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Derivation of the work expression and discussion on the effective principle and the phase separation theorem in unsaturated soil

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Science China(Technological Sciences) 2008年第9期51卷 1530-1541页

作者： zhao chenggang ZHANG XueDong School of Civil Engineering and Architecture Beijing Jiaotong UniversityBeijing 100044China

Based on the balance equations for mass, linear momentum, energy in porous media theory and some hypotheses in unsaturated soil mechanics, an expression of the total deformation work W is derived, and with the help of the specific ex-pression of the work, the effective stress conjugated with the displacement of the soil skeleton is suggested by the authors, which has the similar form as the expressions proposed by Wheeler (2003) and some other researchers according to their experience and intuition, but the effective stress presented in this paper is derived on the basis of porous media theory and its assumptions, whose premise and hypothesis are clear. It is also pointed out that due to the complexity of the physical mechanism and various influencing factors, it is impossible in unsatu-rated soil mechanics to determine the deformation of solid skeleton by the effective stress only, like in the saturated soil mechanics. Besides, by using the expression of the deformation work and the free energy Aα for each phase, the applicability of the Phase Separation Principle proposed by Passman (1984) in unsaturated soil is discussed, and it is considered that the principle should not strictly apply to un-saturated soil mechanics.

关键词： total deformation work effective stress unsaturated soil Phase Separation Principle porous media theory

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

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Acta Mechanica Solida Sinica 2006年第2期19卷 141-151页

作者： zhao chenggang Dong Jun Gao Fuping School of Civil Engineering and Architecture Beijing Jiaotong University Beijing 100044 China Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

关键词： Biot's dynamic theory three-dimensional scattering hemispherical alluvial valley,analytical solution

A nonlinear multi-field coupled model for soils

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Science China(Technological Sciences) 2011年第5期54卷 1300-1314页

作者： CAI GuoQing zhao chenggang LIU Yan LI Jian Department of Geotechnique School of Civil Engineering and Architecture Beijing Jiaotong University Beijing 100044 China

A nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory. The balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multi-constituent elastic-plastic solid skeleton (which is different from the linearization method) and viscous liquid and ideal gas. With reasonable constitutive assumptions in such restrictive conditions as the principles of determinism, equipresence, material frame-indifference and the compatible principle in continuum mechanics, a theoretical framework of constitutive relations modeling three-phase soil in both non-equilibrium and equilibrium states is established, thus the closed field equations are formed. In the theoretical framework, the concept of effective generalized thermodynamic forces is introduced, and the nonlinear coupling constitutive relations between generalized dissipation forces and generalized flows within the system at nonequilibrium state are also presented. On such a basis, four special coupling relations, i.e., solid thermal elastic-plastic constitutive relation, liquid visco-elastic-plastic constitutive relation, the generalized Fourier’s law, and the generalized Darcy’s law are put forward. The generalized or nonlinear results mentioned above can degenerate into the linear coupling results given by Bennethum and Singh. Based on a specific dissipation function, the concrete form of generalized Darcy’s law is deduced, which may degenerate into the traditional form of Darcy’s law by neglecting the influence of skeleton deformation and temperature. Without considering temperature and other coupling effects, the nonlinear coupled model in this paper can degenerate into a soil elastic-plastic constitutive model.

关键词： multi-field coupled model for soils hybrid mixture theory non-linear multi-constituent

A DUAL-SURFACE DAMAGE MODEL AND EVALUATION FOR NATURAL SOILS WITHIN THE THERMOMECHANICAL FRAMEWORK

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Acta Mechanica Solida Sinica 2008年第1期21卷 85-94页

作者： Xuan Guo chenggang zhao Dajun Yuan Mengshu Wang Tunnel and Underground of Engineering Experienmental Research Center Beijing Jiaotong University Beijing 100044 China School of Civil Engineering ＆ Architecture Beijing Jiaotong University Beijing 100044 China

Naturally deposited or residual soils exhibit more complicated behavior than remolded clays. A dual-surface damage model for structured soils is developed based on the thermodynamics framework established in our first paper. The shift stresses and the transformation between the generalized dissipative stress space and actual stress space are established following a systematic procedure. The corresponding constitutive behavior of the proposed model is determined, which reflects the internal structural configuration and damage behavior for geomaterials. Four evolution variables κj^i（i=D, R;j=V, S） and the basic parameters λ, s, v and e0 are introduced to account for the progressive loss of internal structure for natural clays. A series of fully triaxial tests and isotropic compression tests are performed for structured and reconstituted samples of Beijing and Zhengzhou natural clays. The validation of the proposed model is examined by comparing the numerical results with the experimental data.

关键词： dual-surface damage model triaxial tests structured soils thermomechanical approach compressibility

A THERMOMECHANICAL DAMAGE APPROACH TO CONSTITUTIVE MODELS FOR RATE-INDEPENDENT DISSIPATIVE GEOMATERIALS

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Acta Mechanica Solida Sinica 2008年第1期21卷 73-84页

This paper builds the formulations of hyperplastic damage theory for rate-independent geomaterials to describe the bulk and the likely damage behavior of granular materials. Using 2 kinematic internal variables and the conjugates, dissipative and yield function can be reasonably introduced. A systematic constitutive presentation of 32 possible ways within the thermodynamical damage framework is presented, which entirely formulates the constitutive behavior through two scalar thermodynamic potentials. Combining the four common thermodynamical energy functions, two independent kinematic internal variables and the accordingly generalized stress are introduced to describe the damage behavior and structural rearrangement of the granules for any bulk deformation. A few Legendre transformations are used to establish the links between energy functions so that the complex incremental response of geomaterials can be entirely established from these four energy functions. The constitutive relations are built with the thermodynamics laws, which account for the important structural aspects of geomaterials. Some examples axe provided in the appendix to validate the applicability and implementation of the framework. This theory is based on previous work by Houlsby et al., and extends to the multi-mechanisms description. This framework paves a way in developing models for specific geomaterials with an examinable basis.

关键词： thermomechanical damage approach hyperplastic energy dissipation

Seismic responses of a hemispherical alluvial valley to SV waves: a three-dimensional analytical approximation

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Acta Mechanica Sinica 2006年第6期22卷 547-557页

作者： chenggang zhao Jun Dong Fuping Gao D.-S. Jeng School of Civil Engineering and Architecture Beijing Jiaotong University Beijing 100044 China Institute of Mechanics Chinese Academy of Sciences Beijing 100080 China School of Civil Engineering The University of Sydney Sydney NSW 2006 Australia

Abstract An analytical solution to the three-dimen-sional scattering and diffraction of plane SV-waves by a saturated hemispherical alluvial valley in elastic half-space is obtained by using Fourier-Bessel series expan-sion technique. The hemispherical alluvial valley with saturated soil deposits is simulated with Biot＇s dynamic theory for saturated porous media. The following conclusions based on numerical results can be drawn：（1） there are a significant differences in the seismic response simulation between the previous single-phase models and the present two-phase model; （2） the nor-malized displacements on the free surface of the alluvial valley depend mainly on the incident wave angles, the dimensionless frequency of the incident SV waves and the porosity of sediments; （3） with the increase of the incident angle, the displacement distributions become more complicated; and the displacements on the free surface of the alluvial valley increase as the porosity of sediments increases.

关键词： Biot's dynamic theory Saturated porous media Three-dimensional scattering Hemispherical alluvial valley

Strain-threshold- and frequency-dependent seismic simulation of nonlinear soils

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Earthquake Science 2014年第6期27卷 615-626页

作者： Duguo Wang chenggang zhao School of Civil Engineering Beijing Jiaotong University China Earthquake Disaster Prevention Center

A one-dimensional equivalent linear method （EQL） is widely used in estimating seismic ground response. For this method, the shear modulus and damping ratio of inelastic soil are supposed to be frequency independent. However, historical earthquake records and laboratory test results indicate that nonlinear soil behavior is frequency- dependent. Several frequency-dependent equivalent linear methods （FDEQL） related to the Fourier amplitude of shear strain time history have been developed to take into account the frequency-dependent soil behavior. Furthermore, the shear strain threshold plays an important role in soil behavior. For shear strains below the elastic shear strain threshold, soil behaves essentially as a linear elastic mate- rial. To consider the effect of elastic-shear-strain-threshold- and frequency-dependent soil behavior on wave propaga- tion, the shear-strain-threshold- and frequency-dependent equivalent linear method （TFDEQL） is proposed. A series of analyses is implemented for EQL, FDEQL, and TFDEQL methods. Results show that elastic-shear-strain-threshold- and frequency-dependent soil behavior plays a great influence on the computed site response, especially for the high- frequency band. Also, the effect of elastic-strain-threshold- and frequency-dependent soil behavior on the site response is analyzed from relatively weak to strong input motion, and results show that the effect is more pronounced as input motion goes from weak to strong.

关键词： Nonlinear soil behavior Strain threshold Frequency-dependent Site response

Spatio-temporal characteristics of strong aftershocks of the M_S8.0 Wenchuan earthquake

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Earthquake Science 2010年第3期23卷 215-221页

作者： Jisheng zhao Yanqiong Liu Zhenghua Zhou chenggang zhao School of Civil Engineering Beijing Jiaotong University Beijing 100044 China Institute of Engineering Mechanics China Earthquake Administration Harbin 150080 China

Based on Gutenberg-Richter＇s relation,Bath＇s law,Omori＇s law and Well＇s relation of rupture scale,this paper forecasts the temporal decay,total number,possible area and greatest magnitude of strong aftershocks（greater than or equal to M6.0） of the MS8.0 Wenchuan earthquake by using the magnitude and statistical parameters of earthquakes in California area of *** number of strong aftershocks,the parameters of Gutenberg-Richter＇s relation and the modified form of Omori＇s law are validated based on the relocation data of aftershock sequence of the MS8.0 Wenchuan ***,the spatio-temporal characteristics and wave energy release of the strong aftershocks（M≥6.0） are *** result shows that strong aftershocks may occur at the end of local drop and sharp drop on the wave energy release curve.

关键词： Wenchuan earthquake strong aftershock wave energy release statistic of aftershocks

Volume change behavior of unsaturated soils under non-isothermal conditions

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Chinese Science Bulletin 2011年第23期56卷 2495-2504页

作者： CAI GuoQing zhao chenggang LIU Yan LI Jian Department of Geotechnical and Geoenvironmental Engineering School of Civil Engineering and Architecture Beijing Jiaotong UniversityBeijing 100044 China

With the development of modern geotechnical engineering practices such as the construction of high level radioactive waste repositories, exploitation and utilization of geothermal resources, energy-saving buildings and underground storage of CO 2 , research into the influence of temperature on the basic mechanical properties of unsaturated soils has become an important issue internationally. By using the work expression and considering the influence of temperature on the basic properties of unsaturated soils, the average soil skeleton stress, modified suction and temperature were selected as state variables of generalized forces in thermodynamics and the soil skeleton strain, saturation and entropy were chosen as state variables of generalized flows conjugate to the variables of generalized forces. Based on the nonlinear multi-field coupled model and by using existing experimental results, an elastic-plastic constitutive model of unsaturated soils under non-isothermal conditions was developed to analyze the influence of temperature on the deformation properties of unsaturated soils. The model was used to predict and analyze the influence of suction and temperature on the deformation properties of unsaturated soils under isotropic conditions, and was successfully verified using experimental results.

关键词：非饱和土非等温条件高放射性废物处置库弹塑性本构模型行为体积状态变量耦合模型