Finite element limit analysis of ultimate lateral pressure of XCC pile in undrained clay

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Finite element limit analysis of ultimate lateral pressure of XCC pile in undrained clay ⁎

Hang Zhoua,b, , Hanlong Liub, Lehua Wanga, Gangqiang Konga,c a

Hubei Key Laboratory of Disaster Prevention and Mitigation (China Three Gorges University), China Key Laboratory of New Technology for Construction of Cities in Mountain Area, College of Civil Engineering, Chongqing University, Chongqing 400045, China c College of Civil and Transportation Engineering, Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China b

A R T I C L E I N F O

A B S T R A C T

Keywords: Limit analysis Numerical analysis XCC pile Clay Plane strain

X-section Cast in place Concrete (XCC) pile is a non-cylindrical pile that the cross section not obeying plane rotationally symmetric. In this case, the geometry of cross section as well as the lateral load direction may have influence on the ultimate lateral pressure of XCC pile. This paper presents rigorous upper and lower bound solutions for the ultimate lateral pressure of X-section Cast in place Concrete (XCC) pile in clay through two dimensional plane strain finite element limit analysis (FELA). The geometric effect, lateral load direction and the adhesion factor at the pile-soil interface are selected for parametric study. Subsequently, an empirical closedform equation of the ultimate lateral pressure factor is proposed for predicting the lateral force acting on a XCC pile in undrained clay. It is found that the XCC pile with relatively small ratio of b/a has larger ultimate lateral pressure than the conventional circular pile under the condition of the same area of cross section.

1. Introduction Recently, a new type of cross-sectional shaped pile, known as the Xsection Cast-in-place Concrete (XCC) pile, is developed in China [1–8]. This new pile is mainly used for soft ground improvement during highway and railway construction in China [1]. It has a special cross section “X” shape, which creates an XCC pile with larger side surface than the conventional circular pile (see Fig. 1). As a cast-in-place pile, the key procedure for installing a XCC pile is to create a X-shaped cavity in the soil using a steel pile mold with pile shoe (see Fig. 2), which has a X-shaped cross section, and then pouring the concrete into the cavity to form a XCC pile solid [2]. Generally, the XCC pile has higher vertical bearing capacity compared to the circular pile with the same area of cross section since XCC pile has larger side surface [3]. However, little research about the performance of the laterally bearing capacity of XCC pile has been conducted until to now. Therefore, it is necessary to present a solution to give insight into the lateral bearing capacity mechanism and such a solution may provide theoretical support to the application of the new developed XCC pile in practice. It is known that a key quantity for evaluating the capacity of laterally loaded pile is the ultimate pressure (or force per unit length on the pile) which the soil was assumed to apply. Randolph et al. present an elegant and exact solution for the ultimate pressure on a circular pile

loaded laterally in cohesive soil based on the classical plasticity theory [9]. Furthermore, Martin improved Randolph's upper bound solution and proved that the upper and lower bound solutions are almost the same, which yielded the true collapse loaded exactly [10]. However, Randolph's plasticity solution is only suitable for the circular pile and cannot be used to calculate the ultimate pressure of non-circular cross section pile, such as the XCC pile. In addition, some scholars developed a lot of analytical solutions for the problems of the rigid disc or piles in the elastic field of a media under the action of static and dynamic loading (for different loading e.g., lateral, normal, rocking and torsional). Ahmadi and Eskandari investigated the problem of normal, rocking, and torsional forced time-harmonic vibrations of a rigid circular disc in a transversely isotropic full-space [11,12]. Eskandari et al. presented a closed-form solution for the asymmetric problem of lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space is addressed with the aid of appropriate Green’s functions [13]. Pak derived a semi- analytical solution for the dynamic response of a finite flexible pile, partially embedded in an elastic half-space and under transverse loadings [14]. Abedzadeh and Pak presented a rigorous mathematical formulation for a flexible tubular pile of finite length embedded in a semi-infinite soil medium under lateral loading [15]. Ji and Pak proposed an exact theoretical formulation for the analysis of a thin-walled pile embedded in an elastic

⁎ Corresponding author at: Key Laboratory of New Technology for Construction of Cities in Mountain Area, College of Civil Engineering, Chongqing University, Chongqing 400045, China. E-mail addresses: [email protected] (H. Zhou), [email protected] (H. Liu), [email protected] (L. Wang), [email protected] (G. Kong).

http://dx.doi.org/10.1016/j.compgeo.2017.10.015 Received 12 September 2017; Received in revised form 23 October 2017; Accepted 28 October 2017 0266-352X/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Zhou, H., Computers and Geotechnics (2017), http://dx.doi.org/10.1016/j.compgeo.2017.10.015

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Fig. 1. Typical XCC piles in site.

Fig. 2. Installation equipment: (a) X-shaped cross section pile mold; (b) conical shoe with X cross section.

Fig. 3. XCC pile cross section.

half-space under vertically-incident P-wave excitation in the framework of three-dimensional elastodynamics and a shell theory [16]. Unlike the circular cross section pile, the new XCC pile has an Xshaped cross section not obeying plane rotationally symmetric and this leads to the two additional factors (geometry of cross section and the lateral load direction) that may have influence on the ultimate lateral pressure and of course the final lateral capacity of pile. Therefore, the aim of this paper is to present a new rigorous plasticity solution for the ultimate lateral pressure of XCC pile through two dimensional plane strain finite element limit analysis, which allows the influence of the geometry of cross section and the lateral load direction to be captured. The present plasticity solution serves the important purpose of providing a theoretical basis that could be further developed to investigate the three dimensional performance of the laterally loaded XCC pile.

Fig. 4. Horizontal section through the XCC pile.

2. Problem definition and basic assumptions 2.1. Description of the XCC pile cross section Fig. 3 shows the XCC pile cross section, which contains four flat sections and four cambered sections. The center of the cambered section is located at the point o. Three parameters a, b, θ are used to control the size and shape of the XCC pile cross section. The parameter a describes the distance between the two flat section sections in the diagonal direction. And the parameter b is the length of the flat section, 2

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Fig. 5. Numerical model of laterally loaded XCC pile or circular pile in OptumG2.

while the variable θ defines the angle of the cambered section. In practice, the value of θ = 90° is often used for convenience and other two parameters can varies in a wide range. Fig. 6. Comparison of the numerical solution for laterally loaded circular pile with Randolph’s closed-form solution.

2.2. Manner of laterally load on XCC pile cross section Unlike the conventional circular pile, XCC pile has an X-shaped cross section, which is not plane rotationally symmetric. Therefore, the direction of the lateral load (the “lateral” here means that the load is in

=0

= 0.2

= 0.4

= 0.6

= 0.8

=1

3

Fig. 7. Plastic multiplier of soil surrounding XCC pile, b/ a = 0.13.

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(b) Fig. 9. (a) Lower bound and (b) upper bound solutions for the variation of normalized ultimate resistance with α. Fig. 8. (a) Lower bound and (b) upper bound solutions for the variation of normalized ultimate resistance with the ratio of b/a.

used here. (d) The adhesion τ at the pile-soil interface is assumed as a constant factor of the soil cohesion αsu (0 ≤ α ≤ 1). In terms of the above assumptions and definitions, the normalized ultimate lateral pressure NF can be expressed as the function of the three dimensionless parameters (δ = b/a, α, β):

the cross section plane) may have influence on the XCC pile performance, particularly in the ultimate lateral pressure. In this paper, the angle between the lateral load F and the x-axis is defined as β (see Fig.4). Since the XCC pile cross section has a quarter symmetry, the angle β varies from 0 to π/4. When β = 0, the laterally load is applied perpendicular to the flat section of XCC pile cross section and the laterally load towards the center of the cambered section for β = π/4. In addition, the following four assumptions were used in the following analysis: (a) plane strain is assumed in the pile cross section plane; (b) it is assumed that the surrounding undrained clay is rigid, perfectly plastic material, with an undrained shear strength su independent of the current stress level. In accordance with associated flow rule, the soil is also assumed to deform at constant volume. (c) Right handed rectangular coordinate system with the center of the pile taken as the origin is

NF =

F = f (δ ,α,β ) su de

(1)

where de is the equivalent diameter of the XCC pile cross section; de= (4AXCC/π)1/2; AXCC describes the area of XCC pile cross section. Then, the problem is reduced to find the function in Eq. (1). Here, it should be noted that Eq. (1) should be derived from the lower bound solution of FELA of OptumG2 since a lower bound solution provide a safe estimate on the real ultimate lateral pressure of XCC pile. 4

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3. Numerical methods of analysis The finite element limit analysis (FELA) using OptumG2 is used here for determining the ultimate lateral pressure of XCC pile [17]. This numerical technique is powerful in dealing with the problem of ultimate load of a plane strain problem. It has been successfully applied to solve various bearing capacity and stability problems in geotechnical engineering. The FELA of OptumG2 combines the finite element discretization technique and boundary conditions using the plastic bound theorem to bracket the rigorous ultimate load by upper and lower bound solution. In addition, automatic mesh adaptivity allows more precise lower and bound solution to be obtained. In the following analysis, the models of laterally loaded XCC pile were analyzed by OptumG2 using automatic mesh adaptivity with shear dissipation as the adaptivity control. Fig. 5 shows the numerical model of laterally loaded XCC pile in OptumG2. In the model, the displacement is not allowed at the outer boundary. The undrained clay is modeled using the rigidplastic Tresca material with the associate flow rule. The plane XCC pile segment is modeled as the rigid solid. The undrained strength su of soil is used as 50 kPa. The geometrical parameters of b/a can be used in the range of 0.05–0.8. The adhesion factor α varies from 0 to 1, while the load direction angle β changes between 0 and π/4. In order to validate the accuracy of the numerical model particularly in checking the using of the number of the elements and the radius of the outer boundary, the FELA results of laterally loaded circular pile were compared with Randolph’s closed-form plasticity solution (Randolph et al. [9]). Two cases were used in the numerical model. For case 1, the radius of the outer boundary is 50a and five iterations steps of adaptive meshing with the number of elements increasing from 5000 to 10,000. For case 2, the radius of the outer boundary is 60a and five iterations steps of adaptive meshing with the number of elements increasing from 50,000 to 100,000. It can be seen from Fig. 6 that the lower bound solution is in good agreement with the closed-form solution for both cases 1 and 2. The upper bound solution calculated from case 1 is higher than the closed-form solution, while case 2 could provide enough accuracy. Therefore, case 2 is used in the following analysis of XCC pile

(a)

4. Results and discussion Fig. 7 plots the plastic multiplier of soil around XCC pile with b/ a = 0.13 for α = 0, 0.2, 0.4, 0.6, 0.8, 1. It can be seen that a bounding square zone of X-shaped rigid disc (elastic core) forms around the XCC pile when α = 1 (perfectly rough). In this zone, the soil is in elastic state and it moves along with the rigid XCC pile cross section under the lateral load. The bounding square zone gradually becomes weaken with the decrease of the adhesion factor α. Fig. 8(a) and (b) respectively presents the lower and upper bound solutions for the variation of normalized ultimate resistance with the ratio of b/a for the five cases of α = 0, 0.25, 0.5, 0.75, 1. It can be clearly seen from Fig. 8 that the parameter b/a has significant influence on the ultimate lateral pressure. The increasing of the ratio of b/a results in the non-linearly decreasing of normalized limit pressure. In fact, this means that the decreasing of b with constant value of a will increase the lateral bearing capacity and meanwhile the concrete use for XCC pile will reduce. In addition, it can be seen that the upper bound solution is not sensitive to the adhesion factor α when b/a is less than 0.3. Furthermore, the obtained data from the FELA of OptumG2 are fitted using an empirical function. It is found that the power function can be used to fit the lower bound data, while the upper bound data can be fitted through an exponential function. This indicates that the parameter b/a should appears in Eq. (1) in the form of the power function. Fig. 9(a) and (b) respectively shows the lower and upper bound solutions for the variation of normalized ultimate resistance with the adhesion factor α for the four cases of b/a = 0.07, 0.33, 0.4, 0.73. It can be clearly found that the upper bound results for the limit pressure

(b) Fig. 10. (a) Lower bound and (b) upper bound solutions for the variation of normalized ultimate resistance with β.

varies almost linearly with the adhesion factor α. Moreover, the normalized ultimate lateral pressure increases with the increasing of α, but the increased trend is not obvious. For the lower bound results, the normalized limit pressure increase nearly linearly with the increase of α when the ratio of b/a is relatively large. For the cases of relatively small ratio of b/a, the non-linear relationship between the normalized limit pressure and the adhesion factor α is found. Moreover, a parabolic Table 1 Optimal value of constant coefficients.

5

A1

A2

B0

B1

B2

C0

C1

C2

C3

1.429

−0.155

3.503

1.202

−0.676

2.014

0.054

−0.357

0.246

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Table 2 Comparison of the FELA data and theoretical predictions for the ultimate lateral pressure. β

δ

α

FELA

Prediction

Error (%)

β

α

δ

FELA

Prediction

Error (%)

δ

α

β

FELA

Prediction

Error (%)

0.00

0.07

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

14.38 15.02 15.77 16.38 17.02 17.41 17.68 17.73 17.76 17.80 17.86

15.21 15.70 16.14 16.51 16.83 17.09 17.29 17.43 17.51 17.53 17.49

5.77 4.52 2.30 0.78 −1.11 −1.85 −2.22 −1.73 −1.43 −1.54 −2.05

0.00

0.07

0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67 0.73

14.38 13.38 12.80 12.29 12.10 11.54 11.44 11.22 10.88 10.76 10.66

15.68 14.08 13.23 12.65 12.22 11.88 11.60 11.36 11.15 10.97 10.81

9.03 5.22 3.33 2.93 0.97 2.93 1.41 1.30 2.51 1.97 1.42

0.13

0.00

0.00 0.09 0.17 0.26 0.35 0.44 0.52 0.61 0.70 0.79

13.30 13.31 13.52 13.61 13.84 14.14 14.29 14.31 14.25 14.23

13.82 13.83 13.82 13.78 13.72 13.65 13.58 13.52 13.46 13.42

3.89 3.92 2.18 1.25 −0.86 −3.41 −4.92 −5.53 −5.57 −5.71

0.00

0.33

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

12.36 12.69 12.99 13.26 13.49 13.65 13.74 13.81 13.88 13.93 13.95

11.96 12.35 12.69 12.99 13.23 13.44 13.59 13.70 13.77 13.79 13.76

−3.21 −2.71 −2.33 −2.06 −1.93 −1.59 −1.06 −0.76 −0.79 −1.05 −1.38

0.00

0.25

0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67 0.73

16.05 14.77 13.90 13.19 12.85 12.42 12.09 11.86 11.69 11.36 11.26

16.46 14.78 13.88 13.27 12.82 12.47 12.17 11.92 11.71 11.52 11.35

2.50 0.07 −0.15 0.64 −0.18 0.35 0.66 0.54 0.13 1.38 0.78

0.13

0.20

0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67

14.50 14.57 14.67 14.85 14.93 14.90 14.80 14.68 14.63 14.54

14.68 14.67 14.65 14.61 14.57 14.52 14.46 14.40 14.35 14.30

1.19 0.73 −0.15 −1.62 −2.39 −2.55 −2.30 −1.90 −1.91 −1.65

0.00

0.40

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

11.55 11.85 12.16 12.43 12.61 12.80 12.88 12.98 13.07 13.12 13.17

11.61 11.99 12.32 12.60 12.85 13.04 13.19 13.30 13.36 13.38 13.35

0.53 1.14 1.32 1.42 1.89 1.88 2.42 2.47 2.27 2.02 1.39

0.00

0.50

0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67 0.73

17.41 16.20 14.52 13.99 13.35 12.90 12.58 12.34 12.00 12.08 11.85

17.22 15.46 14.52 13.89 13.42 13.04 12.73 12.47 12.25 12.05 11.87

−1.11 −4.57 0.03 −0.70 0.47 1.10 1.23 1.10 2.07 −0.27 0.20

0.13

0.40

0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67

15.29 15.35 15.48 15.39 15.29 15.18 15.00 14.85 14.78 14.80

15.30 15.30 15.28 15.24 15.19 15.14 15.08 15.02 14.96 14.91

0.07 −0.29 −1.30 −0.97 −0.61 −0.26 0.54 1.16 1.26 0.77

0.00

0.60

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

10.86 11.13 11.39 11.64 11.83 11.99 12.19 12.29 12.40 12.49 12.53

10.90 11.26 11.57 11.84 12.06 12.25 12.39 12.49 12.55 12.57 12.54

0.38 1.09 1.57 1.67 1.96 2.15 1.66 1.61 1.19 0.63 0.07

0.00

0.75

0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67 0.73

17.74 16.31 14.81 14.16 13.56 13.13 12.83 12.61 12.34 12.40 12.21

15.68 14.08 13.23 12.65 12.22 11.88 11.60 11.36 11.15 10.97 10.81

−11.60 −13.63 −10.69 −10.65 −9.86 −9.53 −9.59 −9.94 −9.59 −11.52 −11.45

0.13

0.60

0.07 0.13 0.20 0.27 0.33 0.40 0.47 0.53 0.60 0.67

16.22 15.79 15.67 15.53 15.42 15.24 15.10 14.97 14.92 14.92

15.72 15.72 15.69 15.65 15.61 15.55 15.49 15.43 15.37 15.32

−3.08 −0.46 0.13 0.83 1.18 2.03 2.57 3.07 3.03 2.65

0.00

0.73

0.00 0.10 0.20 0.30 0.40 0.50 0.60

10.67 10.93 11.19 11.43 11.66 11.83 12.00

10.58 10.92 11.22 11.48 11.70 11.88 12.02

−0.89 −0.10 0.25 0.49 0.38 0.44 0.13

0.00

1.00

0.07 0.13 0.20 0.27 0.33 0.40 0.47

17.86 16.36 14.92 14.24 13.66 13.24 12.96

15.68 14.08 13.23 12.65 12.22 11.88 11.60

−12.20 −13.94 −11.37 −11.15 −10.54 −10.30 −10.50

0.13

0.80

0.07 0.13 0.20 0.27 0.33 0.40 0.47

16.23 15.87 15.71 15.62 15.48 15.31 15.14

15.92 15.92 15.89 15.86 15.81 15.75 15.69

−1.92 0.32 1.15 1.48 2.12 2.88 3.59

bound data can be also fitted through the cubic polynomial function but with different coefficients. Another interesting phenomenon should be noted that the normalized ultimate lateral pressure NF for XCC pile is identical to that for circular pile are when the area of the cross section of XCC pile is equal to circular pile. It is known from Fig. 6 that the maximum value of NF for circular pile is about 11.94, which is less than most of the data (exclude the case of relatively large ratio of b/a) in Fig. 8 to Fig. 10. It indicates that the XCC pile with relatively small ratio of b/a has larger ultimate lateral pressure than the conventional circular pile under the condition of the same area of cross section.

function can be used to fit the lower bound data very well. Now, the function of α in the final expression of limit pressure (Eq. (1)) are also obtained. In addition, the influence of the parameter β on the ultimate lateral pressure is depicted in Fig. 10. It is very interesting to be noted that the relation between normalized limit pressure and β is not simple monotonic relationship like the previous two parameters. Fig. 10(a) shows that the lower bound solution of limit pressure decreases with the increase of the parameter β when α is larger than 0.6. However, when α is less than 0.6, the normalized limit pressure increases with the increase of β until it reaches a maximum value, then it decreases as β increases. In this case, the lower bound data are fitted using the cubic polynomial function. For the upper bound solution, the normalized limit pressure increases with the increase of β when β is less than 10 degree (≈0.2 rad) and then reduces as β increases. The limit pressure is not sensitive to β when β is larger than 40 degree (≈0.7 rad). The upper

5. Presented empirical closed-form lower bound solution for ultimate lateral pressure Based on the above parametric analysis, the general form of Eq. (1) can be determined as 6

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b A2 NF = A1 ⎛ ⎞ (B2 α 2 + B1 α + B0)(C3 β 3 + C2 β 2 + C1 β + C0) ⎝a⎠

of Basic Research and Frontier Technology (cstc2017jcyjAX0261); (Hubei Key Laboratory of Disaster Prevention and Mitigation China Three Gorges University) (2017KJZ02).

(2)

where A1, A2, B1, B2, B0, C3, C2, C1, C0 are constant coefficients. Then, it is necessary to determine the nine constant coefficients in Eq. (2). In this paper, the optimal solutions of nine constant coefficients are derived by conducting a nonlinear regression analysis with the least square method and are listed in Table 1. The FELA data and the calculation results using Eq. (2) are compared in Table 2. It can be found that most of the differences between the predictions using Eq. (2) and FELA data are less than 5%. This indicates that the proposed closedfrom Eq. (2) could provide enough accuracy for predicting the ultimate lateral pressure of XCC pile.

References [1] Lv Y, Liu H, Ding X, Kong G. Field tests on bearing characteristics of X-section pile composite foundation. J Perform Constr Facil 2011;26(2):180–9. [2] Liu H, Zhou H, Kong G. XCC pile installation effect in soft soil ground: a simplified analytical model. Comput Geotech 2014;62:268–82. [3] Lv Y, Liu H, Ng CW, Ding X, Gunawan A. Three-dimensional numerical analysis of the stress transfer mechanism of XCC piled raft foundation. Comput Geotech 2014;55:365–77. [4] Lv Y, Liu H, Ng CW, Gunawan A, Ding X. A modified analytical solution of soil stress distribution for XCC pile foundations. Acta Geotech 2014;9(3):529–46. [5] Zhang D, Lv Y, Liu H, Wang M. An analytical solution for load transfer mechanism of XCC pile foundations. Comput Geotech 2015;67:223–8. [6] Kong GQ, Zhou H, Ding XM, Cao ZH. Measuring effects of X-section pile installation in soft clay. Proc Inst Civ Eng-Geotech Eng 2015;168(4):296–305. [7] Sun G, Kong G, Liu H, Amenuvor AC. Vibration velocity of X-section cast-in-place concrete (XCC) pile–raft foundation model for a ballastless track. Can Geotech J 2017;999:1–6. [8] Zhou H, Liu H, Randolph MF, Kong G, Cao Z. Experimental and analytical study of X-section cast-in-place concrete pile installation effect. Int J Phys Model Geotech 2017:1–19. [9] Randolph MF, Houlsby GT. The limiting pressure on a circular pile loaded laterally in cohesive soil. Geotechnique 1984;34(4):613–23. [10] Martin CM, Randolph MF. Upper-bound analysis of lateral pile capacity in cohesive soil. Géotechnique 2006;56(2):141–5. [11] Ahmadi SF, Eskandari M. Vibration analysis of a rigid circular disk embedded in a transversely isotropic solid. J Eng Mech 2013;140(7):04014048. [12] Ahmadi SF, Eskandari M. Rocking rotation of a rigid disk embedded in a transversely isotropic half-space. Civ Eng Infrastruct J 2014;47(1):125–38. [13] Eskandari M, Shodja HM, Ahmadi SF. Lateral translation of an inextensible circular membrane embedded in a transversely isotropic half-space. Eur J Mech-A/Solids 2013;39:134–43. [14] Pak RY, Jennings PC. Elastodynamic response of pile under transverse excitations. J Eng Mech 1987;113(7):1101–16. [15] Abedzadeh F, Pak RY. Continuum mechanics of lateral soil-pile interaction. J Eng Mech 2004;130(11):1309–18. [16] Ji F, Pak RY. Scattering of vertically-incident P-waves by an embedded pile. Soil Dyn Earthq Eng 1996;15(3):211–22. [17] Krabbenhoft K, Lyamin A, Krabbenhoft J. Optum computational engineering (OptumG2); 2015. Available on: < www.optumce.com > .

6. Conclusion This paper presents rigorous upper and lower bound solutions for the ultimate lateral pressure of X-section Cast in place Concrete (XCC) pile in undrained clay through two dimensional plane strain finite element limit analysis. The influence of the three main factors of the geometry of cross section, the lateral load direction and the pile-soil interface adhesion on the ultimate lateral pressure of XCC pile were investigated through parametric analysis. Then, an empirical closedform lower bound solution is proposed for predicting the ultimate lateral pressure of XCC pile based on the parametric study. Comparison between the predicted value using the proposed closed-form solution with the FELA data shows that the closed-from Equation could provide enough accuracy for predicting the ultimate lateral pressure of XCC pile. In addition, it is found that the XCC pile with relatively small ratio of b/a has larger ultimate lateral pressure than the conventional circular pile under the condition of the same area of cross section. Acknowledgement The work is supported by the National Natural Science Foundation of China (51420105013 and 51708063); Chongqing Research Program

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