The semi-analytical solutions to Fredlund and Hasan's one-dimensional (1D) consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the ...The semi-analytical solutions to Fredlund and Hasan's one-dimensional (1D) consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations (PDFs), which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pres- sures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are con- ducted on the pore-air and pore-water pressures at different ratios (the air permeability coefficient to the water permeability coefficient) and depths.展开更多
Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution ...Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.展开更多
This paper describes a quasi 3-D finite element model of the groundwater flow in two -aquifer system which is constructed from a sequence of aquifer flow equations coupled by leakage terms representing flow through th...This paper describes a quasi 3-D finite element model of the groundwater flow in two -aquifer system which is constructed from a sequence of aquifer flow equations coupled by leakage terms representing flow through the aquitard . It is applied to evaluate the maximum rate of groundwater resources exploited from the coastal aquifer without seawater intrusion . The main task in this model is to determine the drainage boundary of the aquifer extending under the sea . The information of the boundary can be obtained from the fluctuations of the groundwater level caused by sea-tide fluctuations . A new idea, Equivalent Drainage Boundary (EDB), is proposed and the corresponding methods , determining the EDB, are developed with tidal fluctuations data observed in boreholes . The quasi 3-D model and the methods determining EDB have been applied to the aquifer system of Beihai peninsula , Guangxi Autonomous Region of China for calculating the available groundwater resources .展开更多
An analytical solution is derived from the generalized governing equations of equal-strain consolidation with vertical drains under multi-ramp surcharge preloading. The hydraulic boundary conditions at both top and bo...An analytical solution is derived from the generalized governing equations of equal-strain consolidation with vertical drains under multi-ramp surcharge preloading. The hydraulic boundary conditions at both top and bottom of the consolidating soil are modelled as impeded drainage. The impeded drainage is described by using the third type boundary condition with a characteristic factor of drainage efficiency. Fully drained and undrained boundary conditions can also be modelled by applying an infinite and a zero characteristic factor, respectively. Simultaneous radial and vertical flow conditions are considered, together with the effects of drain resistance and smear. An increase in total stress due to multi-ramp loading is reasonably modelled as a function of both time and depth. A solution to calculate excess pore-water pressure at any arbitrary point in soil is derived, and the overall average degree of consolidation is obtained. It shows that the proposed solution can be used to analyze not only vertical-drain consolidation but also one-dimensional consolidation under either one-way or two-way vertical drainage conditions. The characteristic factors of drainage efficiency of top and bottom boundaries have a potentially important influence on consolidation. The boundary may be considered fully drained when the characteristic factor is greater than 100 and fully undrained when the characteristic factor is less than 0.1. The stress distribution along depth induced by the surcharge loading has a limited effect on the overall average degree of consolidation.展开更多
The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundar...The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.展开更多
This paper presents the one-dimensional(1D)viscoelastic consolidation system of saturated clayey soil under continuous drainage boundaries.The fractional-derivative Merchant(FDM)model has been introduced into the cons...This paper presents the one-dimensional(1D)viscoelastic consolidation system of saturated clayey soil under continuous drainage boundaries.The fractional-derivative Merchant(FDM)model has been introduced into the consolidation system to simulate the viscoelasticity.Swartzendruber’s flow law is also introduced to describe the non-Darcian flow characteristics simultaneously.The generalized numerical solution of the 1D consolidation under continuous boundaries is given by the finite difference scheme.Furthermore,to illustrate the effectiveness of the numerical method,two simplified cases are compared against the current analytical and numerical results.Finally,the effects of boundary parameters and model parameters on the viscoelastic consolidation were illustrated and discussed.The results indicated that the boundary parameters have a significant influence on consolidation.The larger the values of boundary parameters,the faster the whole dissipation of the excess pore-water pressure and soils’settlement rate.Fractional-order and viscosity parameter have little effect on consolidation,which are primarily significant in the middle and late consolidation phases.With the increase of the modulus ratio,the whole consolidation process becomes faster.Moreover,considering Swartzendruber’s flow delays the consolidation rate of the soil layer.展开更多
On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method o...On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.展开更多
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con...We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.展开更多
In response to the existing consolidation theory for stone column composite foundations which cannot consider the time-dependent loading and the well resistance effect of stone columns under time-dependent boundaries,...In response to the existing consolidation theory for stone column composite foundations which cannot consider the time-dependent loading and the well resistance effect of stone columns under time-dependent boundaries,a consolidation model that can reflect these characteristics is developed in this study,and the corresponding analytical solutions are obtained under permeable top surface with permeable bottom surface(PTPB)and permeable top surface with impermeable bottom surface(PTIB),respectively.In addition,the reliability of the proposed solutions is verified by comparing them with existing analytical solutions.Extensive calculations are then performed by the proposed solutions to analyze the consolidation behaviors of stone column composite foundations under time-dependent boundaries,the results show that the interface parameters have a large effect on the distribution of excess pore water pressure(EPWP)along the depth;for projects with longer construction time,the permeability of the top and bottom surfaces of the composite foundation has a smaller effect on the average consolidation rate.Finally,the proposed solution is applied to the settlement calculation in an actual engineering project,and the theoretical results show a general agreement with the measured data by considering the influence of the interface parameters.展开更多
Pressure transient analysis has been used to evaluate performance of a well located between one sealing fault and one constant pressure boundary. Type curves were generated by determining 1) dimensionless pressure and...Pressure transient analysis has been used to evaluate performance of a well located between one sealing fault and one constant pressure boundary. Type curves were generated by determining 1) dimensionless pressure and 2) rate of change of dimensionless pressure drop with respect to dimensionless time. When the well is located closer to the no flow boundary, both sets of type curves have three distinct slopes. These slopes characterize: 1) flow in an infinite reservoir, 2) presence of the no flow, and 3) the constant-pressure boundaries. When the well is closer to the constant pressure boundary, the type curves show two distinct slopes. These correspond to: 1) flow in an infinite reservoir, and 2) the presence of a constant pressure boundary. The type curves can be used to match actual pressure drawdown data and determine the drainage area and relative well location with respect to physical boundaries.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.41630633 and11672172)
文摘The semi-analytical solutions to Fredlund and Hasan's one-dimensional (1D) consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations (PDFs), which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pres- sures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are con- ducted on the pore-air and pore-water pressures at different ratios (the air permeability coefficient to the water permeability coefficient) and depths.
基金Projects(51678547,41672296,51878634,51878185,41867034)supported by the National Natural Science Foundation of China。
文摘Following the assumptions proposed by MESRI and ROKHSAR,the one-dimensional nonlinear consolidation problem of soil under constant loading is studied by introducing continuous drainage boundary.The numerical solution is derived by using finite difference method and its correctness is assessed by comparing with existing analytical and numerical solutions.Based on the present solution,the effects of interface parameters,stress ratios(i.e.,final effective stress over initial effective stress,N_(σ))and the ratio c_(c)/c_(k)of compression index to permeability index on the consolidation behavior of soil are studied in detail.The results show that,the characteristics of one-dimensional nonlinear consolidation of soil are not only related to c_(c)/c_(k)and N_(σ),but also related to boundary conditions.In the engineering practice,the soil drainage rate of consolidation process can be designed by adjusting the values of interface parameters.
文摘This paper describes a quasi 3-D finite element model of the groundwater flow in two -aquifer system which is constructed from a sequence of aquifer flow equations coupled by leakage terms representing flow through the aquitard . It is applied to evaluate the maximum rate of groundwater resources exploited from the coastal aquifer without seawater intrusion . The main task in this model is to determine the drainage boundary of the aquifer extending under the sea . The information of the boundary can be obtained from the fluctuations of the groundwater level caused by sea-tide fluctuations . A new idea, Equivalent Drainage Boundary (EDB), is proposed and the corresponding methods , determining the EDB, are developed with tidal fluctuations data observed in boreholes . The quasi 3-D model and the methods determining EDB have been applied to the aquifer system of Beihai peninsula , Guangxi Autonomous Region of China for calculating the available groundwater resources .
基金Project(51278171)supported by the National Natural Science Foundation of ChinaProject(B13024)supported by Program of Introducing Talents of Discipline to Universities("111" Project),ChinaProject(2014B04914)supported by the Fundamental Research Funds for the Central Universities of China
文摘An analytical solution is derived from the generalized governing equations of equal-strain consolidation with vertical drains under multi-ramp surcharge preloading. The hydraulic boundary conditions at both top and bottom of the consolidating soil are modelled as impeded drainage. The impeded drainage is described by using the third type boundary condition with a characteristic factor of drainage efficiency. Fully drained and undrained boundary conditions can also be modelled by applying an infinite and a zero characteristic factor, respectively. Simultaneous radial and vertical flow conditions are considered, together with the effects of drain resistance and smear. An increase in total stress due to multi-ramp loading is reasonably modelled as a function of both time and depth. A solution to calculate excess pore-water pressure at any arbitrary point in soil is derived, and the overall average degree of consolidation is obtained. It shows that the proposed solution can be used to analyze not only vertical-drain consolidation but also one-dimensional consolidation under either one-way or two-way vertical drainage conditions. The characteristic factors of drainage efficiency of top and bottom boundaries have a potentially important influence on consolidation. The boundary may be considered fully drained when the characteristic factor is greater than 100 and fully undrained when the characteristic factor is less than 0.1. The stress distribution along depth induced by the surcharge loading has a limited effect on the overall average degree of consolidation.
基金Project supported by the National Natural Science Foundation of China (No. 12002195)the National Science Fund for Distinguished Young Scholars (No. 12025204)the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)。
文摘The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.
基金Projects(51879104,52078206)supported by the National Natural Science Foundation of China。
文摘This paper presents the one-dimensional(1D)viscoelastic consolidation system of saturated clayey soil under continuous drainage boundaries.The fractional-derivative Merchant(FDM)model has been introduced into the consolidation system to simulate the viscoelasticity.Swartzendruber’s flow law is also introduced to describe the non-Darcian flow characteristics simultaneously.The generalized numerical solution of the 1D consolidation under continuous boundaries is given by the finite difference scheme.Furthermore,to illustrate the effectiveness of the numerical method,two simplified cases are compared against the current analytical and numerical results.Finally,the effects of boundary parameters and model parameters on the viscoelastic consolidation were illustrated and discussed.The results indicated that the boundary parameters have a significant influence on consolidation.The larger the values of boundary parameters,the faster the whole dissipation of the excess pore-water pressure and soils’settlement rate.Fractional-order and viscosity parameter have little effect on consolidation,which are primarily significant in the middle and late consolidation phases.With the increase of the modulus ratio,the whole consolidation process becomes faster.Moreover,considering Swartzendruber’s flow delays the consolidation rate of the soil layer.
文摘On the basis of Terzaghi's one-dimensional consolidation theory, the variation of effective stress ratio in layered saturated soils with impeded boundaries under time-dependent loading was studied. By the method of Laplace transform, the solution was presented. Influences of different kinds of cyclic loadings and impeded boundaries conditions were discussed. Through numerical inversion of Laplace transform, useful illustrations were given considering several common time-dependent loadings. Pervious or impervious boundary condition is just the special case of the problem considered here. Compared with average index method,the results from the method illustrated are more accurate.
基金supported by the NSFC(12071413)the Guangxi Natural Sci-ence Foundation(2023GXNSFAA026085)the European Union's Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No.823731 CONMECH。
文摘We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems.
基金supported by the National Natural Science Foundation of China(Grant No.51878320).
文摘In response to the existing consolidation theory for stone column composite foundations which cannot consider the time-dependent loading and the well resistance effect of stone columns under time-dependent boundaries,a consolidation model that can reflect these characteristics is developed in this study,and the corresponding analytical solutions are obtained under permeable top surface with permeable bottom surface(PTPB)and permeable top surface with impermeable bottom surface(PTIB),respectively.In addition,the reliability of the proposed solutions is verified by comparing them with existing analytical solutions.Extensive calculations are then performed by the proposed solutions to analyze the consolidation behaviors of stone column composite foundations under time-dependent boundaries,the results show that the interface parameters have a large effect on the distribution of excess pore water pressure(EPWP)along the depth;for projects with longer construction time,the permeability of the top and bottom surfaces of the composite foundation has a smaller effect on the average consolidation rate.Finally,the proposed solution is applied to the settlement calculation in an actual engineering project,and the theoretical results show a general agreement with the measured data by considering the influence of the interface parameters.
文摘Pressure transient analysis has been used to evaluate performance of a well located between one sealing fault and one constant pressure boundary. Type curves were generated by determining 1) dimensionless pressure and 2) rate of change of dimensionless pressure drop with respect to dimensionless time. When the well is located closer to the no flow boundary, both sets of type curves have three distinct slopes. These slopes characterize: 1) flow in an infinite reservoir, 2) presence of the no flow, and 3) the constant-pressure boundaries. When the well is closer to the constant pressure boundary, the type curves show two distinct slopes. These correspond to: 1) flow in an infinite reservoir, and 2) the presence of a constant pressure boundary. The type curves can be used to match actual pressure drawdown data and determine the drainage area and relative well location with respect to physical boundaries.