Numerical modeling bearing capacity in wetting unsaturated expansive soils

To address the load-bearing deterioration of expansive soils uplift pile foundation after moisture absorption, a coupled seepage-soil deformation model for unsaturated expansive soils is implemented into ABAQUS. This modeling work consists primarily of two aspects: (1) The total strain of expansive soils has been decoupled into two parts, i.e., one caused by external loads and calculated by using Mohr-Coulomb plasticity model, and the other induced by wetting swelling and modeled by defining the moisture-swelling relation curve of expansive soils; (2) User-defined field subroutine (USDFLD) is developed by defining suction-dependent soil’s parameters (elastic modulus, cohesion and internal friction angle), and employed to simulate softening behaviors of expansive soils after moisture absorption. he above model is subsequently used to perform 3D finite element modeling and hydraulic-stress coupling analysis on the bearing capacity of pile in expansive soils before and after rainfall. Eventually, the proposed numerical method is validated by simulating a group of full-scale tests.


Introduction
Expansive soils are characterized by high plasticity and its special expansion and contraction properties, while pile is one of fundation forms to effectively deal with the problems of expansive soils.However, the behavior of the pile foundation in expansive soils is more complex compared to conventional pile foundation.When water infiltrates into the expansive soils around the pile, it causes a change in matrix suction, which leads to a significant wetting response, and thus requires in-depth study of the pile foundation bearing behavior and intrinsic mechanism.
The finite element method is a powerful tool to study the behavior of pile foundation in unsaturated soils, which can be used to couple the hydraulic behavior of unsaturated expansive soils with the behavior of unsaturated pile-soil interfaces by establishing an effective principal model.Some scholars have used the theory of unsaturated soils for numerical simulation of coupled flow and consolidation of pile foundation or other structures in expansive soils [1][2][3], and most of them used ABAQUS for modeling.In ABAQUS, the way to simulate the properties of expansive soils is divided into two categories: writing coupled seepage-soil deformation model and defining the moisture-swelling curve.Among them, in terms of writing coupled seepage-soil deformation model, Wu and Vanapalli [4] developed five user material subroutines (USDFLD, UMAT, UMATHT, UEXPAN, FRIC) in ABAQUS, which were used for accessing and transmitting the stress and strain, and for calculating the stress-deflection, hydraulic behavior, expansive strains and pile-soil interface behavior, respectively.In terms of defining the wetswelling characteristics, Shams and other scholars [5,6] considered the total strain of the soil as a superposition of the bulk variation due to moisture change and effective stress change, and defined soil as an elastic porous medium with wet swelling characteristic in order to study the structural deformation in expansive soils.
In the past, most of the numerical simulation studies on pile foundation buckling focus on the constitutive model of pile-soil interface.However, when the equal-section pile is pulled out, it will bring out a thin layer of soil, the rupture surface is inside the soil, so it is vital to simulate the strength and deformation of the expansive soils itself.

Wet swelling deformation of expansive soils and defination of wet swelling property
The total strain of expansive soils consists of two parts [7] and can be expressed by following equation: Where:  total is the total strain,  eff is the strain due to the change in effective stress in soil skeleton, and  is the strain induced by wetting swelling.
The first part of the strain  eff , which related to the change in external loads, is calculated by using Mohr-Colomn model built into ABAQUS, based on the Bishop's effective stress.
The second part of the strain caused by wetting swelling has been previously applied by the equivalent humidity method [8][9][10][11].However, this method ignores the difference between the mechanism of thermal and hygroscopic expansion, not to mention the concept of suction in unsaturated soils.The approach used in this paper is to define the moisture-swelling property of material and set the expansive strain as a function of humidity, realizing that the porous dielectric material expands as its own saturation increases.

Intensity criterion based on capillary saturation
The intrinsic model of materials in ABAQUS is defined based on Bishop's effective stress (1961), as shown in Equation (2) [12]: Where:  ‾ is the effective stress;  is the total stress;  is a parameter determined by testing, depending on the type of soil and degree of saturation, when the soil is fully saturated  = 1.0, and when the soil is dry  = 0.0, due to the lack of test data, the software equates  to the total saturation  ;  is the liquid pressure;  is the gas pressure, the software ignores the existence of air pressure, so the hydraulic pressure is the negative pore pressure, which is the suction .Based on this, the effective stress can be expressed as: Based on the above definition of effective stress, for shear damage along a certain damage surface, the Mohr-Coulomb criterion in ABAQUS can be expressed as: Where:  and  are the positive and shear stresses acting on the shear surface, respectively;  and  are the effective cohesion and effective internal friction angle of the soil, respectively.However, the strength of the soil body mainly depends on the capillary action, so it is necessary to replace the soil-water retention curve ( − ) with capillary-water retention curve ( − ) in the definition of the material properties to differentiate the effects of two different actions.Lin et al [13,14] proposed a bimodal soil-water retention curve that divided saturation into capillary saturation and adsorption saturation, realizing the decoupling of the capillary part and the adsorption part, and then the shear strength criterion can be expressed as follows: Where  and  follow the suction variation and need to be defined through the field variable subroutine.

Calculation of Unsaturated Elactic Modulus
The bearing performance of pile foundations in unsaturated expansive soils is closely related to elastic modulus of the foundation soil.The methods for solving the relationship between elastic modulus and suction can be divided into two types: experimental conversion and model prediction.
(1) Experiment conversion In general, stress-strain data from triaxial shear tests can be mathematically represented by a hyperbola of the following form (Duncan and Chang, 1970): Where:  is the axial strain,  is the initial tangential modulus of elasticity,  and  are the principal and secondary principal stresses, respectively, ( −  ) is the ultimate bias stress at large strain.
In order to obtain the parameter values of  and ( −  ) , Equation 6can be transformed into a relation between axial strain/bias stress ( −  ) and axial strain () (Equation 7).The expression can be represented by a straight line shown in Figure 1 (2) Semi-empirical model Oh and Vanapalli (2016) [15] proposed a semi-empirical model (Equation ( 8)) for explaining and predicting the change in the elasic modulus of unsaturated soils in terms of change in matrix suction.This model requires the use of soil-water curves, and has been studied and extended to unsaturated expansive soils [16], Where:  sat is the saturated elastic modulus;  and  are fitting parameters, the value of  is related to the ratio of foundation size to soil grain size and the plasticity index  , and b is a parameter related to the soil type, which is generally  = 1 for coarse-grained soils, and  = 2 for fine-grained soils;  is the atmospheric pressure (101.3kPa).
The model predicts well in the low and medium suction ranges, but in the high suction range (greater than 100MPa ), the results of the semi-empirical model deviate significantly from the experimental results.Since the prediction range of the model has covered the suction floating interval of foundation soil within the atmospheric influence layer during rainfall, the model can be used in carrying out the bearing capacity analysis of expansive soils foundation under rainfall condition.

Field variable subroutine USDFLD
The weakening of the strength parameters and the softening of the elastic modulus of unsaturated expansive foundation described above can be achieved by defining the variation of the relevant parameters with field variables.The subroutines for defining field variables are UFIELD (User subroutine to specify predefined field variables) and USDFLD (User subroutine to redefine field variables at a material point).
UFIELD is used to specify predefined field variables, which are defined directly to the nodes and updated at any time during the analysis.However, it can only assign values to field variables directly and cannot call material specific integration point data.SDFLD is used to redefine field variables at a material point, which will overwrite the field variables in the previous 'Initial conditions', 'Predefined field variables' or UFIELD interpolation results for integration points.It can call material integration point variables such as time, node coordinates, stress-strain, etc. through the utility program GETVRM, and define the field variables as functions of these integration point variables.Since UFIELD can not satisfy the required functionality, this paper opts for the secondary development of the USDFLD subroutine.

Numerical simulation of full-scale test for pile's uplift bearing capacity in expansive soils
A large-scale field test of pile foundation uplift without water immersion and uplift with water immersion was carried out near the Neixiang Power Plant in Neixiang County, Nanyang City, Henan Province [17].The weakening degree of bearing capacity before and after wetting is compared by observing the change of pile foundation settlement, axial force and pile lateral resistance before and after wetting.By combining with the water immersion test, the water content change of the expansive soils foundation and the wetting-induced foundation bulge deformation were also measured.

Model setting
A quarter symmetric model is built to simulation the equal cross-section resisting monopile in expanded soil foundation (Figure 2).The length of the equal-section pile  = 5 m, and the diameter  = 0.9 m.In order to avoid the influence of the boundary effect on calculation results, the calculation range in the horizontal direction is taken as 10 times of the pile diameter, and in the vertical direction is taken as 2 times of the pile length, so the model size is 5 m × 5 m × 10 m.The material parameters of pile and soil are shown in Table 1.In order to characterize expansive soils, it is also necessary to (1) enter the moisture-swelling property of soil, (2) enter the capillary-water retention curve data, (3) enter the saturated permeability coefficient, the permeability coefficient reduction factor and the saturation curve to reflect the permeability of soil. Figure 3 constructs the logical framework for the coupled fluidstructure analysis of expansive soils pile foundation in ABAQUS and explains the interplay of saturation, suction and pore ratio.Extracting the water content distribution data before and after rainfall plotted in Figure 4, it can be showen that the settings of the initial moisture field and the moisture field after rainfall are basically consistent with the measured data from full-scale tests.The shallow soil is dry before wetting, and the water content is about 10%, which gradually increases with the depth until 3 m below the ground surface, stabilizes in the range of 15% ∼ 17%.The water content of the foundation soil at different depths increases to different degrees after wetting, and in general, the increment of water content gradually decreased with the depth of burial.6 shows the axial force distribution of two test piles in the process of upward pullout loading before and after wetting.It can be seen that the distribution of axial force in both full-scale test and numerical simulation decreases gradually along the direction of pile length at each level of loading.Meanwhile, with the increase of load, the slopes of the axial force curves before and after wetting increase gradually, and the curves of the piles after wetting tend to be dense, which indicates that the friction force will reach the limiting value very soon, while the curves of the piles before wetting are sparse, which indicates that there is still a space for the lateral friction force to be exerted.

Figure 3 .
Figure 3. Logical framework for fluid-solid coupling analysis 4.2.Comparison and analysis 4.2.1.Humidity field before and after wetting.Extracting the water content distribution data before and after rainfall plotted in Figure4, it can be showen that the settings of the initial moisture field and the moisture field after rainfall are basically consistent with the measured data from full-scale tests.The shallow soil is dry before wetting, and the water content is about 10%, which gradually increases with the depth until 3 m below the ground surface, stabilizes in the range of 15% ∼ 17%.The water content of the foundation soil at different depths increases to different degrees after wetting, and in general, the increment of water content gradually decreased with the depth of burial.

Figure 4 .
Figure 4. Distribution of water content before and after wetting 4.2.2.Foundation expansion and deformation during wetting.The expansion deformation in the depth range per linear meter after expansion stabilization were extracted and plotted in Figure 5.It can be seen that the measured and numerical simulation results are well fitted: the vertical expansion strain decreases nonlinearly along all depths.In addition, the expansion deformation mainly occurs in shallow foundations with a burial depth of less than 3.5 m, which is basically consistent with the empirical value of the local atmospheric influence layer of 3 ∼ 4 m.

Figure 5 .
Figure 5. Expansion and deformation of foundation at different depths after wetting 4.2.3.Pile Axial Force and Pile Lateral Frictional Resistance.Figure6shows the axial force distribution of two test piles in the process of upward pullout loading before and after wetting.It can be seen that the distribution of axial force in both full-scale test and numerical simulation decreases gradually along the direction of pile length at each level of loading.Meanwhile, with the increase of load, the slopes of the axial force curves before and after wetting increase gradually, and the curves of the piles after wetting tend to be dense, which indicates that the friction force will reach the limiting value very soon, while the curves of the piles before wetting are sparse, which indicates that there is still a space for the lateral friction force to be exerted.

Figure 6 .
Figure 6.Axial force distribution of pile body under different loadsFigure7shows the distribution of pile lateral friction resistance along the depth when the extractable pile reaches the ultimate bearing capacity before and after wetting.The results of fullsacle test and numerical simulation are basically consistent, both reflecting a significant decrease in ultimate lateral friction resistance of pile after wetting, with a decrease of about 35.6%.

Figure 7 .Figure 8 .
Figure 7. Ultimate lateral frictional resistance of piles to elevation before and after wetting 4.2.4.Load-Displacement Curve at Top of Pile.The load-displacement (Q-s) curves of the uplift piles before and after wetting are shown in Figure 8.The Q-s curves of full-scale tests are slowly

Table 1 .
Material parameters