LATERAL CAPACITY OF PILES IN LIQUEFIABLE SOILS

Transcription

1 IGC 9, Guntur, INDIA LATERAL CAPACITY OF PILES IN LIQUEFIABLE SOILS A.S. Kiran M. Tech. (Geotech), Dept. of Civil Engineering, IIT Roorkee, Roorkee 77, India. G. Ramasamy Professor, Dept. of Civil Engineering, IIT Roorkee, Roorkee 77, India. B.K. Maheshwari Assistant Professor, Dept. of Earthquake Engineering, IIT Roorkee, Roorkee 77, India. ABSTRACT: The performance of piles in liquefying ground under earthquake loading is a complex phenomenon. The process of generation of excess pore water pressure in saturated sand during earthquakes causes loss of shear strength of the ground. Many buildings and transportation facilities supported by deep foundations were damaged due to the loss of bearing capacity and excessive settlement during the 19 Niigata & 1995 Kobe earthquakes. Studies of seismic loadings on pile foundations and liquefaction phenomenon have been performed extensively in the last four decades. However, the combined problem of seismic behaviour of piles in liquefiable soil has received relatively less attention, especially the effect of liquefaction on lateral capacity. In this paper, a simplified procedure to evaluate the lateral capacity of piles in liquefiable soils is explained. The excess pore pressure generated due to liquefaction is determined using the method proposed by Seed, Martin & Lysmer. The lateral capacity is then determined using spring model incorporating the effect of excess pore pressure on soil stiffness. Layered soil system, ground water level, the earthquake magnitude and duration of earthquake shaking are accounted. Analysis for lateral load on pile foundation is carried out using Finite Difference scheme. A computer code in C++ has been developed for this purpose. Numerical results have been obtained for a few typical problems using the package and the effect of typical ground conditions on the pile behaviour is brought out. 1. INTRODUCTION Soil liquefaction is the phenomenon by which soil loses its shear strength for a smaller time period, but that is long enough to cause many failures, loss of human life and major financial losses. The loss of soil strength and stiffness due to liquefaction may develop large bending moments and shear forces in piles founded in liquefying soil, leading to pile damage. Such failures were prevalent during the 19 Niigata and the 1995 Kobe earthquakes. Following disastrous earthquakes in Alaska and in Niigata, Japan in 19, Seed & Idriss (1971) developed and published the basic simplified procedure. That procedure has been modified and improved periodically since that time, primarily through landmark papers by Seed (1979), Seed & Idriss (19), and Seed et al. (195). The simplified procedure was developed from empirical evaluations of field observations and field and laboratory test data (Youd et al. 1). Different experimental and analytical numerical models have been used to study the behaviour of soil-pile interaction. The subgrade reaction method currently appears to be the most widely used in a design of laterally loaded piles. Matlock & Reese (19) provided the solutions for a soil profile where the modulus of subgrade reaction has some finite value at the ground surface and continues to increase linearly with depth. Davisson & Gill (193) used the subgrade reaction theory to analyze the behaviour of laterally loaded piles in a two-layer soil system for both free and fixed head conditions and provided the results in non-dimensional forms. Ramasamy (197) used the subgrade reaction theory to study the flexural behavior of axially and laterally loaded piles. Winkler type models for seismic analysis of piles in liquefiable soils have been developed by Kagawa (199). Wilson et al. () presented the first measurements of dynamic p-y behavior for liquefying sand. Liyanapathirana & Poulos (5) presented a pseudostatic approach for pile analysis in liquefiable soils. Nath () and Maheshwari et al. () used Winkler model to study the pile soil interaction for axially and laterally loaded piles in liquefiable soils.. METHODOLOGY The methodology developed for the design of a single pile in liquefiable soil for lateral load is briefly explained below. 1

2 i. The input required are the saturated or bulk densities (γ sat or γ) for each layer of soil, the SPT N values, the depth of water table below ground level (D w ), modulus of elasticity (E) and diameter of pile (d), boundary conditions of the pile, earthquake magnitude (M) and the applied lateral load, Q. ii. The measured values of SPT N, N m along the depth of pile are corrected for overburden pressure. (N 1 ) = C N * N m (1) Where (N 1 ) = SPT blow count normalized to an overburden pressure of approximately kpa (1 ton/sq ft) and a hammer energy ratio or hammer efficiency of %. C N is the overburden correction factor given by the equation (Kayen et al. 199). C N = () ' σ v (1. + Pa Where C N normalizes N m to an effective overburden ' pressure σ v of approximately kpa. i.e. P a = kpa = 1 atmospheric pressure. The maximum value of C N is limited to 1.7 iii. Divide the pile into required number of nodal points. Find the value of SPT N at nodal points by linear interpolation. iv. Evaluate the value of Cyclic Stress Ratio (CSR) at each nodal point using the equation (Seed & Idriss 1971) given below. CSR is the seismic demand on a soil layer or the cyclic shear stress generated by the earthquake shaking. amax σ v CSR =. 5* * *rd (3) g σ v Where a max = peak horizontal acceleration at the ground surface generated by the earthquake, g = acceleration due to gravity, σ vo and σ vo ' are total and effective vertical overburden stresses at the depth considered respectively and r d = stress reduction coefficient which accounts for flexibility of the soil profile v. Using the simplified procedure (Youd et al. 1) for evaluation of liquefaction resistance, determine at each nodal point, the value of Cyclic Resistance Ratio at Earthquake Magnitude of 7.5, CRR 7.5 from Figure 1. Depending on the amount of fines present choose the suitable curves given in Figure 1. vi. Determine the number of cycles to cause liquefaction (N L ) at each nodal point for a particular earthquake magnitude and given soil conditions using the curve (Figure ) given by Jefferies & Bean () (using values of CSR, CRR 7.5 determined in steps iv and v). vii. Determine the equivalent number of uniform stress cycles, N eq, and the effective period of each stress cycle, T eq, representing the induced stress history. Corresponding values of N eq and shaking duration for different earthquake magnitudes are given by Seed et al. (197). If N eq > N L, take the value of horizontal subgrade reaction, K h as zero at that nodal point. CSR/CRR7.5 Cycle Resistance Ratio (CRR7.5) Corrected Blow Count (N 1 ) Fig. 1: SPT Curve for Magnitude 7.5 Earthquakes with Data from Liquefaction Case Histories (Youd et al. 1) Corrected Blow Count (N 1 ) Number of cycles to liquefaction Fig. : Cyclic Triaxial Test Data Normalized to cyclic Resistance Ratio for M = 7.5, CRR 7.5 (Jefferies & Bean ) viii. Else If N eq < N L, determine the excess pore pressure generated, U g at all other nodal points due to earthquake shaking using the model proposed by Seed et al. (197). The pore pressure ratio, r u = (U g / σ vo ') is given by, r u = + arcsin(r N α 1) () π Where r N is cyclic ratio = (N eq /N L ) and α = a function of soil properties and test conditions (α =.7 for best fit). From equation (), find r u and hence U g. Find the new value of effective stress, σ v ' along all the nodal points by subtracting the excess pore pressure generated from the effective stress under static condition. ix. Determine the value of modulus of horizontal subgrade reaction (K h ) from following equation using the value of

3 σ v ' from step viii. Typical values of the factor A applicable to cohesionless soils are given by Poulos & Davis (19). A K = h * σ v (5) 1.35 x. Then using the value of K h from step ix, follow the method of lateral analysis of pile using Modulus of subgrade reaction approach. For getting the finite difference solution Gauss-Seidel iteration is adopted. xi. A program is written for the entire methodology in C++. The program gives the CSR, CRR 7.5, excess pore pressure generated, net effective stress, K h, deflection, bending moment and shear force at each nodal point along the depth of pile as output in Microsoft excel worksheet which makes it easier for further analysis of the results and graph plotting. 3. SOLUTION OF A TYPICAL PROBLEM The solution of a typical problem showing the lateral response of a single pile in liquefiable soil under earthquake loading is illustrated. For this the input data are taken from the case study of storey Hokuriku building during the 19 Niigata earthquake (Bhattacharya, 3). 3.1 Input Data and Problem Statement Table 1 shows the SPT data at site. The building has a basement floor of 7 m height and is founded on reinforced concrete piles. The diameter of the reinforced concrete pile is. m and pile length is m. The pile head is free and the pile tip is fixed. The pile head is 7 m below ground level (Bhattacharya, 3). The pile passed through 5 m of liquefiable soil and remaining through dense soil. The remaining data are assumed as follows Young s modulus of pile, E =.5 * 7 kn/m Position of water table = at Ground level Saturated unit weight = 19 kn /m 3. Lateral load applied at pile head, Q = 5 kn Maximum ground surface acceleration, a max =.5 g According to Seed et al. (197), for an earthquake Magnitude of M = 7.5, Number of uniform stress cycles, N eq = and Duration of strong shaking, T = s. Lateral analysis of the pile in liquefiable soil is carried out under both earthquake and static loading case and the results are as shown in Figures 3 5. Table 1: Soil Profile at Site (Bhattacharya, 3) Depth (m) SPT N value Depth (m) SPT N value Generation of Excess Pore Water Pressure Figure 3 shows the variation of pore pressure ratio with depth. It can be observed that the pore pressure ratio is unity up to 3 m. This shows that excess pore pressure generated up to 3 m is very high and is equal to the effective overburden stress. So the soil up to 3 m is fully liquefied. Below 3 m, the pore pressure ratio is less due to the presence of comparatively stronger soil (larger SPT N values). The larger pore pressure ratio in top layers explains the larger value of deflection at pile head under earthquake loading. Depth Depth (m) (m) Pore Pressure Ratio (U (U g g/σ v') v ) Fig. 3: Variation of Pore Pressure Ratio with Depth 3.3 Effect of Liquefaction on Pile Head Deflection In Figure, the variation of pile deflection along the depth of pile for static and earthquake loading are shown. The pile head deflection is obtained as 9. mm and.9 mm respectively for static lateral loading and earthquake loading case. It shows that due to liquefaction, deflection increased by about.3 times. This explains the dangerous effect of liquefaction on pile deflection. Depth (m) Horizontal Deflection Deflection (mm) (mm) Earthquake Loading Static Loading Fig. : Deflection Along the Depth of Pile 3

4 3. Effect of Liquefaction on Bending Moment In Figure 5, the variation of Bending Moment along the depth of pile for static and earthquake loading are shown. The maximum value of bending moment increased from about 3 knm for static loading to knm for earthquake loading. It shows a. times increase from the static case value. These results explain the structural failure of piles during liquefaction reported in the literature (e.g. NHK building, 19 Niigata earthquake). So during design in liquefiable soils, a higher value of Factor of safety should be applied for bending moment. Depth (m) (m) Bending Movement Moment (knm) Earthquake Loading Static Loading Fig. 5: Bending Moment Variation along the Depth of Pile. CONCLUSIONS The following major conclusions may be drawn from the study. 1. A simple method to determine the lateral capacity of single pile in liquefiable soils is developed. The method is based on the commonly available field tests data (SPT).. This method can be used for both long and short piles. 3. The lateral capacity of a single pile in liquefiable soil deposit reduces drastically as compared to the static case because the maximum deflection increases about times.. The results from the analysis show that the maximum bending moment increases by about 3 times in liquefied soils than in the static case. This explains the structural failure of piles reported for some liquefaction induced damages in the past. REFERENCES Bhattacharya S. (3). Pile Instability during Earthquake liquefaction, Ph. D. Thesis, University of Cambridge, Cambridge, U.K. Davisson M.T. and Gill H.L. (193). Laterally Loaded Piles in a Layered Soil, Jl. of Soil Mech.& Found. Div., ASCE, 9(3): 3 9. Jefferies M. and Been K. (). Soil Liquefaction: A Critical State Approach, Taylor & Francis, New York. Kagawa T. (199). Effect of Liquefaction on Lateral Pile Response, Geotechnical Special Publication, ASCE, 3: 7 3. Kayen R.E., Mitchell J.K., Seed R.B., Lodge A., Nishio S. and Coutinho, R. (199). Evaluation of SPT-, CPT-, and Shear Wave-based Methods for Liquefaction Potential Assessment using Loma Prieta data, Proc., th Japan U.S. Workshop on Earthquake-Resistant Des. of Lifeline Fac. and Countermeasures for Soil Liquefaction, 1: 177. Liyanapathirana D.S. and Poulos H.G. (5). Pseudostatic Approach for Seismic Analysis of Piles in Liquefying Soil, Jl. of Geotech & Geoenvironmental Engg., ASCE, 131(): Maheshwari B.K., Nath U.K. and Ramasamy G. (). Influence of Liquefaction on Pile-soil Interaction in Vertical Vibration, ISET Jl. of Earthquake Technology, 5(1-): 1. Matlock H. and Reese L.C. (19). Generalized Solutions for Laterally Loaded Piles, Jl. of Soil Mech. & Found. Div., ASCE, (5): Nath U.K. (). Pile-Soil Interaction in Liquefiable Soils, M. Tech. Dissertation, Dept. of Civil Engineering, Indian Institute of Technology Roorkee, Roorkee. Poulos H.G. and Davis E.H. (19). Pile Foundation Analysis and Design, John Wiley and Sons, New York. Ramasamy, G. (197). Flexural Behavior of Axially and Laterally Loaded Individual Piles and Group of Piles, Ph. D. Thesis, Indian Institute of Science, Bangalore. Seed H.B. and Idriss I.M. (1971). Simplified Procedure for Evaluation of Soil Liquefaction Potential, Jl. of Soil Mech. & Found. Div., ASCE, 97(9): Seed H.B., Martin P.P. and Lysmer J. (197). Pore-Water Pressure Changes during Soil Liquefaction, Jl. of Geotech. Engg. Div., ASCE, (GT): Seed H.B. (1979). Soil Liquefaction and Cyclic Mobility Evaluation for Level Ground During Earthquakes, Jl. of Geotech. Engg. Div., ASCE, 5(), Seed H.B. and Idriss I.M. (19). Ground Motions and Soil Liquefaction During Earthquakes, Earthquake Engineering Research Institute Monograph, Oakland, Calif. Seed H.B., Tokimatsu K., Harder L.F. and Chung R.M. (195). The Influence of SPT Procedures in Soil Liquefaction Resistance Evaluations, Jl. of Geotech. Engg. Div., ASCE, 111(): Wilson D.W., Boulanger R.W. and Kutter B.L. (). Seismic Lateral Resistance of Liquefying Sand, Jl. of Geotech. & Geoenviron. Engg., ASCE, (): 9 9. Youd T.L., Idriss I.M., Andrus R.D., Arango I., Castro G., Christian J.T., Dobry R., Finn W.D.L., Harder Jr. L.F., Hynes M,E., Ishihara K., Koester J. P., Liao S.S.C., Marcuson III W.F., Martin G.R., Mitchell J.K., Moriwaki Y., Power M.S., Robertson P.K., Seed R.B. and Stokoe II K.H. (1). Liquefaction resistance of soils: Summary report from the 199 NCEER and 199 NCEER/NSF workshops on evaluation of liquefaction resistance of soils, Jl. of Geotech. & Geoenvironmental Engg., ASCE, 7():

5 5 Lateral Capacity of Piles in Liquefiable Soils