarewaju, et al, 2010; George, et al, 2007).

CONCLUSION Analytical and numerical methods of analysis could be used to study the response of underground pipes due

to static and dynamic load. However, it must be noted that soil exists as a semi-infinite half space and as a result numerical method is better than analytical method. Numerical methods to be employed must incorporate the notion of infinity in the formation. Integral equation method and boundary element method can handle infinite domain naturally. Finite difference and finite element methods are domain descritization methods. They can not be applied to semi-infinite domain directly. There is a way out of handling such infinite domains. This is by considering a finite domain for descritization with approximate boundary conditions. Exact solutions to general partial differential equations are difficult to obtain. This is due to irregular and geometrically complicated domains. There is difficulty in applying finite difference method and variational methods. This difficulties lies in considering approximate functions of the dependent variable. These functions need to satisfy the geometric boundary conditions on irregular domains. This is suitably considered in the numerical tool, Abaqus code. Linear response of underground pipes under static load was studied using Abaqus numerical tool and result compared well with that of Sap code. Non-linear response of underground pipes due internal explosion was studied using Abaqus numerical tool, though other commercially available codes like ANSYS and AUTODYN could also be used. Equivalent earthquake parameters on the ground surface were determined and compared with that of San Fernando Earthquake of February 9, 1971.

ACKNOWLEDGEMENT The project is funded by Ministry of Science, Technology and Innovation, MOSTI, Malaysia under e-

Science Grant no. 03-01-10-SF0042.

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