A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, F...A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.展开更多
Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics,...Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.展开更多
A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of La...A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.展开更多
In order to study deposited sediment settlement and consolidation mechanisms, sediment settlement experiments were conducted using a settlement column. Based on the experimental results, sediment settlement stage defi...In order to study deposited sediment settlement and consolidation mechanisms, sediment settlement experiments were conducted using a settlement column. Based on the experimental results, sediment settlement stage definition, excessive pore pressure （EPP） dissipation, and consolidation constitutive equations are discussed. Three stages, including the free settlement, hindered settlement, and self-weight consolidation settlement stages, are defined. The results of this study show that sediment settlement is mainly affected by the initial sediment concentration and initial settlement height, and the interface settlement rate is linearly attenuated with time on bilogarithmic scales during the hindered settlement and self-weight consolidation settlement stages. Moreover, the deposited sediment layer in the self-weight consolidation settlement stage experiences large strains, and the settlement amount in this stage is about 32% to 59% of the initial height of deposited sediment. EPP is nonlinearly distributed in the settlement direction, and consolidation settlement is faster than EPP dissipation in the self-weight consolidation settlement stage. Consolidation constitutive equations for the hydraulic conductivity and effective stress, applicable to large-strain consolidation calculation, were also determined and fitted in the power function form.展开更多
The Loess Plateau is one typical area of serious soil erosion in the world. China has implemented ′Grain for Green′(GFG) project to restore the eco-environment of the Loess Plateau since 1999. With the GFG project s...The Loess Plateau is one typical area of serious soil erosion in the world. China has implemented ′Grain for Green′(GFG) project to restore the eco-environment of the Loess Plateau since 1999. With the GFG project subsidy approaching the end, it is concerned that farmers of fewer subsidies may reclaim land again. Thus, ′Gully Land Consolidation Project′(GLCP) was initiated in 2010. The core of the GLCP was to create more land suitable for farming in gullies so as to reduce land reclamation on the slopes which are ecological vulnerable areas. This paper aims to assess the effect of the GLCP on soil erosion problems by studying Wangjiagou project region located in the central part of Anzi valley in the middle of the Loess Plateau, mainly using the revised universal soil loss equation(RUSLE) based on GIS. The findings show that the GLCP can help to reduce soil shipment by 9.87% and it creates more terraces and river-nearby land suitable for farming which account for 27.41% of the whole study area. Thus, it is feasible to implement the GLCP in places below gradient 15°, though the GLCP also intensifies soil erosion in certain places such as field ridge, village land, floodplain, natural grassland, and shrub land. In short, the GLCP develops new generation dam land and balances the short-term and long-term interests to ease the conflicts between economic development and environmental protection. Furthermore, the GLCP and the GFG could also be combined preferably. On the one hand, the GFG improves the ecological environment, which could offer certain safety to the GLCP, on the other hand, the GLCP creates more farmland favorable for farming in gullies instead of land reclamation on the slopes, which could indirectly protect the GFG project.展开更多
Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applie...Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Blot＇s consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that （1） the effect of the stress path should be taken into account in the simulation of the soil consolidation question; （2） this decoupling method can predict the evolvement of pore water pressure; （3） the settlement using cam-clay model is less than that using numerical model because of dilatancy.展开更多
Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reve...Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.展开更多
A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this as...A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying the same experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical calculating results based on finite element method is presented. The results of the comparison show that the analytical solution obtained here takes on better agreement with practical cases than that of linear one, and they also show that, compared with the solutions based on nonlinear theory, the settlement and the consolidation degree based on linear theory are smaller.展开更多
The problem of a rigid disk acting with normal force on saturated soil was studied using Biot consolidation theory and integral equation method and the Merchant model to describe the saturated soil rheology. Using int...The problem of a rigid disk acting with normal force on saturated soil was studied using Biot consolidation theory and integral equation method and the Merchant model to describe the saturated soil rheology. Using integral transform techniques, general solutions of Biot consolidation functions and the dual integral equations of a rigid disk on saturated soil were established based on the boundary conditions. These equations can be simplified using Laplace-Hankel and Abel transform methods. The numerical solutions of the integral equations, and the corresponding inversion transform were used to obtain the settlement and contact stresses of the rigid disk. Numerical examples showed that the soil settlement is small if only consolidation is considered, so the soil rheology must be taken into account to calculate the soil settlement. Numerical solution of Hankel inverse transform is also given in this paper.展开更多
The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the for...The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.展开更多
In this paper,we study a new finite element method for poroelasticity problem with homogeneous boundary conditions.The finite element discretization method is based on a three-variable weak form with mixed finite elem...In this paper,we study a new finite element method for poroelasticity problem with homogeneous boundary conditions.The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity,i.e.,the stress tensor,displacement and pressure are unknown variables in the weak form.For the linear elasticity formula,we use a conforming finite element proposed in[11]for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow.We will show that the newly proposed finite element method maintains optimal convergence order.展开更多
基金the National Natural Science Foundation of China (50578121)
文摘A new method is developed to solve Biot＇s consolidation of a finite soil layer in the cylindrical coordinate system. Based on the governing equations of Biot＇s consolidation and the technique of Laplace transform, Fourier expansions and Hankel transform with respect to time t, coordinate θ and coordinate r, respectively, a relationship of displacements, stresses, excess pore water pressure and flux is established between the ground surface （z = 0） and an arbitrary depth z in the Laplace and Hankel transform domain. By referring to proper boundary conditions of the finite soil layer, the solutions for displacements, stresses, excess pore water pressure and flux of any point in the transform domain can be obtained. The actual solutions in the physical domain can be acquired by inverting the Laplace and the Hankel transforms.
基金Project supported by the National Natural Science Foundation of China(Nos.51478435,11402150,and 11172268)
文摘Green＇s functions for Blot＇s dynamic equation in the frequency domain can be a highly useful tool for the investigation of dynamic responses of a saturated porous medium. Its applications are found in soil dynamics, seismology, earthquake engineering, rock mechanics, geophysics, and acoustics. However, the mathematical work for deriving it can be daunting. Green＇s functions have been presented utilizing an analogy between the dynamic thermoelasticity and the dynamic poroelasticity in the frequency domain using the u-p formulation. In this work, a special term ＂decoupling coefficient＂ for the decomposition of the fast and slow dilatational waves is proposed and expressed to present a new methodology for deriving the poroelastodynamic Green＇s functions. The correct- ness of the solution is demonstrated by numerically comparing the current solution with Cheng＇s previous solution. The separation of the two waves in the present methodology allows the more accurate evaluation of Green＇s functions, particularly the solution of the slow dilatational wave. This can be advantageous for the numerical implementation of the boundary element method （BEM） and other applications.
基金supported by the National Natural Science Foundation of China (No. 50578121)
文摘A new analytical method is presented to study the axisymmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axisymmetric Blot＇s consolidation, and based on the property of Laplace transform, the relation of basic variables for a point of a finite soil layer is established between the ground surface （z= 0） and the depth z in the Laplace and Hankel transform domains. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be obtained by inverse Laplace and Hankel transforms. A numerical analysis for the axisymmetric consolidation of a finite soil layer is carried out.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2009B13514)the Doctoral Fund of the Ministry of Education of China(Grant No.20100094110002)
文摘In order to study deposited sediment settlement and consolidation mechanisms, sediment settlement experiments were conducted using a settlement column. Based on the experimental results, sediment settlement stage definition, excessive pore pressure （EPP） dissipation, and consolidation constitutive equations are discussed. Three stages, including the free settlement, hindered settlement, and self-weight consolidation settlement stages, are defined. The results of this study show that sediment settlement is mainly affected by the initial sediment concentration and initial settlement height, and the interface settlement rate is linearly attenuated with time on bilogarithmic scales during the hindered settlement and self-weight consolidation settlement stages. Moreover, the deposited sediment layer in the self-weight consolidation settlement stage experiences large strains, and the settlement amount in this stage is about 32% to 59% of the initial height of deposited sediment. EPP is nonlinearly distributed in the settlement direction, and consolidation settlement is faster than EPP dissipation in the self-weight consolidation settlement stage. Consolidation constitutive equations for the hydraulic conductivity and effective stress, applicable to large-strain consolidation calculation, were also determined and fitted in the power function form.
基金Under the auspices of National Natural Science Foundation of China(No.41130748,41471143)
文摘The Loess Plateau is one typical area of serious soil erosion in the world. China has implemented ′Grain for Green′(GFG) project to restore the eco-environment of the Loess Plateau since 1999. With the GFG project subsidy approaching the end, it is concerned that farmers of fewer subsidies may reclaim land again. Thus, ′Gully Land Consolidation Project′(GLCP) was initiated in 2010. The core of the GLCP was to create more land suitable for farming in gullies so as to reduce land reclamation on the slopes which are ecological vulnerable areas. This paper aims to assess the effect of the GLCP on soil erosion problems by studying Wangjiagou project region located in the central part of Anzi valley in the middle of the Loess Plateau, mainly using the revised universal soil loss equation(RUSLE) based on GIS. The findings show that the GLCP can help to reduce soil shipment by 9.87% and it creates more terraces and river-nearby land suitable for farming which account for 27.41% of the whole study area. Thus, it is feasible to implement the GLCP in places below gradient 15°, though the GLCP also intensifies soil erosion in certain places such as field ridge, village land, floodplain, natural grassland, and shrub land. In short, the GLCP develops new generation dam land and balances the short-term and long-term interests to ease the conflicts between economic development and environmental protection. Furthermore, the GLCP and the GFG could also be combined preferably. On the one hand, the GFG improves the ecological environment, which could offer certain safety to the GLCP, on the other hand, the GLCP creates more farmland favorable for farming in gullies instead of land reclamation on the slopes, which could indirectly protect the GFG project.
文摘Elasto-plastic consolidation is one of the classic coupling questions in geomechanics. To solve this problem, an elasto-plastic constitutive model is derived based on the numerical modeling method. The model is applied to Blot＇s consolidation theory. Incremental governing partial differential equations are established using this method. According to the stress path, the decoupling condition of these equations is discussed. Based on these conditions, an incremental diffusion equation and uncoupling governing equations are presented. The method is then applied to numerical analyses of three examples. The results show that （1） the effect of the stress path should be taken into account in the simulation of the soil consolidation question; （2） this decoupling method can predict the evolvement of pore water pressure; （3） the settlement using cam-clay model is less than that using numerical model because of dilatancy.
文摘Differential equations of electromagnetic and similar physical fields are generally solved via antiderivative Green’s functions involving integration over a region and its boundary. Research on the Kasner metric reveals a variable boundary deemed inappropriate for standard anti-derivatives, suggesting the need for an alternative solution technique. In this work I derive such a solution and prove its existence, based on circulation equations in which the curl of the field is induced by source current density and possibly changes in associated fields. We present an anti-curl operator that is believed novel and we prove that it solves for the field without integration required.
文摘A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying the same experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical calculating results based on finite element method is presented. The results of the comparison show that the analytical solution obtained here takes on better agreement with practical cases than that of linear one, and they also show that, compared with the solutions based on nonlinear theory, the settlement and the consolidation degree based on linear theory are smaller.
文摘The problem of a rigid disk acting with normal force on saturated soil was studied using Biot consolidation theory and integral equation method and the Merchant model to describe the saturated soil rheology. Using integral transform techniques, general solutions of Biot consolidation functions and the dual integral equations of a rigid disk on saturated soil were established based on the boundary conditions. These equations can be simplified using Laplace-Hankel and Abel transform methods. The numerical solutions of the integral equations, and the corresponding inversion transform were used to obtain the settlement and contact stresses of the rigid disk. Numerical examples showed that the soil settlement is small if only consolidation is considered, so the soil rheology must be taken into account to calculate the soil settlement. Numerical solution of Hankel inverse transform is also given in this paper.
文摘The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot's equations for saturated porous media. The Darcy's laws of unsaturated soil were proved. It is shown that Biot's equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.
基金supported by the National Natural Science Foundation of China under Grant Nos.11501473,11426189 and the Fundamental Research Funds for the Central Universities of China(No.2682016CX108).
文摘In this paper,we study a new finite element method for poroelasticity problem with homogeneous boundary conditions.The finite element discretization method is based on a three-variable weak form with mixed finite element for the linear elasticity,i.e.,the stress tensor,displacement and pressure are unknown variables in the weak form.For the linear elasticity formula,we use a conforming finite element proposed in[11]for the mixed form of the linear elasticity and piecewise continuous finite element for the pressure of the fluid flow.We will show that the newly proposed finite element method maintains optimal convergence order.
