# An Improved Nonlinear Settlement Calculation Method for Soft Clay considering Structural Characteristics

Authors: Binhui Ma; Zhuo Li; Kai Cai; Zhiyong Hu; Minghua Zhao; Chengbin He; Bingchu Chen; Xiaocheng Huang
Journal: Geofluids
 (2021)

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## Abstract

The settlement calculation model for soft clay foundation is established based on Hooke’s law and the Duncan-Chang model. By introducing the concept of damage ratio, the method for determining the deformation modulus of soil before and after damage under load is presented, and a nonlinear settlement calculation method which considers the structural characteristics of soft clay is proposed. In the end, a practical engineering example is analyzed with the proposed method and some current methods for soft clay settlement calculation. The results indicated that the proposed method is feasible and applicable in practical engineering.


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## Body

## 1. Introduction

The structure of soil is defined as the manner of arrangement and state of aggregation of soil grains. Most natural soft clays have a certain structure [1, 2] and are influenced by factors such as precipitation, unloading, and weathering. A large number of practical engineering projects have proven that structure is an important feature of soft clay and an important factor that affects the final settlement and settlement rate of soft clay [3]. Therefore, it is of significance to investigate the settlement calculation method of soft clay and establish a new calculation method of settlement of soft clay considering the structure of soil.For the past decades, many settlement calculation methods for soft clay have been conducted by scholars. Shen [4, 5] introduced the damage theory into the description of the mechanical behavior of structural soils and established the evolution law of soil damage; Zhang [6] established the statistical relationship between laboratory test data and in situ test data based on the practice in the Shanghai-Nanjing Expressway and proposed the settlement calculation method considering the effect of structural characteristics. Shi et al. [7] used the finite element method to analyze the settlement and deformation of the embankment on the soft foundation considering the rheology and damage of the structural soil based on the double yield faced elastoplastic model proposed by Yin. However, the complexity of the constitutive model made it difficult to obtain certain parameters and difficult to be applied in engineering practice; Wang and Chen [8, 9] made piecewise linearization of the curves of consolidation coefficient Cv and consolidation pressure p and permeability coefficient k and consolidation pressure p by taking yield stress as the piecewise point. Based on this, an analytical expression was obtained to calculate the one-dimensional consolidation degree of the structural soft clay foundation, yet such a two-stage simplification would have a certain impact on the calculating accuracy. Based on the Duncan-Zhang model, considering the structure of soft clay, the concept of damage ratio was introduced to modify the Duncan-Zhang model by Wang et al. [10, 11]. Li et al. [12] analyzed the influence of soft clay structure on its own deformation and deformation rate based on the results of one-dimensional consolidation and permeation tests of undisturbed soil and remolded soil. Lu [13] applied the structural damage theory to the settlement calculation of soft clay and proposed a revised settlement calculation formula based on the Duncan-Zhang model, considering the influence of Poisson’s ratio on the settlement of the foundation with the change of its stress. Feng et al. [14] presented a simplified method for calculating multistage creep settlement of multilayer soft clays under one-dimensional strain conditions. Rui et al. [15] used an analytical method to calculate the compressibility of the pile-soil system; the settlement characteristics of granular filler on saturated soft clay foundation with time were studied. Zhao et al. [16] established a nonlinear elastic-viscoplastic creep constitutive model and verified it by experiments. Yu et al. [17] investigated a time-dependent deformation mechanism in depth and obtained the viscoelastoplastic deformation of soft soil using a nonassociated flow rule and the modified Nishihara model. Yu et al. [18] performed the numerical simulations with the use of a two-dimensional discrete element method, in which the numerical model is calibrated to match the stress-strain and permeability-strain responses of the experimental results. Simulation results reveal that the settlement calculation of soft clay considering the structural damage is feasible. However, obviously none of these methods avoids the defect in that the Duncan-Chang model does not consider the volumetric stress.In summary, how to consider the structure of the soil itself in the settlement calculation is a question which is worthy of consideration. Therefore, this paper starts with the discussion of the deformation mechanism of the soil element and combines Hooke’s law and the Duncan-Zhang model to establish a new calculation method for the settlement of the foundation considering the soft clay structure.


## 2. Analytical Model

In order to reflect the settlement process of weak ground more accurately, this paper introduces the Duncan-Zhang model to describe the stress-strain relationship of soil deformation. The Duncan-Zhang model is based on the Kondner hyperbolic relationship [19], and its expression is
(1)σ1−σ3=ε1a+bε1,where σ1 is the vertical stress of soil, σ3 is the confining pressure of soil, ε1 is the vertical strain of soil, and a and b are the triaxial test curve fitting parameters, which can be explicitly calculated by the below formulas:
(2)a=1E0,(3)b=1σ1−σ3u=Rfσ1−σ3f=Rf1−sinφ2ccosφ+2σ3sinφ,where E0 is the initial deformation modulus of soil; Rf is the coefficient of soil failure ratio or strength, generally taken as 0.75~1.0; C is the cohesion of soil; and φ is the friction angle of soil.Apparently, the effect of the soil stress differenceσ1−σ3 on the vertical strain ε1 when the confining pressure σ3 is constant is considered in the Duncan-Zhang model [20], while the effect of the volume stress on the soil compression deformation is not taken into account. The Duncan-Zhang model cannot be used directly for settlement calculation of soft ground. Therefore, this paper divides the additional stress into two parts: partial stress σ1−σ3 and volume stress σ1+σ2+σ3/3=σ3. Therefore, the deformation of the soft clay foundation under the effect of additional stress should be determined by the deviatoric stress and volumetric stress. The layer-wise summation method is still used to calculate the settlement of soft soil foundation. The total settlement of the soft clay foundation is
(4)s=∑i=1Nisi=∑i=1Nisi′+si″,where i is the total compression deformation of the i layer soil, si′ is the deformation of the i layer of soil under the action of volume stress σ3, si″ is the deformation of the i layer of soil under the action of deviatoric stress σ1−σ3, Ni is the number of layers of the ground compression layer, and di is the thickness of the i layer of soil. The solution process of deformation si′ and si″ of each compressive layer of soft clay under the effect of additional stress will be described in the following sections.


## 3. Establishment of Method

In this study, the principle of damage mechanics is introduced into the calculation of foundation settlement and the traditional layered sum method is further modified.In addition, the gravity stress also causes the initial mechanical parameters due to the different stress history of each soil layer, that is, during deformation of soils. This phenomenon also should be studied.However, as the physical and mechanical parameters of the soft soil, especially its deformation modulus, will also change during the deformation process, it is difficult to solve it with the traditional control differential equation method. Therefore, based on the idea of step loading, this paper introduces the incremental method which is used to calculatesi′ and si″, and a settlement calculation method for soft clay foundation is proposed.It can be seen that when the damage principle is combined with the layer-wise summation method to calculate the settlement of the soft clay foundation, the changes in the physical and mechanical parameters of the various soil layers must be considered. Based on the above considerations, a calculation method for the settlement of soft soil foundation as shown in Figure1 is proposed.Figure 1
Calculation flowchart.


### 3.1. Damage VariableD

This article introduces the definition of the damage variableD of Shen [4] and treats the failure process of the soil as a process of gradually transforming from the undisturbed soil to the disturbed soil (damaged soil). Constantly changing, its changing law can be expressed by the following formula:
(5)E′=E1−D,where D=1−e−mεv+nεβ(6)εv=ε1+2ε3,εβ=ε1−ε3,where D is the damage variable, εv is the volumetric strain, and m and n are the test parameters, obtained from confined and unconfined compression tests. Let em be the turning point void ratio when the compression curve of the undisturbed soil and the compression curve of the remolded soil are substantially parallel in the confined compression test. Assuming that D is 0.95, the expression of m can be obtained as
(7)m=ln20e0−em/1+e0−n,where e0 is the initial porosity of soil.We suppose thatD=0.95 at the turning point εn at the later stage of the descending section of the stress-strain curve in the confinement test. Considering εv=0 at this time, the expression of n can be obtained as
(8)n=ln201.5εn.Considering thatεn is difficult to calculate, the empirical formula of reference [5] is still cited:
(9)εn=em1+e0.


### 3.2. Initial Deformation Modulus

As a result, the structure of the soft soil itself is affected by the load, and the soil is damaged, which causes the deformation-related mechanical parameters, that is, the deformation modulus, to change continuously. At the same time, different stress history conditions, that is, gravity stress, will cause different degrees of damage to the soil. Therefore, the change law and determination method of the deformation modulus of each soil layer of the foundation should be studied in depth.Let the horizontal direction be thex-axis and the y-axis, and the vertical direction be the z-axis. Since the soil layers below the centerline of the foundation are mainly subject to gravity stress, in this coordinate system, the stress state of each soil element is the main stress state. The large principal stress is σ1, and the small principal stress is σ2=σ3. Then, the expression of the i compression layered gravity stress is
(10)σ1i=∑t=1i−1γtdt+γidi2,(11)σ3i=k0σ1i,where γt is the gravity of the t layer soil, dt is the thickness of the t layer soil, σ3i is the lateral stress of the i soil element, σ1i is the vertical average gravity stress of the i soil element, and k0 is the lateral pressure coefficient. Under lateral conditions, its expression is
(12)k0=μ1−μ,where μ is Poisson’s ratio of the soil. Considering the deformation mechanism of the soil element, the gravity stress of the soil element is divided into two parts which are the gravity volumetric stress σ3iv and the gravity partial stress σ1−3ip. The expressions are
(13)σ3iv=σ3i+σ3i+σ3i3=σ3i,(14)σ1−3ip=σ1i−σ3i.The completed compressive deformation caused by the gravity volumetric stress and the gravity partial stress can be calculated by Hooke’s law and the Duncan-Zhang model, respectively. At the same time, the idea of step loading is introduced and the effect of the gravity volumetric stress and the gravity partial stress on the soil itself is. During the loading process, the number of loading stages isN. Among them, σ3iv and σ1−3ip represent the stress increment caused by the j gravity volumetric stress and the gravity partial stress of the i soil in the compression layer.
(15)σ3ijv=Eij−1ε3ijv+μσ3ijv+σ3ijv,where ε3ijv is the strain under the j gravity volumetric stress and Eij−1 is the deformation modulus of the i layer soil after the j−1 level gravity stress, so that
(16)ε3ijv=1−2μσ3ijvEij‐1.This article introduces the damage principle proposed by Shen [4]. The change formula of the deformation modulus Eij of the i layer soil at the j gravity volumetric stress is
(17)Eij=Eij−11−Dijv,where
(18)Dijv=1−e−3mε3ijv.Since the increment of thej-th gravity partial stress will inevitably cause further damage to the soil, under the action of the corresponding gravity partial stress increment σ1−3ijp, its deformation modulus Eij will continue to change accordingly, assuming the soil element at this time. The stress-strain relationship obeys the Duncan-Chang model, where Eij is used as the initial tangent modulus of the model, and the tangent modulus of the Duncan-Chang model curve is the deformation modulus of the soil after the increase of the weight and deflection stress when the deflection stress is σ1−3ijp. Through the above two steps, the deformation modulus of the i layer of soil can be obtained after the j gravity volumetric stress and deviatoric stress. The specific calculation method is as follows:According to formula (1), the deformation of the soil under the action of the j gravity partial stress increment σ1−3ijp is
(19)ε1−3ijp=aσ1−3ijp1−bσ1−3ijp,(20)ε3ijp=−με1−3ijp,where
(21)a=1Eij,(22)b=Rf1−sinφ2ccosφ+2σ3ijpsinφ.The relationship between the deformation modulus Eij of the i layer of soil before and after the j gravity partial stress increase σ1−3ijp is
(23)Eij=Eii−11−Dijp,where
(24)Dijp=1−e−m1−2μ+n1+με1−2ijp.From this, it can be seen that using formulas (17) and (23) to calculate the initial modulus of each soil layer is an iterative process. The specific calculation steps are as follows:
(1)
Give the initial deformation modulusEi0 and Poisson’s ratio μ at the zero-stress level of the i layer of soil(2)
From formulas (10) to (14), the first-layer gravity volumetric stress ε3i1v and the gravity partial stress σ1−3ilp of the i layer of soil are calculated. Calculate the vertical strain ε3i1v under the gravity volumetric stress σ3i1v from equation (16)(3)
From equations (17) and (18), the change value Ei1 of the deformation modulus of the i layer soil caused by the gravity volumetric stress σ3i1v at the first level can be obtained(4)
Taking the deformation modulusEi1 as the initial modulus before the gravity partial stress σ1−3ilp, the vertical strain ε1−3ilp under the gravity partial stress σ1−3ilp is calculated from equations (19) to (22)(5)
Calculate the deformation modulusEi1 of the i layer soil after acting on the first-level gravity partial stress σ1−3ilp from equations (23) and (24)(6)
Return to Step (2); continue to calculate the deformation modulus of thei layer soil under the influence of various levels of loads, until the deformation modulus EiN of the soil after the N layer gravity stress loading is obtained; and calculate it as the additional stress settlement initial modulusThe following will further study the calculation method of foundation settlement analysis.


### 3.3. Settlement Calculation Steps

This paper believes that the total settlement of the foundation should be divided into the sum of the settlement caused by additional volume stress and the settlement caused by additional deviatoric stress, that is, the sum of the compression layerssi′ and si″ in the settlement model established earlier. The consolidation deformation calculation steps have been completed for analysis and calculation.Meanwhile, Boussinesq’s stress solution is introduced to obtain the vertical stress and lateral stress caused by the additional stress in the soil of thei layer. The corresponding additional volume stress and additional deviator stress are σ3i and σ1i−σ3i, respectively. The deformation of the i layered soil is si′ and si″. The solution process is as follows:
(1)
The soft clay foundation compressed soil layer is divided intoNi layers, the thickness of each layer is di, and the initial deformation modulus Ei0 and Poisson ratio μ of each compressed layered soil are given(2)
The final change value of the deformation modulusEiN caused by the soil damage caused by the gravity stress of the compressive layered soil of the soft clay in Section 3.2 was calculated by the method in Section 3.2, and EiN was used as the initial modulus of the settlement calculation of the i layer soil(3)
Let the number of additional stress loadings beM and the load at each stage be pi. The additional volume stress σ3i1v and the additional deviatoric stress σ1−3ilp of the i layer of foundation soil under the action of the first-stage additional load pi can be obtained from Boussinesq’s solution(4)
LetEi0 denote the initial modulus of the foundation soil of the i layer, that is, Ei0=EiN, as the strain ε3i1v and deformation modulus Ei1 of the foundation soil of the i layer after the action of the first-level load σ3i1v can be obtained by formulas (16)–(18)(5)
TakingEi1 as the initial modulus before the second-stage loading, the strain σ1−3ilp and deformation modulus Ei1 of the i layer soil after the action of the first-stage additional deviatoric stress σ1−3ilp are obtained by equations (22) to (26)(6)
Multiplying the strain of each soil layer under the first-level additional stress by the thickness of the corresponding layer is the total settlement of the soft clay foundation under the first-level additional stress:(25)s1=∑i=1Nisi1′+si1″=∑i=1Niε3i1v+ε1−3i1pdi.(7)
According to the above steps, we continue to calculate the strain, deformation modulus, and total settlement of each soil layer of the foundation under theM-level additional stress(8)
The total settlement is obtained by superimposing the settlement of each soil layer under theM-level additional stress:(26)s=∑j=1Msj.


## 3.1. Damage VariableD

This article introduces the definition of the damage variableD of Shen [4] and treats the failure process of the soil as a process of gradually transforming from the undisturbed soil to the disturbed soil (damaged soil). Constantly changing, its changing law can be expressed by the following formula:
(5)E′=E1−D,where D=1−e−mεv+nεβ(6)εv=ε1+2ε3,εβ=ε1−ε3,where D is the damage variable, εv is the volumetric strain, and m and n are the test parameters, obtained from confined and unconfined compression tests. Let em be the turning point void ratio when the compression curve of the undisturbed soil and the compression curve of the remolded soil are substantially parallel in the confined compression test. Assuming that D is 0.95, the expression of m can be obtained as
(7)m=ln20e0−em/1+e0−n,where e0 is the initial porosity of soil.We suppose thatD=0.95 at the turning point εn at the later stage of the descending section of the stress-strain curve in the confinement test. Considering εv=0 at this time, the expression of n can be obtained as
(8)n=ln201.5εn.Considering thatεn is difficult to calculate, the empirical formula of reference [5] is still cited:
(9)εn=em1+e0.


## 3.2. Initial Deformation Modulus

As a result, the structure of the soft soil itself is affected by the load, and the soil is damaged, which causes the deformation-related mechanical parameters, that is, the deformation modulus, to change continuously. At the same time, different stress history conditions, that is, gravity stress, will cause different degrees of damage to the soil. Therefore, the change law and determination method of the deformation modulus of each soil layer of the foundation should be studied in depth.Let the horizontal direction be thex-axis and the y-axis, and the vertical direction be the z-axis. Since the soil layers below the centerline of the foundation are mainly subject to gravity stress, in this coordinate system, the stress state of each soil element is the main stress state. The large principal stress is σ1, and the small principal stress is σ2=σ3. Then, the expression of the i compression layered gravity stress is
(10)σ1i=∑t=1i−1γtdt+γidi2,(11)σ3i=k0σ1i,where γt is the gravity of the t layer soil, dt is the thickness of the t layer soil, σ3i is the lateral stress of the i soil element, σ1i is the vertical average gravity stress of the i soil element, and k0 is the lateral pressure coefficient. Under lateral conditions, its expression is
(12)k0=μ1−μ,where μ is Poisson’s ratio of the soil. Considering the deformation mechanism of the soil element, the gravity stress of the soil element is divided into two parts which are the gravity volumetric stress σ3iv and the gravity partial stress σ1−3ip. The expressions are
(13)σ3iv=σ3i+σ3i+σ3i3=σ3i,(14)σ1−3ip=σ1i−σ3i.The completed compressive deformation caused by the gravity volumetric stress and the gravity partial stress can be calculated by Hooke’s law and the Duncan-Zhang model, respectively. At the same time, the idea of step loading is introduced and the effect of the gravity volumetric stress and the gravity partial stress on the soil itself is. During the loading process, the number of loading stages isN. Among them, σ3iv and σ1−3ip represent the stress increment caused by the j gravity volumetric stress and the gravity partial stress of the i soil in the compression layer.
(15)σ3ijv=Eij−1ε3ijv+μσ3ijv+σ3ijv,where ε3ijv is the strain under the j gravity volumetric stress and Eij−1 is the deformation modulus of the i layer soil after the j−1 level gravity stress, so that
(16)ε3ijv=1−2μσ3ijvEij‐1.This article introduces the damage principle proposed by Shen [4]. The change formula of the deformation modulus Eij of the i layer soil at the j gravity volumetric stress is
(17)Eij=Eij−11−Dijv,where
(18)Dijv=1−e−3mε3ijv.Since the increment of thej-th gravity partial stress will inevitably cause further damage to the soil, under the action of the corresponding gravity partial stress increment σ1−3ijp, its deformation modulus Eij will continue to change accordingly, assuming the soil element at this time. The stress-strain relationship obeys the Duncan-Chang model, where Eij is used as the initial tangent modulus of the model, and the tangent modulus of the Duncan-Chang model curve is the deformation modulus of the soil after the increase of the weight and deflection stress when the deflection stress is σ1−3ijp. Through the above two steps, the deformation modulus of the i layer of soil can be obtained after the j gravity volumetric stress and deviatoric stress. The specific calculation method is as follows:According to formula (1), the deformation of the soil under the action of the j gravity partial stress increment σ1−3ijp is
(19)ε1−3ijp=aσ1−3ijp1−bσ1−3ijp,(20)ε3ijp=−με1−3ijp,where
(21)a=1Eij,(22)b=Rf1−sinφ2ccosφ+2σ3ijpsinφ.The relationship between the deformation modulus Eij of the i layer of soil before and after the j gravity partial stress increase σ1−3ijp is
(23)Eij=Eii−11−Dijp,where
(24)Dijp=1−e−m1−2μ+n1+με1−2ijp.From this, it can be seen that using formulas (17) and (23) to calculate the initial modulus of each soil layer is an iterative process. The specific calculation steps are as follows:
(1)
Give the initial deformation modulusEi0 and Poisson’s ratio μ at the zero-stress level of the i layer of soil(2)
From formulas (10) to (14), the first-layer gravity volumetric stress ε3i1v and the gravity partial stress σ1−3ilp of the i layer of soil are calculated. Calculate the vertical strain ε3i1v under the gravity volumetric stress σ3i1v from equation (16)(3)
From equations (17) and (18), the change value Ei1 of the deformation modulus of the i layer soil caused by the gravity volumetric stress σ3i1v at the first level can be obtained(4)
Taking the deformation modulusEi1 as the initial modulus before the gravity partial stress σ1−3ilp, the vertical strain ε1−3ilp under the gravity partial stress σ1−3ilp is calculated from equations (19) to (22)(5)
Calculate the deformation modulusEi1 of the i layer soil after acting on the first-level gravity partial stress σ1−3ilp from equations (23) and (24)(6)
Return to Step (2); continue to calculate the deformation modulus of thei layer soil under the influence of various levels of loads, until the deformation modulus EiN of the soil after the N layer gravity stress loading is obtained; and calculate it as the additional stress settlement initial modulusThe following will further study the calculation method of foundation settlement analysis.


## 3.3. Settlement Calculation Steps

This paper believes that the total settlement of the foundation should be divided into the sum of the settlement caused by additional volume stress and the settlement caused by additional deviatoric stress, that is, the sum of the compression layerssi′ and si″ in the settlement model established earlier. The consolidation deformation calculation steps have been completed for analysis and calculation.Meanwhile, Boussinesq’s stress solution is introduced to obtain the vertical stress and lateral stress caused by the additional stress in the soil of thei layer. The corresponding additional volume stress and additional deviator stress are σ3i and σ1i−σ3i, respectively. The deformation of the i layered soil is si′ and si″. The solution process is as follows:
(1)
The soft clay foundation compressed soil layer is divided intoNi layers, the thickness of each layer is di, and the initial deformation modulus Ei0 and Poisson ratio μ of each compressed layered soil are given(2)
The final change value of the deformation modulusEiN caused by the soil damage caused by the gravity stress of the compressive layered soil of the soft clay in Section 3.2 was calculated by the method in Section 3.2, and EiN was used as the initial modulus of the settlement calculation of the i layer soil(3)
Let the number of additional stress loadings beM and the load at each stage be pi. The additional volume stress σ3i1v and the additional deviatoric stress σ1−3ilp of the i layer of foundation soil under the action of the first-stage additional load pi can be obtained from Boussinesq’s solution(4)
LetEi0 denote the initial modulus of the foundation soil of the i layer, that is, Ei0=EiN, as the strain ε3i1v and deformation modulus Ei1 of the foundation soil of the i layer after the action of the first-level load σ3i1v can be obtained by formulas (16)–(18)(5)
TakingEi1 as the initial modulus before the second-stage loading, the strain σ1−3ilp and deformation modulus Ei1 of the i layer soil after the action of the first-stage additional deviatoric stress σ1−3ilp are obtained by equations (22) to (26)(6)
Multiplying the strain of each soil layer under the first-level additional stress by the thickness of the corresponding layer is the total settlement of the soft clay foundation under the first-level additional stress:(25)s1=∑i=1Nisi1′+si1″=∑i=1Niε3i1v+ε1−3i1pdi.(7)
According to the above steps, we continue to calculate the strain, deformation modulus, and total settlement of each soil layer of the foundation under theM-level additional stress(8)
The total settlement is obtained by superimposing the settlement of each soil layer under theM-level additional stress:(26)s=∑j=1Msj.


## 4. Illustrative Example

In order to verify the accuracy and rationality of the method proposed in this paper, the parameters collected in this paper based on the experimental data of Zhanjiang clay [21] are shown in Table 1, and ea=0.81, εb=0.26, and the surface load is 300 kPa, divided into 6 Add 50 kPa per day for stage loading to calculate the settlement and deformation of the foundation under the strip foundation, as shown in Figure 2.Table 1
Parameters for calculation.
Soil layerPoisson’s ratio,μUnit weight,γ (kN·m-3)Cohesion, C (kPa)Friction angle,φ (°)Initial porosity,e0Initial deformation modulus,E0 (MPa)Zhanjiang clay0.3817.33623.51.453.4Figure 2
Diagram of soil layers under strip foundation.Using the above data to calculate the settlement using this method, the specific process is as follows:(1)
When the additional stressσzi and average gravity stress σczi of the i layer soil satisfy σzi/σczi≤0.1, the calculated total thickness of the compression layer can be determined to be 6.4 m, and the layer thickness can be determined according to di≤0.4b (b as the basic width), which is 0.4 m for each layer (total 16 layers)(2)
Calculate the gravity stressesσ1ic and σ3ic of each soil layer in the compression layer range and divide them into 5 levels of loading, that is, N=5(3)
Determine the additional stressesσ1iz and σ3iz of each compression layer under the upper load of each stage(4)
According to the calculation method steps of Section3.2, the total settlement of the foundation soil is 17.53 cmThe calculation results are compared with the results in reference [21], as shown in Table 2.Table 2
Calculating results.
Calculation methodSettlement (cm)Measured settlement (cm)Method by Reference [21]15.015.16This study17.5315.16It can be found in Table2 that the method in this paper agrees well with the actual measured values of the project. The damage mechanics model considering the damage process of clay structures established in [21] has developed a corresponding finite element program for calculation. Nine parameters need to be determined by confined and unconfined compression tests of undisturbed soil. Therefore, the settlement calculation method proposed in this paper has more engineering practical value.


## 5. Conclusions

Based on the consideration of soft clay structure, this paper discusses the deformation mechanism of soft clay foundation in depth. Based on Hooke’s law, the Duncan-Zhang model, and the step loading method, and considering the structural characteristics of soft clay, which considers the structure of the soil itself and the calculation method of the weak and soft foundation settlement, the following conclusions are obtained:(1)
A new method for determining the deformation modulus of soft clay considering damage evolution is proposed, which provides new ideas for establishing a new method for calculating nonlinear settlement of soft clay(2)
Based on the deformation mechanism of soft clay foundation, a calculation method of soft clay settlement based on Hook’s law and the Duncan-Zhang model is established. This method requires few parameters and provides engineering survey reports. It does not need to be determined by experiments and can provide reference for engineering practice(3)
Through comparative analysis with a certain engineering example, the calculation accuracy of the settlement calculation method proposed in this paper can meet the actual engineering requirements, and it has certain rationality and feasibility(4)
Though the new method has its advantages, the Duncan-Zhang model is still an elastic model with variable modulus based on incremental generalized Hooke’s law, which cannot comprehensively reflect the complex characteristics of soft clay, especially the creep property. Moreover, the settlement of soft clay in practical engineering is affected by many comprehensive factors, especially geological factors. Thus, the proposed method in this paper should be modified with engineering experience



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