Analytical models for consolidation of combined composite ground improved by impervious columns and vertical drains

In recent years, a new technique of ground improvement, which involves the combined use of impervious column and vertical drains, has been proposed and utilized in many field projects to accelerate consolidation and increase bearing capacity of soft soil ground. To cover the possible distribution patterns of impervious columns and vertical drains, 2 analytical models, including Model A with outward flow and Model B with inward flow within the soils, are proposed to predict the consolidation of combined composite ground by considering the following factors: (1) disturbance effects of both impervious columns and vertical drains, (2) the well resistance of vertical drains, and (3) time‐variant loadings. The average degrees of consolidation predicted by the proposed analytical models are compared with several existing solutions and then against the measured data in the literature. The consolidation behavior of a combined composite ground is investigated by the proposed analytical solutions. The results show that the combined use of impervious columns and vertical drains can remarkably accelerate the consolidation rate of soft soils compared with the single use of either of them. The average degrees of consolidation predicted by both analytical models agree well with the measured data. Compared with Model B, Model A usually predicts a faster consolidation rate because of a shorter drainage path. Many factors can influence consolidation behavior of combined composite ground, such as loading scheme, distribution patterns and the disturbance effects of impervious columns and vertical drains, and compression modulus ratio of impervious column to soil.     

Production rate analysis of multiple-fractured horizontal wells in shale gas reservoirs by a trilinear flow model

Most multiple-fractured horizontal wells experience long-term linear flow due to the ultralow permeability of shale gas reservoirs. Considering the existence of natural fractures caused by compression and shear stresses during the process of tectonic movement or the expansion of high-pressure gas, a shale gas reservoir can be more appropriately described by dual-porosity medium. Based on the assumption of slab dual-porosity, this paper uses the trilinear flow model to simulate the transient production behavior of multiple-fractured horizontal wells in shale gas reservoirs, which takes the desorption of adsorbed gas, Knudsen diffusion and gas slippage flow in the shale matrix into consideration. Production decline curves are plotted with the Stehfest numerical inversion algorithm, and sensitivity analysis is done to identify the most influential reservoir and hydraulic fracture parameters. It was found that the density and permeability of the natural fracture network are the most important parameters affecting the production dynamics of multiple-fractured horizontal wells in shale gas reservoirs. The higher the density and permeability of the natural fractures are, the shorter the time is required to exploit the same amount of reserve, which means a faster investment payoff period. The analytical model presented in this paper can provide some insight into the reserve evaluation and production prediction for shale gas reservoirs.     

Analytical solution for the consolidation of a composite ground reinforced by partially penetrated impervious columns

Composite ground improved by partially penetrated impervious columns consists of a reinforced zone and an underlying stratum. Based on the axisymmetric consolidation model, the governing equations for the average excess pore water pressure were developed within the surrounding soil and the underlying untreated soil. The corresponding solutions were given on the basis of the consolidation theory of a double-layer subsoil ground, and the overall average degree of consolidation of the composite ground was obtained. The accuracy of the proposed solution was examined by FEM. The proposed solution and FEM results show a good match. A parametric analysis of consolidation behavior of the composite ground was then investigated. The results indicate that the consolidation rate of the composite ground strongly depends on the penetration ratio of the impervious columns (ratio of column length to soil thickness) in the way that the higher the ratio, the faster the consolidation rate. In addition, an increasing area replacement ratio of an impervious column decreases the consolidation rate. The consolidation rate of the composite ground decreases with the increasing of the constrained modulus ratio of an impervious column to its surrounding soil for a lower penetration ratio, while it increases with the increasing of the constrained modulus ratio for a higher penetration ratio.     

基于非牛顿指数描述的非达西渗流一维固结分析

基于非牛顿指数描述的非达西渗流定律,同时考虑地基内部竖向附加应力随深度线性变化以及变荷载的影响,建立了一维固结控制方程并应用有限差分法进行数值求解,同时对不同参数单级加荷下的固结性状进行分析。结果表明：基于非达西渗流比达西渗流下固结速率要慢,且渗流模型中非牛顿指数越大,土层的固结速率越慢;土层厚度越厚,固结速率越慢,因此,传统固结理论中室内土样与地基土层之间的相似关系不再成立;作用于土层的平均附加应力越大,土层的固结速率越快;在单面排水情况下,附加应力分布对土层固结速率有较大影响;相反,双面排水条件下土层固结速率与附加应力的分布是无关的;荷载的加荷速率越快,则土层的固结速率越快。最后,讨论了达西渗流计算固结变形的适用范围。     

A dual-porosity model considering the displacement effect for incompressible two-phase flow

The dual-porosity model is usually employed to simulate the flow in fractured reservoirs. However, its original form for the multiphase flow does not consider the displacement effect under macropressure gradient. Especially for the incompressible multiphase flow, it predicts zero transfer term between fracture and matrix, which is unreasonable. To improve this, a modified double-porosity model is proposed for incompressible two-phase flow, in which the displacement effect is considered and the corresponding shape factor is derived. For the anisotropic case, the shape factor of displacement depends upon the velocity direction. The accuracy and the efficiency of the proposed dual-porosity model are indicated through numerical tests.     

Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs

The state of the art of modeling fluid flow in shale reservoirs is dominated by dual-porosity models which divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano-pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual-porosity models and Darcy’s law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of the complex flow mechanisms occurring in these reservoirs. This paper presents a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three porosity systems: inorganic matter, organic matter (mainly kerogen), and natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of nano-pores and micro-pores in kerogen are incorporated into the simulator. The multiple-porosity model is built upon a unique tool for simulating general multiple-porosity systems in which several porosity systems may be tied to each other through arbitrary connectivities. This new model allows us to better understand complex flow mechanisms and eventually is extended into the reservoir scale through upscaling techniques. Sensitivity studies on the contributions of the different flow mechanisms and kerogen properties give some insight as to their importance. Results also include a comparison of the conventional dual-porosity treatment and show that significant differences in fluid distributions and dynamics are obtained with the improved multiple-porosity simulation.     

Simulation of multiphase flow in fractured reservoirs using a fracture-only model with transfer functions

We present a fracture-only reservoir simulator for multiphase flow: the fracture geometry is modeled explicitly, while fluid movement between fracture and matrix is accommodated using empirical transfer functions. This is a hybrid between discrete fracture discrete matrix modeling where both the fracture and matrix are gridded and dual-porosity or dual-permeability simulation where both fracture and matrix continua are upscaled. The advantage of this approach is that the complex fracture geometry that controls the main flow paths is retained. The use of transfer functions, however, simplifies meshing and makes the simulation method considerably more efficient than discrete fracture discrete matrix models. The transfer functions accommodate capillary- and gravity-mediated flow between fracture and matrix and have been shown to be accurate for simple fracture geometries, capturing both the early- and late-time average behavior. We verify our simulator by comparing its predictions with simulation results where the fracture and matrix are explicitly modeled. We then show the utility of the approach by simulating multiphase flow in a geologically realistic fracture network. Waterflooding runs reveal the fraction of the fracture–matrix interface area that is infiltrated by water so that matrix imbibition can occur. The evolving fraction of the fracture–matrix interface area turns out to be an important characteristic of any particular fracture system to be used as a scaling parameter for capillary driven fracture–matrix transfer.     

基于非达西渗流的软土一维非线性固结半解析解

在土中渗流遵循非达西渗流定律的前提下,考虑软土在固结过程中的非线性固结特性,根据饱和土体一维固结的连续条件,推导出基于非达西渗流的软土一维非线性固结控制方程。利用半解析方法对其进行求解,并与差分计算结果进行对比,验证半解析方法的可靠性。最后,着重分析非达西渗流与达西定律之间非线性固结性状的差别,以及不同自重应力分布方式对固结速率的影响。结果表明,考虑非达西渗流下的非线性固结速率比达西定律下要慢,且指数和临界水力坡降越大,非线性固结速率越慢。而且,作用的外荷载越小、地基土层越厚,非达西渗流下非线性固结速率的减慢愈明显。自重应力均匀分布下的非线性固结速率要比自重应力线性分布下慢,但随着荷载的增大、土层的变薄,两者之间的差别会越来越小。     

Nonlinear analysis of footings on granular bed–stone column improved soft soil

In this paper, a model for the analysis of footings having finite flexural rigidity resting on a granular bed on top of stone columns improved saturated soft (clayey) soil has been proposed. Soft soil has been modeled as a Kelvin–Voigt body to represent its time dependent behavior. Pasternak shear layer has been used to represent the granular layer and the stone columns have been idealized by means of nonlinear Winkler springs. Nonlinear behavior of granular fill, soft soil and stone columns has been invoked by means of hyperbolic constitutive relationships. Governing differential equations for the soil–foundation system have been obtained and finite difference method has been adopted for solving these, using the Gauss-elimination iterative scheme. Detailed parametric study for a combined footing has been carried out to study the influence of parameters, like magnitude of applied load, flexural rigidity of footing, diameter of stone column, spacing of stone column, ultimate bearing capacity of granular fill, poor foundation soil and stone column, relative stiffness of stone columns and degree of consolidation, on flexural response of the footing.     

增强型地热系统（EGS）的裂隙模拟方法

增强型地热系统（EGS）是在干热岩技术基础上提出来的一个清洁能源概念,水力压裂建立人工热储是开采地下干热岩热能的有效方法之一。利用TOUGH2系列软件对增强型地热系统进行模拟,具体介绍了对水压致裂过程中裂隙网络模拟的处理方法。裂隙中的水流可以采用不同的概念模型,最为常见的模型包括双空隙率、双渗透率、多重相互作用连续统一体（MINC）以及有效连续统一体（ECM）,这些模型明确了对离散的裂隙和基质的模拟方法。应根据基质的渗透性和裂隙的性质灵活地选择裂隙处理方法,也可将不同方法结合起来使用。提出了几种有效的混合模拟方案,对将来高温岩体地热开发具有重要意义。     

考虑起始坡降双层地基的大应变非线性固结

天然软土成层分布特性及土中渗流存在起始水力坡降的现象已被人们熟知。但变荷载下能同时考虑黏土中起始水力坡降、软土非线性压缩渗透特性及大应变特性的双层地基固结理论还鲜见报道。在拉格朗日坐标系中建立以超静孔压为变量的双层软土地基大应变非线性固结模型并给出其有限差分解。通过与考虑起始水力坡降的单层地基大应变非线性固结数值计算结果对比,验证了差分解的可靠性。着重分析了上、下土层起始坡降无量纲参数R1、R2对双层地基固结性状的影响,分析在大应变与小应变假定下双层地基超静孔压消散及固结沉降变形的异同。结果表明：上层土无量纲参数R1对双层地基固结性状的影响程度较下层土无量纲参数R2显著;大应变假定下双层地基渗流前锋的下移速度要快于小应变假定下的移动速度;大应变假定下考虑起始水力坡降的双层软土地基超静孔压消散速率要比小应变假定下快,且大应变假定下考虑起始水力坡降的双层地基最终沉降量要比小应变假定下大。     

双重介质含水层求参方法探讨

双重介质模型能较好地刻画天然裂隙含水层的非均质性及液体流动和溶质迁移特征。在石油开采、核废物处置安全评价和环境水文地质等方面受到广泛重视。但是,双重介质模型的实际应用远远落后于其理论发展。其原因除了双重介质模型复杂、计算工作量大以外,模型参数确定的理论和测试方法很不完善,难以取得两套较客观的模型参数是另一重要原因。本文就双重介质含水层参数的确定问题,从其介质特征和水流运动特征入手,探讨了双重介质含水层中抽水和注水条件下的井流动力学方程及其求解方法,并讨论了其适用条件及存在的问题,最后,用实际资料说明了求参过程,检验了公式。     

Analytical modeling on consolidation of stiffened deep mixed column-reinforced soft soil under embankment

Stiffened deep mixed (SDM) column is a new ground improvement technique to improve soft soil, which can be used to increase bearing capacity, reduce deformation, and enhance stability of soft soil. This technique has been successfully adopted to support the highway and railway embankments over soft soils in China and other countries. However, there have been limited investigations on its consolidation under embankment loading. This paper developed an analytical solution for the consolidation of embankment over soft soil with SDM column in which core pile is equal to or shorter than outer DM column. The consolidation problem was simplified as a consolidation of composite soil considering the load shear effect of core pile. The developed solution was verified by a comparison with the results computed by three-dimensional (3-D) finite element analysis. A parametric study based on the derived solution was conducted to investigate influence factors—length of core pile, diameter of core pile, diameter of SDM column, modulus of DM column, and permeability coefficient of DM column—on the consolidation behavior of SDM column-supported embankment over soft soil. The developed solution was applied to a case history of SDM column-supported embankment, and a good agreement was found between the predictions and the field measurements.     

指数形式渗流定律下软土非线性大变形固结分析

考虑土中指数形式渗流定律以及土体的非线性固结特性,以超静孔隙水压力为变量在拉格朗日坐标系内建立了软土一维大变形固结问题的控制方程及其求解条件,并运用有限差分法获取其数值解答。在指数形式渗流定律退化为达西定律下,通过将差分解与已有的半解析解进行对比,验证了数值计算的可靠性。最后对指数形式渗流定律下软土一维非线性大变形固结性状进行计算分析,结果表明： 1时,软土的非线性大变形固结速率会随外载增大而减慢; 1时,软土的非线性大变形固结速率会随着外荷载的增加而加快;软土非线性大变形固结速率要比非线性小变形固结速率快,且差别会随荷载增大而加剧;此外,大变形固结理论的最终沉降值要小于小变形固结理论,且差别会随着荷载的增大而加剧。     

变荷载下基于指数形式渗流的一维固结分析

建立了考虑指数形式渗流以及变荷载条件下的一维固结微分方程,采用相对稳定的Crank-Nicolson差分格式获得控制方程的差分解答并验证了计算程序的可靠性。结果表明,当指数大于1时,较小时间因子下固结速率比达西渗流快,较大时间因子下固结速率比达西渗流慢;而当指数小于1时,较小时间因子下固结速率比达西渗流慢,较大的时间因子下固结速率比达西渗流快。在土层厚度相同的情况下,指数大于1时作用于土层的荷载越小,固结速率越慢;基于指数形式渗流,传统一维固结理论中室内土样固结与实际地基土层固结之间的相似关系不再成立;加荷速率越快,则土层的固结速率越快。     

Transient bacterial contamination of the dual-porosity aquifer at Walkerton,Ontario, Canada

Contamination of the Paleozoic carbonate aquifer at Walkerton (Ontario, Canada) by pathogenic bacteria following heavy rain in May 2000 resulted in 2,300 illnesses and seven deaths. Subsequent tracer testing showed that there was rapid groundwater flow in the aquifer, and also rapid exchange between the aquifer and the ground surface. Electrical conductivity (EC) profiling during a 3-day pumping test showed that most flow was through bedding-plane fractures spaced about 10 m apart, that there were substantial contrasts in EC in the major fracture flows, and that there were rapid changes over time. Total coliform sampling revealed transient groundwater contamination, particularly after heavy rain and lasting up to a few days. These characteristics can be understood in terms of the dual-porosity nature of the aquifer. Most of the storage is in the matrix, but this can be considered to be static in the short term. Almost all transport is through the fracture network, which has rapid groundwater flow (～100 m/day) and rapid transmission of pressure pulses due to the high hydraulic diffusivity. Rapid recharge can occur through thin and/or fractured overburden and at spring sites where flow is reversed by pumping during episodes of surface flooding. These characteristics facilitated the ingress of surface-derived bacteria into the aquifer, and their rapid transport within the aquifer to pumping wells. Bacterial presence is common in carbonate aquifers, and this can be explained by the well-connected, large-aperture fracture networks in these dual-porosity aquifers, even though many, such as at Walkerton, lack karst landforms.     

考虑加载过程及桩体固结变形的碎石桩复合地基固结解析解

为了完善碎石桩复合地基固结理论,通过假设从桩体排出的水量等于流入桩体的水量与桩体体积变化之和以及地基扰动区土体水平渗透系数呈线性变化,并考虑上部荷载逐渐施加,推导了考虑桩体体积变化的碎石桩复合地基超静孔压及固结度解析解。当加载时间趋于零时,本文解可退化为瞬时加载情况下的解;当加载时间及桩径同时趋于零时,本文解可进一步退化为Terzaghi一维固结解,这证明了本文解的正确性。通过与已有解的比较,对地基固结性状进行了分析。结果表明,加载过程对地基固结度影响显著,加载历时越长,固结越慢;在各种条件下,不考虑桩体固结变形时地基固结始终比考虑桩体变形时快,并且其影响随着加载历时变小、桩径比变小、桩土模量比变小、桩土渗透系数变小而逐渐增大,这说明在实际工程固结计算中不考虑桩体固结变形是偏于不安全的。     

裂隙刚度随应力变化对双重孔隙介质热-水-应力耦合影响的有限元分析

引入并修正了变刚度的连续屈服节理模型,同时考虑应力拉压和压力（化学）溶解对裂隙开度的综合影响,对所建立的双重孔隙-裂隙介质热-水-应力耦合有限元计算程序作了改进。通过一个假定的高放废物地质处置库的数值模拟,就岩体裂隙刚度变化的2种工况,分析了岩体中的温度、裂隙刚度、正应力、孔（裂）隙水压力和地下水流速的变化、分布情况。结果显示：与裂隙刚度是常数时相比,裂隙刚度是法向应力的函数时计算域中温度较低;岩体应力的大小也有一定不同,其分布与裂隙刚度“场”有明显的相似性;并且负孔（裂）隙水压力的绝对值要略小一点,约是常数时的98%。     

热-水-应力耦合影响的有限元分析

为了考虑应力拉压和压力（化学）溶解对裂隙开度的综合影响,对所建立的双重孔隙-裂隙介质热-水-应力耦合模型中裂隙开度的计算模型作了改进。通过一个假定的高放废物地质处置库算例,就岩体裂隙开度变化的3种工况,分析了岩体中的温度、孔（裂）隙水压力、地下水流速和主应力的变化、分布情况。结果显示：3种工况的计算域中温度场基本相同;孔（裂）隙水渗流场形态相似,但其量值有一定差别;工况1的裂隙开度在应力和压力（化学）溶解的共同作用下闭合量最大,负孔（裂）隙水压力增值最高;核废物的释热效应明显地改变了岩体自重应力场的水平分量,但对其垂直分量影响较小。     

裂隙剪胀效应对双重孔隙介质热-水-应力耦合现象影响的有限元分析

为了探讨在法向应力和剪应力的共同作用下裂隙开度的变化对于耦合的温度场、渗流场和应力场的作用,引入裂隙的渗透系数与开度关系的“立方定律”,建立了裂隙渗透系数演化式。应用开发的遍有节理岩体双重孔隙-裂隙介质热-水-应力耦合二维有限元程序,以一个假定的位于非饱和地层中的高放废物地质处置库为算例,分别在2组裂隙斜交和正交的条件下,针对与裂隙开度3种计算方式对应的6种工况进行了数值分析,考察了围岩中的温度、孔隙和裂隙水压力、裂隙开度、裂隙的渗透系数、地下水流速、应力的变化、分布状态。结果显示,当裂隙开度仅取决于法向应力时,裂隙开度受压应力作用产生的闭合量最大,从而裂隙水压力最高;而当裂隙开度是法向应力和剪切位移的函数时,由于“剪胀”效应,裂隙开度闭合量较前述情况为小,裂隙水压力居中;而当裂隙开度是常数时,裂隙水压力最低