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Performance of piles with different batter angles in laterally spreading soil: a probabilistic investigation

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Abstract

Load imposed by laterally spreading soil increases the vulnerability of pile foundations to seismic damage. A probabilistic investigation has been carried out for evaluation of behavior of single piles, with different batter angles (0°, ± 10°, ± 20°) and slenderness ratios (15, 20, 25), subjected to laterally spreading ground displacements through Beam on Nonlinear Winkler Foundation approach. Effect of shapes of p–y curves of liquefiable soil layer on the response of piles has been evaluated. It is inferred that the conventional concave p–y curves underestimate the pile response compared to the convex p–y curves. Prediction models for maximum bending moment and pile head displacement are proposed for piles with different batter angles. Probability of failure of piles under different performance criteria are then evaluated using Monte–Carlo simulation technique. Finally, probabilistic risk factors are evaluated to assess the risk imposed by various random parameters on the overall response of piles.

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Abbreviations

α :

Batter angle

β :

Slope of ground

β0, β1… βN :

Regression coefficients

\( \delta \) :

Soil–pile interface friction angle

δ phd :

Pile head displacement

γ :

Unit weight of soil

γ to :

Take-off strain

σ c :

Effective confining stress

τ max :

Ultimate shear strength

\( \psi \) :

Modification factor

θ :

Inclination angle for batter pile

\( \varphi \) :

Angle of internal friction of sand

\( \lambda \) :

Adjustment factor to consider medium-loose to loose sand in coulomb’s theory

ε :

Non-dimensional site parameter

ε e :

Errors

C :

Cohesion

c, a1–a5, b1–b10 :

Coefficients for prediction model

c σ :

Correction factor for overburden pressure

D :

Diameter of pile

DrNL, DrL :

Relative density of surface crust and liquefiable layer

d :

Depth along the pile

d c :

Depth factor

e, f, g, h :

Coefficients for calculating reduction factors for ultimate resistance and stiffness

E f :

Effect of each factor

EI :

Flexural rigidity of pile

\( \overline{{F_{ + 1} }} \) :

Mean response at high level setting of a factor

\( \overline{{F_{ - 1} }} \) :

Mean response at low level setting of a factor

G :

Shear modulus of soil

G1, G2 :

Initial shear modulus and shear modulus at large strain

G max :

Tangent shear modulus at small strains

H L :

Thickness of liquefiable layer

H NL :

Thickness of surface crust

I r :

Rigidity index

k 0 :

Earth pressure coefficient at rest

k API :

Stiffness values from API (2000)

k f :

Initial tangent

\( k_{pb} ,k_{p} \) :

Passive earth pressure coefficient for batter pile and vertical pile

k T :

Initial stiffness modulus of vertical pile

k Tb :

Initial stiffness modulus of batter pile

K 0 :

Earth pressure coefficient at rest

\( K_{c}^{d} \), \( K_{q}^{d} \) :

Effective earth pressure constants

\( K_{c}^{D} \), \( K_{q}^{D} \) :

Effective earth pressure constants at any arbitrary depth

\( K_{c}^{0} \), \( K_{q}^{0} \) :

Effective earth pressure constants at ground surface

\( K_{c}^{\infty } \), \( K_{q}^{\infty } \) :

Effective earth pressure constants at large depth

l, N :

Number of regression coefficients

L :

Length of pile

LS :

Least square function

M max :

Maximum bending moment

m :

Number of observations for regression analysis

Nc, Nq :

Bearing capacity factor

N f :

Number of samples exceeding failure criteria

Ns, Ms :

Stress and strain scaling factors

N t :

Total number of samples for Monte Carlo simulation

p, k :

Subscripts for ultimate resistance and stiffness

p d :

Resultant pressure per unit front area of pile

p1, pu :

Initial and ultimate lateral resistance of vertical pile

p ub :

Ultimate lateral resistance of batter pile

P f ′ :

Normalized probability of failure

Pf1, Pf2 :

Probability of failure considering bending moment and pile head displacement

M, Q1, Q3 :

Median, 25th and 75 th percentile values

\( \bar{q} \) :

Effective overburden pressure

q u :

Ultimate tip resistance

R f :

Probabilistic risk factor

R o :

Interface reduction

R 2 :

Coefficients of multiple determinations

r0, r1, r2, …, rN :

Least square estimators of regression coefficients

s :

Depth above or below liquefiable layer

s c :

Characteristic length

S′ :

Normalized sensitivity

t u :

Ultimate vertical resistance

\( U_{gr} \) :

Ultimate free-field ground displacement

x1, x2… xN :

Input factors for regression analysis

y 50 :

Displacement at which 50% of ultimate lateral resistance is mobilized

\( \widehat{{y_{i} }} \), \( y_{i} \), \( \bar{y} \) :

Expected, predicted and mean values of response parameters

y :

Response parameter

y1, yu :

Initial and ultimate lateral displacement

\( z \) :

Depth below ground surface

z c :

Critical deflection at pile tip

z 50 :

Displacement at which 50% of ultimate tip resistance is mobilized

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Acknowledgements

The first author acknowledges the financial support provided by MHRD, Govt. of India. The second author gratefully acknowledges the financial support provided by the Earth System Science Organization, Ministry of Earth Sciences, Government of India vide Grant No. MoES/P.O.(Seismo)/1(303)/2017 to conduct this research.

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  1. Department of Civil Engineering, IIT (ISM) Dhanbad, Dhanbad, 826004, India

    J. S. Rajeswari & Rajib Sarkar

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Rajeswari, J.S., Sarkar, R. Performance of piles with different batter angles in laterally spreading soil: a probabilistic investigation. Bull Earthquake Eng 18, 6203–6244 (2020). https://doi.org/10.1007/s10518-020-00936-7

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