Viscosity effect on consolidation of poroelastic soil due to groundwater table depression

In this study, the viscosity effect on consolidation of poroelastic soil due to groundwater table depression is examined. A viscoelastic consolidation numerical model is developed to conduct this examination. By nondimensionalizing the governing equations the viscosity number that depends on hydraulic conductivity, viscous moduli, and thickness of soil is obtained to represent the viscosity effect on consolidation of poroelastic soil. The case of clay stratum sandwiched between sandy strata subjected to sudden and gradual groundwater table depressions is used to investigate the importance of viscosity effect to poroelastic consolidation. The results show that the displacement and pore water pressure of clay stratum are strongly related to the viscosity effect. The overestimation of soil displacement will occur if the viscosity effect is neglected. Hence, the viscosity effect needs to be considered in modeling consolidation of poroelastic soil under groundwater table depression.     

高层建筑荷载引发地面沉降与隆起变形三维数值模拟

针对地下水埋深较浅地区,由高层建筑荷载引起的土体变形问题,以比奥固结理论为基础,结合土体非线性流变理论,将土体本构关系推广到黏弹塑性;同时考虑土体力学参数及水力参数的动态变化关系,建立了高层建筑荷载引发地面沉降与隆起变形的三维有限元数值模型,详细研究了高层建筑荷载影响下的土体变形特征及此过程中土体力学参数及水力学参数的变化特征。结果表明：由高层建筑荷载引起的地面沉降呈现漏斗状,以建筑物中心为漏斗中心,高层建筑荷载施加初期,高层建筑周围出现隆起,到达最大值后隆起逐渐消失;高层建筑底部浅层土体孔隙度、渗透系数及泊松比均呈现缓慢减小趋势,弹性模量呈现缓慢增大趋势;而高层建筑周围浅层土体的孔隙度、渗透系数及泊松比呈现先增大后减小的变化趋势,弹性模量则呈现先减小后增大的变化趋势;高层建筑影响区域浅部土体参数的变化趋势与土体的回弹及压缩有关。     

Effects of body force on transient poroelastic consolidation due to groundwater pumping

By applying linear poro-elasticity theory, the body force effect on steady soil consolidation, i.e., settlement, caused by constant water table depression due to groundwater pumping was investigated. The result shows that when the soil is soft or thick, or both, neglecting the body force effect can lead to severe underestimation of soil displacement and incremental effective stress. However, the transient response of soil consolidation was not analyzed. In addition, the water table depression due to groundwater pumping in fact varies with time. In this study, the body force effect on transient consolidation of soil subjected to variable water table depression is further examined. A poroelastic consolidation numerical model is developed herein to conduct this examination.     

Evaluation of deformation parameter for deep excavation in sand through case histories

This study back analyzed deformation parameters of in situ sand through two excavation case histories in Kaohsiung, Taiwan. Two main features are highlighted; deformation prediction based on monitoring data at the first excavation stage and in situ Young’s modulus evaluation for sand considering monitoring data at the overall excavation stages. The former tends to establish a reliable method to predict the wall deflection at the critical stage based on the data at the first stage and the latter to enrich the limited database of Young’s modulus correlation for sand, specifically applicable for deep excavations analysis. The two constitutive models, linear elastic perfectly plastic and non-linear stress–strain constitutive models, were selected. The stiffness parameters of the models were discretely distributed along the subdivided soil body mesh to reflect the effect of overburden pressure on the in situ soil. In addition, relationship between Standard Penetration Test value (SPT-N value) and Young’s modulus and relationships for estimating the in situ Young’s modulus of the Kaohsiung sand as a function of depth were evaluated. The results greatly enhanced a framework for estimating the in situ Young’s modulus of sand.     

考虑土体非线性的CCSG桩复合地基固结解

混凝土芯砂石桩（CCSG）桩复合地基是一种新型多元复合地基。通过引入地基土体的e-lgσ和e-lgk对数模型,考虑地基土体固结过程中压缩模量和渗透系数非线性变化的特征,推导出基于等应变假设的CCSG桩复合地基非线性固结解析解,且现有的考虑土体非线性的砂井固结解和碎石桩复合地基固结解均是文中解的特例。根据该解析解得到桩土模量比、土体压缩指数与渗透指数比、荷载增量等无量纲参数变化时,CCSG桩复合地基的固结度曲线。分析结果表明,按应力和按变形定义的两种固结度不相等,通常按变形定义的固结速度较快;土体压缩模量和渗透系数的非线性变化对固结影响较大。最后通过和由实测数据获得的固结度曲线对比,验证了解析解的正确性。     

注浆体对土钉受力特性的影响研究

基于土钉抗拔力学模型的解析解,结合现场土钉抗拉试验工程实测数据,分析了水泥注浆体弹性模量Eg及钉土剪切变形系数K的变化对土钉受拉力学特性的影响。结果表明,随着Eg的增大,最大荷载下钉头位移逐渐减小,浅部钉土间相对位移和剪力有所减小,而深部则有所增大。Eg越大,钉土间相对位移和剪力沿钉身的变化越小,各部分侧阻分布趋于均匀。随着K的增大,最大荷载下土钉沿钉长各处的相对位移均减小,且减小比率逐渐降低,注浆对土钉的影响逐渐趋弱。相同变化率下K对土钉荷载-位移曲线的影响要大于Eg,而对钉土间剪力的影响则不及Eg的影响大。     

Three-dimensional finite element modelling for consolidation due to groundwater withdrawal in a desaturating anisotropic aquifer system

A poroelastic numerical model is presented to evaluate three-dimensional consolidation due to groundwater withdrawal from desaturating anisotropic porous media. This numerical model is developed based on the fully coupled governing equations for groundwater flow in deforming variably saturated porous media and the Galerkin finite element method. Two different cases of unsaturated aquifers are simulated for the purpose of comparison: a cross-anisotropic soil aquifer, and a corresponding isotropic soil aquifer composed of a geometrically averaged equivalent material. The numerical simulation results show that the anisotropy has a significant effect on the shapes of three-dimensional hydraulic head distribution and displacement vector fields. Such an effect of anisotropy is caused by the uneven partitioning of the hydraulic pumping stress between the vertical and horizontal directions in both groundwater flow field and solid skeleton deformation field. Copyright © 1999 John Wiley & Sons, Ltd.     

Group interaction on vertically loaded piles in saturated poroelastic soil

The pile-to-pile interaction was obtained for vertically loaded piles embedded in homogeneous poroelastic saturated soil. Deduced from Biot’s theory, the fundamental functions of the quasi-static development for the force, displacement and pore pressure were acquired in cylindrical coordinates. The pile–soil system was decomposed into extended soil and fictitious piles, and the compatibility condition was set up between the axial strain of the fictitious piles and the corresponding average strain over the extended soil. This approach results in the governing equations, which consist of the Fredholm integral equations of the second kind and the basic unknowns of the axial forces along the fictitious pile shaft. The axial force and settlement along the pile shaft were calculated based on the axial forces of the fictitious piles. The interaction between the piles was investigated under different consolidation conditions through a two-pile model, and two pile interaction factors were obtained. Stemming from the two-pile analysis, numerical analyses on the settlement of the pile groups were conducted to probe pile interaction with consolidation. The conventional solutions for the single-phase soil-pile problem seem to underestimate the interaction factor if the consolidation effect is taken into account as pile settlement continues. The pile-to-pile interaction can also aggravate the percentage of consolidation settlement (PCS), and as the pile number increases, the value of the PCS will also increase. Several key factors, such as the pile stiffness, pile slenderness ratio and pile spacing, are investigated to better understand the impact of consolidation on pile analysis.     

Observed Behaviour of Laterally Expanded Stone Column in Soft Soil

The paper describes the behavior of remolded kaolin clay reinforced by stone column as investigated in laboratory. The installation of stone column was simulated by performing lateral expansion at different rates within hollow cylindrical remolded kaolin specimens initially subjected to K0 consolidation path. These specimens were, then, subjected to classical consolidated undrained triaxial tests while recording excess pore pressure values. The objective of the experimental programme was to quantify the effects of consolidation stress and stone column on the undrained Young’s modulus and shear strength of kaolin clay. Obtained results showed a significant improvement in Young’s modulus when the cavity expansion ratio and the consolidation stress increase. It was also found that the increase in undrained shear strength of improved kaolin clay mainly occurred at lower consolidation stress. Another important finding of this study is that the ratio of undrained Young’s modulus to undrained shear stress increases when the consolidation stress decreases. Finally, the paper presents a model developed for the design of stone columns.     

自钻式原位剪切旁压模型不同固结荷载颗粒流数值试验

自钻式原位剪切旁压仪具有扰动小,能同时测出不同深度土的变形和强度参数,在精确测定土体参数方面具有广阔的应用前景。然而,目前受分析手段与研究水平的限制,对SBISP多级加载过程中周围土体的变形响应研究较少,而土体变形参数的确定与其变形机制是密切相关的。基于此,应用PFC3D颗粒流程序对不同固结荷载SBISP模型进行了仿真数值试验,试验结果表明:随着剪应力的逐级施加,中间区域颗粒的位移量不断增大,且位移矢量方向性更加显著,在第5级剪应力作用下,影响区域位移矢量形状呈现为倒锥形;而随着上覆固结压力的增大,探头周围试样的受影响范围逐渐变小;在探头作用下球颗粒的运动轨迹呈台阶状,台阶形态随距探杆中心距离增大而趋于平缓,球颗粒的Z向位移量亦随之呈负指数形式衰减;此外,剪应力与探头摩擦系数呈正相关关系,但当摩擦系数达到某一阈值时,剪应力-位移曲线不再变化。其研究成果对于深入开展SBISP试验多级加载过程中影响域内土体变形过程与变形模量之间关系研究具有重要启迪意义。     

软土固结试验数值模拟

基于太沙基一维固结理论,采用有限差分法对室内固结试验进行了数值分析,编制了室内固结试验的C++数值程序和自动求解固结系数的Matlab拟合程序,该程序能够模拟不同尺寸（排水高度）软土试样的固结过程。讨论了试样尺寸、渗透系数和初始固结应力对模拟结果的影响。数值结果显示随着排水高度和渗透系数的增加,由时间平方根法和时间对数法求解的固结系数比不断减小,且排水高度较小时固结系数比变化较快。土体初始应力越小,主固结完成所需的时间越长。与日本广岛重塑土大尺寸试样固结试验结果进行了比较分析。研究结果表明所采用的数值方法能够较好地模拟软土的固结试验过程,可以进行一定条件下大尺寸软土试样的固结特性研究,研究成果对于揭示软土的固结变形发展有一定的理论价值和实际意义。     

Effect of Model Scale and Particle Size Distribution on PFC3D Simulation Results

This paper investigates the effect of model scale and particle size distribution on the simulated macroscopic mechanical properties, unconfined compressive strength (UCS), Young’s modulus and Poisson’s ratio, using the three-dimensional particle flow code (PFC3D). Four different maximum to minimum particle size (d _max/d _min) ratios, all having a continuous uniform size distribution, were considered and seven model (specimen) diameter to median particle size ratios (L/d) were studied for each d _max/d _min ratio. The results indicate that the coefficients of variation (COVs) of the simulated macroscopic mechanical properties using PFC3D decrease significantly as L/d increases. The results also indicate that the simulated mechanical properties using PFC3D show much lower COVs than those in PFC2D at all model scales. The average simulated UCS and Young’s modulus using the default PFC3D procedure keep increasing with larger L/d, although the rate of increase decreases with larger L/d. This is mainly caused by the decrease of model porosity with larger L/d associated with the default PFC3D method and the better balanced contact force chains at larger L/d. After the effect of model porosity is eliminated, the results on the net model scale effect indicate that the average simulated UCS still increases with larger L/d but the rate is much smaller, the average simulated Young’s modulus decreases with larger L/d instead, and the average simulated Poisson’s ratio versus L/d relationship remains about the same. Particle size distribution also affects the simulated macroscopic mechanical properties, larger d _max/d _min leading to greater average simulated UCS and Young’s modulus and smaller average simulated Poisson’s ratio, and the changing rates become smaller at larger d _max/d _min. This study shows that it is important to properly consider the effect of model scale and particle size distribution in PFC3D simulations.     

Consolidation in spatially random unsaturated soils based on coupled flow‐deformation simulation

This paper integrates random field simulation of soil spatial variability with numerical modeling of coupled flow and deformation to investigate consolidation in spatially random unsaturated soil. The spatial variability of soil properties is simulated using the covariance matrix decomposition method. The random soil properties are imported into an interactive multiphysics software COMSOL to solve the governing partial differential equations. The effects of the spatial variability of Young's modulus and saturated permeability together with unsaturated hydraulic parameters on the dissipation of excess pore water pressure and settlement are investigated using an example of consolidation in a saturated‐unsaturated soil column because of loading. It is found that the surface settlement and the pore water pressure profile during the process of consolidation are significantly affected by the spatially varying Young's modulus. The mean value of the settlement of the spatially random soil is more than 100% greater than that of the deterministic case, and the surface settlement is subject to large uncertainty, which implies that consolidation settlement is difficult to predict accurately based on the conventional deterministic approach. The uncertainty of the settlement increases with the scale of fluctuation because of the averaging effect of spatial variability. The effects of spatial variability of saturated permeability k_sat and air entry parameters are much less significant than that of elastic modulus. The spatial variability of air entry value parameters affects the uncertainties of settlement and excess pore pressure mostly in the unsaturated zone. Copyright © 2016 John Wiley & Sons, Ltd.     

Response of Euler–Bernoulli beam on spatially random elastic soil

A new method is developed for analysis of flexible foundations (beams) on spatially random elastic soil. The elastic soil underneath the beams is treated as a continuum, characterized by spatially random Young’s modulus and constant Poisson’s ratio. The randomness of the soil Young’s modulus is modeled using a two-dimensional non-Gaussian, homogeneous random field. The beam geometry and Young’s modulus are assumed to be deterministic. The total potential energy of the beam-soil system is minimized, and the governing differential equations and boundary conditions describing the equilibrium configuration of the system are obtained using the variational principles of mechanics. The differential equations are solved using the finite element and finite difference methods to obtain the beam and soil displacements. Four different beam lengths, representing moderately short, moderately long and long beams are analyzed for beam deflection, differential settlement, bending moment and beam shear force. The statistics of the beam responses are investigated using Monte Carlo simulations for different beam-soil modulus ratios and for different variances and scales of fluctuations of the soil Young’s modulus. Suggestions regarding the use of the analysis in design are made. A novelty in the analysis is that the two-dimensional random heterogeneity of soil is taken into account without the use of traditional two-dimensional numerical methods, which makes the new approach computationally efficient.     

外荷载作用下软土压缩模量的动态演化规律研究

在软土地基的压缩性评价和变形计算中,压缩模量是一个重要的土性参数,目前一般是通过室内侧限压缩试验曲线得到,通常是一个常数。实际上,压缩模量在地基固结过程中会随着土体固结度的增加而逐渐增大,因此,探讨外荷载作用下软土压缩模量的变化规律显得十分必要。以珠江三角洲地区某高速公路代表性软土地基为研究对象,采集天然状态和超载预压后两种状态的淤泥质土样,分别开展不同压力条件下的室内固结试验,通过分析比较两种状态土样的试验数据,得出了两种状态下淤泥质土压缩模量随压力变化的定量关系和压缩模量随压力及时间演化的规律。在此基础上,结合天然状态和超载预压后的淤泥质土样在室内再压缩前后的微观结构图像,分析了两种状态下淤泥质土压缩模量随压力和时间演化的机理。从而为软土变形计算的参数合理取值提供了有用的参考,且对软基堆载预压过程中控制加荷速率和分级荷载的大小具有重要的现实意义。     

地下水渗流与地面沉降耦合模拟

为了准确模拟由地下水开采导致渗流场和应力场发生变化而引起的地面沉降问题,根据Terzaghi有效应力原理,建立了地下水三维渗流与一维垂向固结的地下水渗流与地面沉降耦合数值模拟模型和以比奥固结理论为基础,并结合土体非线性流变理论,将土体本构关系推广到粘弹塑性,同时考虑土体力学参数及水力参数的动态变化关系的地下水渗流与地面沉降三维全耦合数值模拟模型.通过对比分析,结果表明:基于Terzaghi有效应力原理建立的地下水三维渗流与一维垂向固结地下水渗流与地面沉降耦合数值模拟模型模拟所得地面沉降与地下水位呈现出同步变化的趋势,并且当地下水位逐步回升至初始水位时,地面沉降也逐步回升到初始的零沉降状态.而以比奥固结为基础建立的地下水渗流与地面沉降三维全耦合数值模拟模型模拟所得的地面沉降变化趋势滞后于地下水位的变化趋势,并且当地下水位逐步回升至初始水位时,地面沉降虽也逐步得到回升,但回不到初始的零沉降状态,存在一个永久的残余沉降量.在土体参数变化方面,土体的孔隙度、渗透系数及泊松比均呈现先减小后增大的变化趋势,而弹性模量则呈现先增大后减小的变化趋势,与地面沉降的变化相对应.      

BEM analysis of the interaction factor for vertically loaded dissimilar piles in saturated poroelastic soil

This paper focuses on an analysis by the boundary element method (BEM) of the pile-to-pile interaction for pile groups with dissimilar piles of different pile lengths embedded in saturated poroelastic soil. The behaviour of the poroelastic homogeneous soil is governed by Biot’s consolidation equations. The pile–soil system is decomposed into extended soil and fictitious piles. Considering the compatibility of vertical strain between fictitious piles and soil, the second kind of Fredholm integral equations were obtained to predict the axial force and settlement along pile shafts numerically. For the analysis of the interaction factor, two loading conditions for a two-dissimilar-pile system were proposed: (a) only one pile is loaded and (b) each pile is subjected to a load proportional to the pile length. Furthermore, the two-pile system was extended to pile groups with a rigid cap to capture the optimum design where each pile shares the same loading at the pile heads. The optimum results require shortening the peripheral piles and elongating internal piles, and the consolidation effect needs to be considered due to the adjustment of loading distribution among piles.     

Numerical simulation of crack propagation in layered formations

In the present study, a boundary element method based on the higher order displacement discontinuity formulation is presented to solve the general problem of hydraulic fracture propagation in layered formations. Displacement collocation technique is employed to model the higher order displacement variation along the crack and the special crack tip element near its ends. The hydraulic fracture propagation and its interaction with the layer interface in non-homogenous rock materials are studied by the proposed semi-analytical (hybridized boundary element-boundary collocation) method. The maximum tangential stress criterion (or σ-criterion) of fracture mechanics considering different elastic constants (Young modulus and Poisson’s ratio) is used to obtain the fracture path. The fracture propagation from stiff to soft and soft to stiff media for cracks having different inclination angles is modeled, and the effects of elastic constants on the hydraulic fracture propagation is studied. The results show that if the hydraulic fracture originates in the stiffer layer, its capability to cross the layer increases and is vice versa for the softer material. The comparison of the results gained from the numerical method with those in the literature show a good performance of the method in the case of propagation of hydraulic fracture in layered formations.     

Modulus of subgrade reaction that varies with magnitude of displacement of cohesionless soil

Modulus of subgrade reaction is one of the required design parameters in any structural analyses of shallow foundations. However, the constant values of modulus of subgrade reaction that are determined from either from literature studies or the results of plate load tests, regardless of magnitude of soil’s displacement under design loads, have been used in structural designs of foundations. In this study, the results of 43 published full-scale field plate load tests in cohesionles soils were gathered to expose any variation in the values of modulus of subgrade reaction as soil’s displacement increases. Extensive finite element (FE) analyses were carried out while the results of FE analyses were compared with actual measured results of field load tests. The results of analyses indicated that both the modulus of subgrade reaction decrease with increase in magnitude of displacement of soils and internal forces of a design of structural frame is higher with the values of modulus of subgrade reaction that are sensitive to soil’s displacement are implemented into analyses. Therefore, structural dimensions of any structure with the constant values of modulus of subgrade reaction would not be a precise engineering solution.     

Effects of mechanical layering on hydraulic fracturing in shale gas reservoirs based on numerical models

Generally, induced hydraulic fractures are generated by fluid overpressure and are used to increase reservoir permeability through forming interconnected fracture systems. However, in heterogeneous and anisotropic rocks, many hydraulic fractures may become arrested or offset at layer contacts under certain conditions and do not form vertically connected fracture networks. Mechanical layering is an important factor causing anisotropy in sedimentary layers. Hence, in this study, with a shale gas reservoir case study in the Longmaxi Formation in the southeastern Chongqing region, Sichuan Basin, we present results from several numerical models to gain quantitative insights into the effects of mechanical layering on hydraulic fracturing. Results showed that the fractured area caused by hydraulic fracturing indicated a linear relationship with the neighboring layer’s Young’s modulus. An increase of the neighboring layer’s Young’s modulus resulted in better hydraulic fracturing effects. In addition, the contact between two neighboring layers is regarded as a zone with thickness and mechanical properties, which also influences the effects of hydraulic fracturing in reservoirs. The initial hydraulic fracture was unable to propagate into neighboring layers under a relatively low contact’s Young’s modulus. When associated local tensile stresses exceeded the rock strength, hydraulic fractures propagated into neighboring layers. Moreover, with the contact’s Young’s modulus becoming higher, the fractured area increased rapidly first, then slowly and finally became stable.