University of Wollongong Research Online Faculty of Engineering and Information Sciences - Faculty of Engineering and Information Sciences Papers: Part A
2015 Design of earth retaining structures and tailing dams under static and seismic conditions S S. Nimbalkar University of Wollongong, [email protected]
D Choudhury Indian Institute Of Technology, [email protected]
Publication Details Nimbalkar, S. & Choudhury, D. (2015). Design of earth retaining structures and tailing dams under static and seismic conditions. 50th Indian Geotechnical Conference (IGC-2015) (pp. 1-10).
Research Online is the open access institutional repository for the University of Wollongong. For further information contact the UOW Library: [email protected] Design of earth retaining structures and tailing dams under static and seismic conditions
Abstract In this paper the seismic active earth pressure is determined by using pseudo-dynamic method. Mononobe- Okabe method by pseudo-static approach gives the linear distribution of seismic earth pressure behind retaining wall in an approximate way. A rigid vertical retaining wall supporting cohesionless backfill material with horizontal ground has been considered in the analysis with planar rupture surface. Results highlight the non-linearity of seismic earth pressures distribution. Applications of pseudo-dynamic method for stability assessment of gravity dams and tailing dams are presented. A new simplified method to include soil arching effect on determination of earth pressures is also proposed.
Disciplines Engineering | Science and Technology Studies
Publication Details Nimbalkar, S. & Choudhury, D. (2015). Design of earth retaining structures and tailing dams under static and seismic conditions. 50th Indian Geotechnical Conference (IGC-2015) (pp. 1-10).
This conference paper is available at Research Online: http://ro.uow.edu.au/eispapers/4969 DESIGN OF EARTH RETAINING STRUCTURES AND TAILING DAMS UNDER STATIC AND SEISMIC CONDITIONS
S. S. Nimbalkar1, D. Choudhury2
ABSTRACT
The estimation of static and seismic earth pressures is extremely important in geotechnical design. The conventional Coulomb’s approach and Mononobe-Okabe’s approach have been widely used in engineering practice. However the latter approach provides the linear distribution of seismic earth pressure behind retaining wall in an approximate way. Therefore, the pseudo-dynamic method can be used to compute the distribution of seismic active earth pressure in more realistic manner. Effect of both the wall and soil inertia must be considered for the design of retaining wall under seismic conditions. In this paper, by considering pseudo-dynamic seismic forces acting on the soil wedge and the wall, the required weight of the wall under seismic conditions is determined for the design purpose of the retaining wall under active earth pressure condition. The method proposed considers the movement of both shear and primary waves through the backfill and the retaining wall due to seismic excitation.
Seismic stability of tailings dams and embankments is an important topic which needs the special assessments by the researchers. The crude estimate of finding the approximate seismic acceleration makes the pseudo-static approach too conservative to adopt in the stability assessment. In this paper, pseudo- dynamic method of analysis is used to compute the seismic inertia forces acting on the sliding wedge of the tailings dam by considering the effects of time of seismic accelerations, phase differences in the propagating shear and primary waves in the soil during an earthquake, frequency of earthquake excitation etc. with the horizontal and vertical seismic accelerations.
The predictions of the active earth pressure using Coulomb theory are not consistent with the laboratory results, to the development of arching in the backfill soil. A new method is proposed to compute the active earth pressure acting on the backface of a rigid retaining wall undergoing horizontal translation. Effect of soil arching for cohesive backfill soil as well as friction mobilized along wall-soil interface is considered. The theoretical formulae for determining the distribution of active earth pressure and active thrust are derived. The predictions of the proposed method are verified against results of laboratory tests as well as the results from other methods proposed in the past. The results show that the proposed method yields satisfactory results (Figure 1).
1Research Fellow, Centre for Geomechanics and Railway Engineering, Centre for Geomechanics and Railway Engineering, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, Australia, [email protected] 2Professor, Department of Civil Engineering, Indian Institute of Technology Bombay, IIT Bombay, Powai, Mumbai – 400 076, India. and, Adjunct Professor, Academy of Scientific and Innovative Research (AcSIR), CSIR – OSDD Unit, New Delhi, India and CSIR – Central Building Research Institute (CBRI), Roorkee, India, [email protected]
S. S. Nimbalkar, D. Choudhury 0.0
0.5 Proposed model [1] 1.0 Coulomb theory Rankine theory 1.5 Experimental data H 4m (Tsagareli theory,1965) 2.0 Tsagareli [2]
18kN/m3 y (m) y 2.5 32 10 3.0 c 0 q 0 Proposed model 3.5
4.0 0 2 4 6 8 10 12 14 16 18 20 22 (kPa) h Figure 1. Comparison between predicted and experimental data ([1], With permission from ASCE)
In this paper, design approaches of earth retaining structures including dams and tailing dams are presented. Novel applications of the pseudo-dynamic method are discussed.
Keywords: Soil-structure interaction, Earth pressure, Seismic stability, Pseudo-dynamic method, Time dependence, Safety factors
References: 1. Rao, P., Chen, Q., Zhou, Y., Nimbalkar, S. and Chirao, G. (2015), Determination of active earth pressure on rigid retaining wall considering arching effect in cohesive backfill soil, International Journal of Geomechanics, ASCE doi: 10.1061/(ASCE)GM.1943-5622.0000589. 2. Tsagareli, Z. V. (1965), Experimental investigation of the pressure of a loose medium on retaining wall with vertical backface and horizontal backfill surface, Soil Mechanics and Foundation Engineering, 91(4), 197-200.
DESIGN OF EARTH RETAINING STRUCTURES AND TAILING DAMS UNDER STATIC AND SEISMIC CONDITIONS
S. S. Nimbalkar, Research Fellow, University of Wollongong, Australia, email: [email protected] D. Choudhury, Professor, Indian Institute of Technology Bombay, India, email: [email protected]
ABSTRACT: In this paper the seismic active earth pressure is determined by using pseudo-dynamic method. Mononobe-Okabe method by pseudo-static approach gives the linear distribution of seismic earth pressure behind retaining wall in an approximate way. A rigid vertical retaining wall supporting cohesionless backfill material with horizontal ground has been considered in the analysis with planar rupture surface. Results highlight the non- linearity of seismic earth pressures distribution. Applications of pseudo-dynamic method for stability assessment of gravity dams and tailing dams are presented. A new simplified method to include soil arching effect on determination of earth pressures is also proposed.
INTRODUCTION The design and behavior of retaining wall under Study of dynamic active earth pressure is essential seismic conditions is very complex and many for the safe design of retaining wall in the seismic researchers have discussed on this topic. A zone. As pioneering work in this area, the theory of classical seismic design method by using dynamic lateral earth pressure based on pseudo- Mononobe-Okabe method for the design of earth static analysis was proposed, commonly known as retaining structures [19]. Caltabiano et al. [20] Mononobe-Okabe method [1,2]. But this method determined the seismic stability of retaining wall using pseudo-static approach gives the seismic with surchage using Mononobe-Okabe method active earth pressure value in a very approximate along with the soil-wall inertia effect by way. To Rectify the shortcomings of the pseudo- considering pseudo-static seismic acceleration in static approach, a pseudo-dynamic method has horizontal direction. Although several researchers been recently developed to address this problem in the past highlighted the limitations and [3-5]. Effects of both the horizontal and vertical drawbacks of the pseudo-static approach, there are seismic accelerations can be considered to provide very limited studies being reported worldwide for more realistic results [6-9]. the seismic stability assessment of dams and embankments. In one of pioneer studies [10], soil arching was also found to affecting the nonlinear distribution of the Seismic stability of tailings dams and active earth pressure acting on the rigid walls in embankments is an important topic which needs contrast to the assumption made by both Coulomb the special treatment by researchers as it is mainly [11] and Rankine [12] theories. A method for governed by the safety concerns. Many researchers calculating the active earth pressures assuming in the past have attempted to investigate the Coulomb slip was proposed [13]. The seismic seismic stability of dams and embankments by active earth pressure acting on the retaining walls using pseudo-static method of analysis. Semi were evaluated using the pseudo static [14], more empirical stability charts [21] are often used to recent pseudodynamic [4,6,15-17] as well as obtain a preliminary estimate of the permanent, modified pseudodynamic methods of analyses [18]. earthquake induced deformation of earth dams and However, none of these studies considered the embankments. stress trajectory caused by soil arching effect, a common phenomenon in geotechnical engineering. S. S. Nimbalkar, D. Choudhury In recent past, methods for determination of active The mass of an elemental wedge at depth z is earth pressure considering the soil arching effects zH have been proposed [22,23]. However, these zm)( dz (3) tang methods were limited to non-cohesive soils. Considering this, a simplified method for where, is the unit weight of the backfill. The total calculating the active earth pressure acting on a horizontal inertial force acting within the failure rigid retaining wall undergoing translation is zone can be expressed as, proposed. H Qth ( ) m(z)ah (z, t)dz 0 PSEUDO-DYNAMIC METHOD a = h 2 Hcosw (sinwwt sin ) (4) Consider the fixed base vertical cantilever wall of 42 g tan height H as shown in Fig. 1. The wall is supporting where, = TV is the wavelength of the vertically a cohesionless backfill material with horizontal s ground. The shear wave and primary wave are propagating shear wave and = t-H/Vs. And, total assumed to act within the soil media due to vertical inertial force acting within the failure zone can be expressed as, earthquake loading. For most geological materials, H Qt( ) m(z)a (z, t)dz Vp/Vs = 1.87 [24]. The period of lateral shaking, T v v = 2/, where is the angular frequency is 0 a considered in the analysis. Consider a planer v (5) 2 2 Hcos(sin sin ) t rupture surface inclined at an angle, with the 4g tan horizontal. where, = TVp, is the wavelength of the vertically propagating primary wave. And = t – H/Vp. The
Qv total (static plus dynamic) active thrust can be obtained by resolving forces on the wedge and can
Qh be expressed as, Vs, Wsin( ) Q ( t )cos( ) Q ( t )sin( ) Vp hv W Ptae () (6) H cos( )
h Pae F The seismic active earth pressure distribution can be obtained by differentiating the total active thrust as, Fig. 1 Model retaining wall considered for Ptae () z sin( ) computation of pseudo dynamic active earth ptae ( ) z tan cos( ) pressure kz cos( ) z (7) h sin wt tan cos( ) Vs Let us assume that the base of the wall is subjected kz sin( ) z - v sin wt to harmonic horizontal seismic acceleration of tan cos( ) V p amplitude ahg, and harmonic vertical seismic acceleration of amplitude avg, where g is the acceleration due to gravity. Results and Discussion In the case of cohesionless soils, to avoid the The acceleration at any depth z and time t, below phenomenon of shear fluidization for the certain the top of the wall can be expressed as, combinations of kh and kv [25] the values of considered in the analysis are to satisfy the Hz ah ( z , t) ah sin t (1) relationship given by, Vs k tan1 h (8) Hz (2) av ( z , t) av sin t 1 kv Vp
2 At sliding [27], FNbbb tan (11) Fig. 2 shows the comparison of normalized pressure distribution behind rigid retaining wall where, b is the friction angle at the base of the obtained by the present study with that by wall. Thus, Mononobe-Okabe method. It reveals nonlinear P( t )cos Q ( t ) ae hw (12) seismic active earth pressure distribution behind P( t )sin W ( t ) Q ( t ) tan retaining wall in a more realistic manner compared ae w vw b to the pseudo-static method. Weight of the wall is given by, W( tP )( )( t )C t (13) 0.0 waeIE k =0.5k , =300, , H/=0.3, H/=0.16 v h where, CIE(t) is the dynamic wall inertia factor 0.2 Mononobe-Oakbe method given by, Present study cossin tan b 0.4 CtIE () tanb z/H (14) 0.6 Q( t )( ) Q tan t hwvw b Ptae ( ) tanb 0.8
1.0 The relative importance of the two dynamic effects 0.0 0.1 0.2 0.3 0.4 0.5 (i.e., the increased seismic active thrust on the wall p /H ae due to pseudo-dynamic soil inertia forces on the sliding wedge and the increase in driving force due Fig. 2 Comparison of results for kv = 0.5kh , = to time dependent inertia of the wall itself) can be 300, = /2, H/ = 0.3, H/ = 0.16 seen by normalizing them with regard to the static values. Thus defining soil thrust factor, FT as
Kae SEISMIC STABILITY OF DAMS FT K In this section, pseudo-dynamic method is applied a (15) for the seismic design of the retaining wall with and wall inertia factor, FI as respect to the stability of the wall against sliding, CtIE () by considering both the soil and wall inertia effect FI (16) C due to both shear and primary waves propagating I through both the backfill and the wall with time where, variation. cos sin tan b CI tanb Consider the rigid vertical gravity wall of height H and width b , supporting horizontal cohesionless w Considering the product of the soil thrust and wall backfill. Using D’Alembert’s principle [26] for inertia factors as a safety factor applied to weight inertial forces acting on the wall, of the wall to consider both the effects of soil Nb P ae ( t )sin Ww ( t ) Q vw ( t ) (9) inertia and wall inertia, the combined dynamic F P( t )cos Q ( t ) (10) factor, Fw proposed for the design of the wall is b ae hw defined as, where, N and F are the normal and tangential b b Wt() components of the reaction at the base of the wall w FFFw T I (17) respectively. Ww
3 S. S. Nimbalkar, D. Choudhury where, Ww is the weight of the wall required for shown in Fig. 4. The phase of both the horizontal equilibrium against sliding under static condition. and vertical seismic accelerations are varying along the depth of the dam.
Results and Discussions The total horizontal inertia force qhi(t) acting on the Fig. 3 shows variation of combined dynamic ith slice can be expressed as, factor, Fw with kh for different values of vertical qhi (z, t) mih (z).a (z, t) (18) seismic acceleration coefficient (kv). From the plot, it may be seen that the combined dynamic factor, Again, the total vertical inertia force (qvi) acting on the ith slice can be expressed as, Fw increases with the increase in vertical seismic acceleration. For kh = 0.2, Fw increases by 15 % qvi (z, t) miv (z).a (z, t) (19) when kv changes from 0 to 0.5kh and 14 % when kv changes from 0.5kh to kh. Though usually the effect of vertical seismic acceleration on stability of retaining wall is hardly considered in the analysis by many researchers, but the present study reveals the significant influence of vertical seismic acceleration on the stability of retaining wall.
6 = 300, = /2, H/TV = 0.3, H/TV = 0.16, s p
W H/TV =0.012, H/TV =0.0077 5 sw pw k =0.0 v 4 k =0.5k v h k =k v h 3 Fig. 4 Tailings dam section considered in the 2 analysis
1 Combined dynamic factor, F factor, dynamic Combined Detailed mathematical treatment of qhi(t) and qvi(t) can be found elsewhere [8,9]. Similar to the 2N+1 0 0.0 0.1 0.2 0.3 0.4 formulation [28], equilibrium equations can be k written as h (for each slice) gives Fy 0 Fig. 3 Effect of vertical seismic acceleration Vi1 V i W i q vi S isin i N i cos i 0 (20) coefficient (kv) on combined dynamic factor, Fw where, Vi and Vi+1 are vertical inter-slice forces SEISMIC STABILITY OF TAILING DAMS calculated by integration of overburden pressures on horizontal border of slice. In this section, the seismic stability of the tailings dam by using horizontal slice method considering f Again, (for each slice) yields pseudo-dynamic inertia forces along with other r FS 1 seismic input parameters. S cb N tan (21) i FS i i Proposed Analytical Model The tailings dam, of height H, supporting the Substituting for Si from equation (21) into equation compacted tailings overlaid by tailings pond is (20),
4 cb i (22) by about 6.2% and when kv changes from 0.5kh to Vi V ii1 W vi q z,sin t i N FS i tan 1.0kh, required factor of safety (FS) decreases by sin cos FS ii about 8%. (for the whole wedge) MO 0
qhi z, t YGO,1 R sini (23) m Wi q vi z, t XGO,1 Rcosi l i 0 i1 SNXisin i i cos i NS, O SNYcos sin i i i i NS, O
Here, the assumption is made that the normal (Ni) and shear (Si) forces act at the mid-point of base of each slice and thus, h XRcos i NS, O i 2 tan (24) i h YRsin i NS, O i 2 Fig. 5 Effect of horizontal and vertical seismic Substitute S and N in equation (23) to obtain the i i acceleration coefficients on factor of safety, FS factor of safety (FS). The slip circle is assumed as circular in this analysis for the sake of simplicity. Similar trend is observed for the tailing dam full water condition. Thus, effects of both horizontal Results and Discussion and vertical seismic acceleration coefficients (k The values of factor of safety for tailings dam are h and k ) are significant in the computation of reported for both the tailings pond empty and full v stability of the tailings dam. The results reported in water conditions. the present paper are compared with the pseudo static based slope stability analysis of the tailings Fig. 5 shows the effects of both horizontal and dam. Figure 6 shows such a comparison of the vertical seismic acceleration coefficients (k and h results of slope stability analysis using both of k ) on factor of safety (FS) for tailings dam empty v these methods of analysis for the case of tailings and full water condition respectively. It is evident pond empty and full water condition respectively. from Fig. 5 that, the required value of FS shows It is evident that for the static case, both the significant decrease with increase in horizontal and methods report similar results. vertical seismic acceleration coefficients (kh and kv). For finite values of kh and kv, factor of safety (FS) computed by pseudo-dynamic method of analysis Referring to the tailings dam empty condition, for is more than that by pseudo-static method. The k = 0.5k , when k changes from 0 to 0.1, required v h h pseudo-static based approach seriously factor of safety (FS) of decreases by about 22.6%. underestimates the stability of dam due to Also when k changes from 0.1 to 0.2, required h conservative use of constant seismic accelerations factor of safety (FS) decreases by about 21.5%. throughout the height of dam. Also as the seismic Similarly when k changes from 0.2 to 0.3, h increases, the results computed by using pseudo- required factor of safety (FS) decreases by about dynamic method of analysis deviates more from 21%. Also for k = 0.2, when k changes from 0 to h v those of pseudo-static method of analysis. 0.5kh, the required factor of safety (FS) decreases
5 S. S. Nimbalkar, D. Choudhury From Equation (1), it is established that when the 2.5 Present study wall surface is smooth (i.e. = 0), Pseudostatic method (Fakher[28] et al. 2002) 2 KKawa tan (45/ 2) which coincides with 2.0 Rankine’s active earth pressure coefficient. The lateral active earth pressure at the back of the wall 1.5 can be calculated as:
1.0 Hc q 1tan Factor ofFS Safety, Tailings pond empty condition c Tailings pond full condition hK aw (26) 0.5 tan H = 44 m, b = 4 m, n = 2.5, k = 0.5k yH y v h 1 H 1 0.0 0.0 0.1 0.2 0.3 Horizontal seismic acceleration coefficient, k h
Fig. 6 Comparison of factor of safety (FS) obtained by pseudo-dynamic results with those by pseudo- static results [28] with kv = 0.5kh.
EFFECT OF SOIL ARCHING ON STABILITY OF RETAINING STRUCTURES The retaining wall is considered to be rigid and the backfill soil is considered to be cohesive. A planer failure surface is considered in accordance with previous studies [29-34]. The analysis of lateral active earth pressure in cohesive soils is carried out using horizontal flat element method. In this method [35], the failure wedge is divided into a number of horizontal flat elements. Each flat element derives the wall-soil adhesion resistance along the vertical boundaries and the internal frictional resistance induced from the direction of Fig. 7 Trajectory of principal stresses and forces of the principal stresses acting on the horizontal differential flat element ([35], With permission boundaries (Fig. 7). For the sake of simplicity, from ASCE) similar to an earlier method reported [22], it is assumed that the trajectory of minor principal If cracks do not appear in the backfill surface, stresses takes the form of an arc of a circle. integrating Equation (10) with respect to y, the active thrust can be obtained: Analytical Model H H2 cH Ed1 y qH (27) Considering the effects of soil arching and wall- hh 0 2 tan soil friction, a new coefficient of lateral active where earth pressure (Kaw) is defined as: sin cos 1 sin 2 1 sin 2 1 cot arcsin (28) 1 sin 2 sin 2 K (25) 3 aw cos tan 2 1 sin 2sin 22 csc arcsin 2 sin 2 3(1 sin ) From the analysis of Equations (27) and (28), it is observed that when the wall surface is smooth (i.e.
6 2 0.0 = 0), Ka tan (45/ 2) which coincides with the Rankine’s active earth pressure coefficient, and H 10m 19kN/m3 the active thrust is equal to that computed by 0.2 20 Rankine’s theory [12]. 10 q 20kN/m 0.4 If a crack papers at a given the depth (H ) within c c=5kPa c=10kPa the backfill surface, the lateral earth pressure y/H 0.6 c=15kPa within this depth is assumed to be as zero. By c=20kPa integrating Equation (26) with respect to y from hc to H, the lateral active earth pressure force can be 0.8 obtained as follows:
H Ey d 1.0 hh -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 H c (kPa) (29) h HcH H c c c Fig. 8 Variation of active earth pressure H Hcr q1 H tan1 distribution with the cohesion of backfill soil ([35], With permission from ASCE) where 1 Hc Figure 9 shows the lateral active earth pressure c 1 H distribution along the normalised height (y/H) of a 1 translating rigid wall with cohesive backfill soil for Hc 1 r 1 various friction angle (). It is apparent that the H 2 lateral active earth pressure decreases significantly with the increasing value of internal friction angle Results and Discussion of cohesive soil, while the shape of the lateral Figure 8 shows the lateral active earth pressure active earth pressure distribution remained distribution along the normalised height (y/H) of a unchanged. translating rigid wall with cohesive backfill soil for various values of soil cohesion. It is evident that 0.0 the lateral active earth pressure distribution along the rigid wall exhibited nonlinear shape for all the 0.2 values of soil cohesion. With the increase of the H 10m 19kN/m3 soil cohesion c, the lateral active earth pressure c 10kPa decreases significantly, while it is interesting to 0.4 q 10kN /2 note that the normalised height of the point of =150 y/H application of active thrust increased marginally. In 0.6 =200 addition, the depth of tension crack from the =250 =300 surface of the cohesive backfill soil is developed 0 0.8 =35 significantly, attributed to the increasing values of soil cohesion. 1.0 -40 -30 -20 -10 0 10 20 30 40 50 60 (kPa) h Fig. 9 Variation of active earth pressure distribution with soil friction angle ([35], With permission from ASCE)
7 S. S. Nimbalkar, D. Choudhury The normalised height of the point of application propagating in the backfill behind the rigid of the active thrust from the base of the wall retaining wall, the seismic active earth pressure increased marginally. Moreover, as increases, the distribution as well as the total active thrust behind depth of tension crack from the surface of the the retaining wall is altered from that by pseudo- cohesive soil increases significantly. static method. It gives more realistic non-linear seismic active earth pressure distribution behind Comparison with Other Studies the retaining wall as compared to the Mononobe- In order to check the applicability of the proposed Okabe method. formulations, the predictions from the derived equation are compared with experimental results Pseudo-dynamic method is adopted for the analysis [36], where the distribution of the active earth of dam. Seismic stability of dam reduces with pressures acting on the translating rigid retaining increase in the seismic accelerations and phase wall with the height of 4 m were measured. Figure difference in body waves. Seismic inertia forces 10 shows the comparison of the non-dimensional acting on the tailings dam are obtained using the distributions of the active earth pressure with other pseudo-dynamic method. The results of this study studies [11,12,28]. also indicate that, the pseudo-static based procedures conventionally used may underestimate It is evident that the results obtained using the sometimes the stability of tailings dams and proposed equation are in good agreement with the embankments under seismic conditions. By using measured values, especially for capturing the the pseudo-dynamic method, a more rational salient feature of non-linear distribution of active approach can be adopted for the seismic stability earth pressures, which cannot be predicted by using assessment based on correct estimation of dynamic the existing Coulomb’s [11] and Rankine’s theories soil properties and accurate prediction of ground [12]. motion parameters.
0.0 A simplified method for determining the nonlinear
0.5 distribution of the active earth pressure on rigid Proposed model [35] retaining walls under translation mode is proposed. 1.0 Coulomb theory The analysis of active cohesive earth pressure is Rankine theory 1.5 Experimental data carried out using horizontal flat element method, H 4m (Tsagareli theory,1965[36]) and analytical expressions for computing active 2.0 18kN/m3 earth pressure distribution, active thrust and its y (m) y 2.5 32 point of application. The general applicability of 10 the proposed method is demonstrated by 3.0 c 0 comparing its predictions with experimental results q 0 Proposed model 3.5 and other theoretical analyses.
4.0 0 2 4 6 8 10 12 14 16 18 20 22 ACKNOWLEDGEMENTS (kPa) h The authors wish to thank the Australian Research Council (ARC) Centre of Excellence in Fig. 10 Comparison between predicted and Geotechnical Science and Engineering. experimental data ([35], With permission from ASCE) They also appreciate financial support received from the sponsored project no. AERB/CSRP/31/07 by Atomic Energy Regulatory Board, Mumbai, CONCLUSION India for carrying out part of this research. In pseudo-dynamic method by considering the phase change in shear and primary waves
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