Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading

Xie, Kang; Tian, Qinghua; Dong, Ya Qin

doi:10.1631/jzus.2006.a1358

Cited by 26 publications

(22 citation statements)

References 7 publications

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“…Favaretti and Soranzo [13] derived solutions for common types of cyclic loadings. However, soil's constitutive relationships are actually nonlinear [10,14]. The coefficient of compressibility decreases with increasing effective stress.…”

Section: Shock and Vibrationmentioning

confidence: 99%

“…It is well known that when the duration time of the maximum loading phase is 0, the trapezoidal cyclic loading will be transformed into the triangle cyclic loading. However, when the duration time of loading and unloading phase is 0, the trapezoidal cyclic loading will be transformed into the rectangular cyclic loading [10]. Therefore, this paper will discuss the trapezoidal cyclic loading as a result of its flexibility.…”

Section: Introductionmentioning

confidence: 99%

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Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

Cheng

Wang

Chen

et al. 2017

Shock and Vibration

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For one-dimensional (1D) nonlinear consolidation, the governing partial differential equation is nonlinear. This paper develops the finite analytic method (FAM) to simulate 1D nonlinear consolidation under different time-dependent loading and initial conditions. To achieve this, the assumption of constant initial effective stress is not considered and the governing partial differential equation is transformed into the diffusion equation. Then, the finite analytic implicit scheme is established. The convergence and stability of finite analytic numerical scheme are proven by a rigorous mathematical analysis. In addition, the paper obtains three corrected semianalytical solutions undergoing suddenly imposed constant loading, single ramp loading, and trapezoidal cyclic loading, respectively. Comparisons of the results of FAM with the three semianalytical solutions and the result of FDM, respectively, show that the FAM can obtain stable and accurate numerical solutions and ensure the convergence of spatial discretization for 1D nonlinear consolidation.

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Section: Shock and Vibrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

Cheng

Wang

Chen

et al. 2017

Shock and Vibration

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“…He and Jiang (2009) proposed a hyperbolic prediction model that reflects the semicubic nonlinear relationship between the settlement rate and the remaining settlement. In addition, in the study of one-dimensional nonlinear consolidation theory, Davis and Raymond (1965), Barden and Berry (1965), and Xie et al (2006) considered the physical non-linear characteristics of soil based on the relation elgσ ′ . However, the value of the initial consolidation pressure is crucial to the calculation of the foundation settlement by the e -lgσ ′ model.…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

et al. 2020

Front. Earth Sci.

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Initial stress and additional effective stress distributions in soil greatly influence the degree of ground consolidation when calculating one-dimensional soft clay ground consolidation in deep soil. The one-dimensional non-linear consolidation governing equations of soft ground under uniform load are derived and solved with the finite difference method. This method is based on the assumptions that the initial stress in soil varies with the ground depth and that the additional effective stress caused by external loads changes with both the ground depth and consolidation time and the hyperbolic model of the soil stress-strain relationship. Formulas for the degree of consolidation and the settlement of the ground are presented. A case study shows that the degree of consolidation in the ground calculated with the finite difference method agrees well with the traditional analytical solution, and the computational efficiency of the finite difference method can be effectively improved when the segmental calculation method is used throughout the consolidation process. The results of another example show that the settlement of the ground calculated with the finite difference method agrees with the in situ data. The suggested method can greatly simplify the consolidation calculation and has a high application value in engineering.

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“…Kim et al [6] investigated one-dimensional consolidation behavior of saturated clays under time-dependent loadings including haversine cyclic loading based on the lattice Boltzmann method. e latter mainly included the work by Baligh and Levadoux [7], Xie et al [8], Geng et al [9], Cai et al [10], Conte and Troncone [11], Toufigh and Ouria [12], Cheng et al [13], Hu et al [14], and Kim et al [15,16]. Baligh and Levadoux [7] and Toufigh and Ouria [12] analyzed one-dimensional nonlinear consolidation of inelastic clays under rectangular cyclic loading using the superimposing rule.…”

Section: Introductionmentioning

confidence: 99%

“…Baligh and Levadoux [7] and Toufigh and Ouria [12] analyzed one-dimensional nonlinear consolidation of inelastic clays under rectangular cyclic loading using the superimposing rule. Based on the nonlinear consolidation theory proposed by Davis and Raymond [17], Xie et al [8], Conte and Troncone [11], Cheng et al [13], and Kim et al [15] investigated onedimensional nonlinear consolidation of saturated soil subjected to various cyclic loadings. Hu et al [14] proposed a numerical method for modelling one-dimensional nonlinear consolidation of multilayer soil under various cyclic loadings based on the differential quadrature method.…”

Section: Introductionmentioning

confidence: 99%

One-Dimensional Consolidation Analysis of Unsaturated Soils under Cyclic Loadings

Kim¹,

Ri²,

Kim³

et al. 2020

Shock and Vibration

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This paper presents analytical solutions to Fredlund and Hasan’s one-dimensional consolidation equations for unsaturated soils subjected to various cyclic loadings. Two new variables are introduced so that the governing equations for excess pore air and water pressures can be transformed to a set of conventional diffusion equations. Based on the general solutions for two introduced variables, the analytical solutions are derived for one-dimensional consolidation of unsaturated soils under trapezoidal, rectangular, triangular, and haversine cyclic loadings. It shows through the degeneration into the existing solutions for unsaturated and saturated soils that the proposed solutions are more general ones for one-dimensional consolidation of soils from unsaturated to saturated states. A comprehensive parametric study is conducted to investigate the effects of different parameters on one-dimensional consolidation of unsaturated soils under various cyclic loadings. The proposed solutions can be effectively utilized in the analysis of consolidation of unsaturated soils subjected to various cyclic loadings.

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Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading

Cited by 26 publications

References 7 publications

Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

Finite Analytic Method for One-Dimensional Nonlinear Consolidation under Time-Dependent Loading

Finite Difference Method for the One-Dimensional Non-linear Consolidation of Soft Ground Under Uniform Load

One-Dimensional Consolidation Analysis of Unsaturated Soils under Cyclic Loadings

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