Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading          下载免费PDF全文

L. Wang  D. A. Sun  A. F. Qin  Y. F. Xu 《国际地质力学数值与分析法杂志》2017,41(16):1636-1655

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

Torsional dynamic response of a large‐diameter pipe pile in viscoelastic saturated soil     

Changjie Zheng  Hanlong Liu  Xuanming Ding  Yaru Lv 《国际地质力学数值与分析法杂志》2014,38(16):1724-1743

An analytical solution is developed in this paper to investigate the dynamic response of a large‐diameter end‐bearing pipe pile subjected to torsional loading in viscoelastic saturated soil. The wave propagation in saturated soil and pile are simulated by Biot's two‐phased linear theory and one‐dimensional elastic theory, respectively. The dynamic equilibrium equations of the outer soil, inner soil, and pile are established. The solutions for the outer and inner soils in frequency domain are obtained by Laplace transform technique and the separation of variables method. Then, the dynamic response of the pile is obtained on the basis of the perfect contacts between the pile and the outer soil as well as the inner soil. The results in this paper are compared with that of a solid pile in elastic saturated soil to verify the validity of the solution. Furthermore, the solution in this paper is compared with the classic plane strain solution to verify the solution further and check the accuracy of the plane strain solution. Numerical results are presented to analyze the vibration characteristics and illustrate the effect of the soil parameters and the geometry size of the pile on the complex impedance and velocity admittance of the pile head. Finally, the displacement of the soil at different depth and frequency is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

An analytical solution for deforming twin‐parallel tunnels in an elastic half plane          下载免费PDF全文

Jinyang Fu  Junsheng Yang  Li Yan  Syed Muntazir Abbas 《国际地质力学数值与分析法杂志》2015,39(5):524-538

The interaction between twin‐parallel tunnels affects the tunnelling‐induced ground deformation, which may endanger the nearby structures. In this paper, an analytical solution is presented for problems in determining displacements and stresses around deforming twin‐parallel tunnels in an elastic half plane, on the basis of complex variable theory. As an example, a uniform radial displacement was assumed as the boundary condition for each of the two tunnels. Special attention was paid to the effects of tunnel depth and spacing between the two tunnels on the surface movement to gain deep insight into the effect of the interaction between twin‐parallel tunnels using the proposed analytical approach. It is revealed that the influence of twin tunnel interaction on surface movements diminishes with both the increase of the tunnel depth and the spacing between the two tunnels. The presented analytical solution manifests that, similar to most of the existing numerical results, the principle of superposition can be applied to determine ground deformation of twin‐parallel tunnels with a certain large depth and spacing; otherwise, the interaction effect between the two tunnels should be taken into account for predicting reliable ground movement. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

Displacement analytical prediction of shallow tunnel based on unified displacement function under slope boundary     

Fanchao Kong  Dechun Lu  Xiuli Du  Chenpeng Shen 《国际地质力学数值与分析法杂志》2019,43(1):183-211

For slope condition of ground surface, the asymmetrical deformation about the vertical center line and the horizontal center line of the tunnel cross section can be formed. A unified displacement function expressed by the Fourier series is presented to express the asymmetrical deformation of the tunnel cross section. Five basic deformation modes corresponding to the expansion order 2 are a complete deformation mode to reflect deformation behaviors of the tunnel cross section under slope boundary. Such this complete displacement mode is implemented into the complex variable solution for analytically predicting tunneling-induced ground deformation under slope boundary. All of these analytical solutions are verified by good agreements of the comparison between the analytical solutions and finite element method results. A parameter study is carried out to investigate the influence of deformation modes of the tunnel cross section, geometrical conditions of the tunnel and the slope angle, and “Buoyancy effect” on the displacement field. Finally, the proposed method is consistent with measured data of the Hejie tunnel in China qualitatively. The presented solution can provide a simplified indication for evaluating the ground deformation under slope condition of ground surface.  相似文献   

A multidirectional semi‐analytical method for analysis of laterally loaded pile groups in multi‐layered elastic strata          下载免费PDF全文

F.S. Tehrani  M. Prezzi  R. Salgado 《国际地质力学数值与分析法杂志》2016,40(12):1730-1757

A semi‐analytical method for calculating the response of single piles and pile groups subjected to lateral loading is developed in this paper. Displacements anywhere in the soil domain are tied to the displacements of the piles through decay functions. The principle of virtual work and the calculus of variations are used to derive the governing differential equations that describe the response of the piles and soil. The eigenvalue method and the finite difference technique are used to solve the system of coupled differential equations for the piles and soil, respectively. The proposed method takes into account the soil surface displacement along and perpendicular to the loading direction and produces displacement fields that are very close to those produced by the finite element method but at lower computational effort. Compared with the previous method that considered only the soil displacement along the loading direction, accounting for the multi‐directional soil displacement field produces responses for the piles and soil that are closer to those approximated by the finite element method. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

Groundwater mixing between different aquifer types in a complex structural setting discerned by elemental and stable isotope geochemistry          下载免费PDF全文

Dorina Murgulet  Marlon Cook  Valeriu Murgulet 《水文研究》2016,30(3):410-423

Karst aquifers are well known for their intricate stratigraphy and geologic structures, which make groundwater characterization challenging because flowpaths and recharge sources are complex and difficult to evaluate. Geochemical data, collected from ten closely spaced production wells constructed in two karst aquifers (Bangor Limestone (Mb) and Tuscumbia Limestone/Fort Payne Chert (Mftp)) in Trussville, north‐central Alabama, illustrate two distinctive groundwater end‐members: (1) higher major ion, dissolved inorganic carbon, conductivity, alkalinity concentrations, heavier δ¹³C ratios (max: −10.2 ± 0.2‰ Vienna Pee Dee Belemnite (PDB)) and lower residence times (mean: 19.5 ± 2 years, n = 2) of groundwater in the Mb aquifer and (2) lower constituent concentrations, lighter δ¹³C ratios (min: −13.4 ± 0.2‰ PDB) and longer residence times of groundwater (mean: 23.6 ± 2 years, n = 4) in the Mftp aquifer. Summer and fall data and the binary mixing model show aquifer inter‐flow mixing along solution fractures and confirms the distinctive groundwater geochemistry of the two aquifers. Lowering of static water levels over the summer (drawdown from 2 to 5.2 m) leads to more reducing groundwater conditions (lower Eh values) and slightly enriched δ¹⁸O and δD ratios during the fall [δ¹⁸O: −4.8 ± 0.1 to −5.4 ± 0.1‰ Vienna Standard Mean Oceanic Water (VSMOW), n = 9; δD: −25.4 ± 1 to −27.4 ± 1‰ VSMOW, n = 9] when compared with summer season samples (δ¹⁸O: −5.1 ± 0.1 to −5.7 ± 0.1‰ VSMOW, n = 11; δD: −25.0 ± 1 to −30.6 ± 1‰ VSMOW, n = 11). GIS analyses confirm the localized origin of recharge to the investigated aquifers. The combination of GIS, field parameters and geochemistry analyses can be successfully used to identify recharge sources, evaluate groundwater flow and transport pathways and to improve understanding of how groundwater withdrawals impact the sustainability and susceptibility to contamination of karst aquifers. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

An analytical study on three‐dimensional versus two‐dimensional water table‐induced flow patterns in a Tóthian basin          下载免费PDF全文

Jun‐Zhi Wang  Xiao‐Wei Jiang  Zhi‐Yuan Zhang  Li Wan  Xu‐Sheng Wang  Hailong Li 《水文研究》2017,31(22):4006-4018

Although it has been increasingly acknowledged that groundwater flow pattern is complicated in the three‐dimensional (3‐D) domain, two‐dimensional (2‐D) water table‐induced flow models are still widely used to delineate basin‐scale groundwater circulation. However, the validity of 2‐D cross‐sectional flow field induced by water table has been seldom examined. Here, we derive the analytical solution of 3‐D water table‐induced hydraulic head in a Tóthian basin and then examine the validity of 2‐D cross‐sectional models by comparing the flow fields of selected cross sections calculated by the 2‐D cross‐sectional model with those by the 3‐D model, which represents the “true” cases. For cross sections in the recharge or discharge area of the 3‐D basin, even if head difference is not significant, the 2‐D cross‐sectional models result in flow patterns absolutely different from the true ones. For the cross section following the principal direction of groundwater flow, although 2‐D cross‐sectional models would overestimate the penetrating depth of local flow systems and underestimate the recharge/discharge flux, the flow pattern from the cross‐sectional model is similar to the true one and could be close enough to the true one by adjusting the decay exponent and anisotropy ratio of permeability. Consequently, to determine whether a 2‐D cross‐sectional model is applicable, a comparison of hydraulic head difference between 2‐D and 3‐D solutions is not enough. Instead, the similarity of flow pattern should be considered to determine whether a cross‐sectional model is applicable. This study improves understanding of groundwater flow induced by more natural water table undulations in the 3‐D domain and the limitations of 2‐D models accounting for cross‐sectional water table undulation only.  相似文献   

Steady‐state analytical solutions of flow and deformation coupling due to a point sink within a finite fluid‐saturated poroelastic layer          下载免费PDF全文

P. Li  K. Wang  G. Fang  D. Lu 《国际地质力学数值与分析法杂志》2017,41(8):1093-1107

An exact steady‐state closed‐form solution is presented for coupled flow and deformation of an axisymmetric isotropic homogeneous fluid‐saturated poroelastic layer with a finite radius due to a point sink. The hydromechanical behavior of the poroelastic layer is governed by Biot's consolidation theory. Boundary conditions on the lateral surface are specifically chosen to match the appropriate finite Hankel transforms and simplify the transforms of the governing equations. Ordinary differential equations in the transformed domain are solved, and then the analytical solutions in the physical space for the pore pressure and the displacements are finally obtained by using finite Hankel inversions. The analytical solutions at some special locations such as the top and bottom surfaces, lateral surface, and the symmetrical axis are given and analyzed. And a case study for the consolidation of a water‐saturated soft clay layer due to pumping is conducted. The analytical solution is verified against the finite element solution. Meanwhile, an analysis of coupled hydromechanical behavior is carried out herein. The presented analytical solution is an exact solution to the practical poroelastic problem within an axisymmetric finite layer. It can provide us a better understanding of the poroelastic behavior of the finite layer due to fluid extraction. Besides, it can be applied to calibrate numerical schemes of axisymmetric poroelasticity within finite domains. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

电感耦合等离子体质谱法测定铅合金中的微量杂质元素镉和锡   总被引：1，自引：1，他引：0  

郝原芳  刘新  宋丽华  李丽君  徐英奎 《岩矿测试》2016,35(4):378-383

铅合金中的镉和锡由于含量较低,国家标准方法均为单一元素分析,步骤繁琐,检出限高,难以达到理想的检出要求。本文建立了应用电感耦合等离子体质谱法(ICP-MS)测定铅合金中微量级(μg/g级)杂质元素镉和锡的分析方法。采用单一的低浓度硝酸溶解铅合金,用低温慢溶的方式使样品溶解更加完全,减少了多离子对仪器的干扰;通过铅基体匹配和加入酒石酸保证了标准与样品介质的一致性,同时避免了锡的水解;以~(103)Rh作为内标元素,~(111)Cd和~(118)Sn作为测量同位素克服了质谱干扰。方法检出限为镉0.05 ng/g、锡0.04 ng/g,比国家标准方法的检出限(1~6μg/g)低,精密度小于4%。该方法试剂用量少,减少了处理样品的复杂性,实现了合金中微量级元素的准确测定。  相似文献   

利用LA-ICP-MS在16 μm和10 μm激光束斑条件下测定独居石U-Th-Pb年龄     

汪双双  韩延兵  李艳广  魏小燕  靳梦琪  程秀花 《岩矿测试》2016,35(4):349-357

我国锂钾主要矿产资源大多分布在西部偏远地区,其勘查找矿或综合利用迫切需要现场快速分析技术的支持。本文介绍了自行开发的便携式Li-K分析仪的主要性能及其在锂辉石中锂的分析应用。Li-K分析仪是一种基于大气压的液体阴极辉光放电光谱仪,以待测液体为放电阴极,实现样品中Li、K等元素的原子化和激发。该仪器以光纤传导CCD光谱仪作为检测器,其波长范围为345～1015 nm,分辨率3 nm;以Li 670.78 nm和K 769.90 nm分析谱线,在最佳仪器工作条件下测定Li、K的精密度（RSD,n=14）均低于2%,检出限为0.03 μg/mL,检测范围0.1～10 μg/mL。研究表明,不同酸度和酸的类型对谱线强度影响较大,且存在显著的样品基体效应,标准曲线法分析锂辉石中Li的结果偏差高达267%;而标准加入法可克服基体效应的影响,获得与ICP-OES一致性较好的分析结果,为现场开展固体样品中Li的测定奠定了基础。  相似文献