Study of horizontal drain effect on slope stability

Slope failure usually occurs when soil particles are unable to build a strong bond with each other and become loose because of the presence of water. Water pressure weakens the ties between the particles and they tend to slip. Therefore, this study focused on the use of horizontal drains to reduce water entry and control the ground water level as a method of slope stabilization. Several previous studies have shown that the use of horizontal drains to lower the water level in soil is one of the fastest and cheapest slope stabilization methods. The main objective of this study is to analyze the effect of horizontal drains on slope stability. Information on slope condition during the landslides which happened at Precinct 9, Putrajaya, Malaysia was used for analytical simulation. Seep/W and Slope/W analyses were carried out with GeoStudio version 2007 software. Slopes with and without horizontal drains were then compared in terms of groundwater level and factor of safety (FOS) values. Scenarios were created for seven types of soil namely: residual, clay, silt, loam, sandy loam, sandy clay loam, and silt clay loam for a case wise analysis. The effect of daily steady rainfall and realcondition rainfall was studied. These cases were studied to find the effectiveness of horizontal drains as a slope stabilization tool. The results revealed that when a drain was installed on a slope, the groundwater level dropped immediately and the safety factor of the slope increased. Sandy loam (sL) soil was identified as the best candidate for a horizontal drain. Its highly saturated hydraulic conductivity Ks facilitated groundwater drain through the horizontal drain effectively. Silt clay loam (scL) soil was identified as the least effective candidate.     

Effectiveness of horizontal drains for slope stability

Horizontal drains have been commonly used in stabilising unsaturated residual soil slopes. This study examines the effectiveness of horizontal drains in stabilising residual soil slopes against rainfall-induced slope failures under a tropical climate. The study includes field instrumentation at two residual soil slopes complemented with a parametric study relating to drain position. Field monitoring results indicate that rainfall infiltration is limited to a certain depth below which infiltration becomes insignificant. This zone tends to be unsuitable for horizontal drains. Horizontal drains were found to be most effective when located at the base of a slope. The parametric study indicated conditions under which horizontal drains are effective or ineffective in improving the stability of a slope. It was also found that horizontal drains have little role in minimising infiltration in an unsaturated residual soil slope. Benefits of using horizontal drains can be obtained through the lowering of the water table.     

Performance of the horizontal drains in upstream shell of earth dams on the upstream slope stability during rapid drawdown conditions

Slope stability analysis during rapid drawdown is an important consideration in the design of embankment dams. During rapid drawdown, the stabilizing effect of the water on the upstream face is lost, but the pore water pressures within the embankment may remain high. As a result, the stability of the upstream face of the dam can be much reduced. Installing horizontal drains is a very efficient and cost-effective method for reducing the pore water pressure and increasing the stability of the upstream slope. The theory of horizontal drains in the upstream shell of earth dams is well established, but there seems to be limited resources available for the design of this type of horizontal drains. Hence, this study is focused on the performance of horizontal drains in the upstream shell of the slope of earth dams on the upstream slope stability during rapid drawdown conditions. The parametric study has been conducted on the variation of horizontal drain parameters such as the number of drains, their length, and their location. In this study, ten scenarios were analyzed based on different drainage configurations and the performance of each scenario is investigated on the seepage and the upstream slope stability during rapid drawdown conditions using finite element and limit equilibrium methods. The results demonstrated that the stability of the upstream slope during rapid drawdown conditions increases by increasing the number of drains. The length of drains extending further from its intersection with the critical failure surface does not provide any significant change in the factor of safety. Finally, the study also found that installing drains in the lower region of the upstream shell of earth dams gives more stability than those installed in higher elevations.     

Vertical drain consolidation analysis in one,two and three dimensions

A new method, the η or ‘eta’ method, for modeling consolidation by vertical and horizontal drains is presented. The approach is applicable in one, two and three dimensional as well as axisymmetric cases. Material and geometry properties are familiar from unit cell vertical drain analysis and are consistent across dimensions. An uncoupled finite element method (FEM) program is used to test the efficacy of the new approach. Because drains are not explicitly modeled in the finite element mesh, mesh complexity and computational time are greatly reduced. Unlike existing plane strain matching methods there is no special transformation of permeability or drain properties. The analyses conducted indicate that the η method provides an efficient and consistent means of modeling drains in any dimension.     

Development of drain hole design optimisation: a conceptual model for open pit mine slope drainage system with fractured media using a multi-stage genetic algorithm

High rainfall in equatorial regions leads to high groundwater levels or pore pressures and a high risk of landslides on the slopes of open pit mines, hindering mining operations. To lower the groundwater level surrounding a slope, a drainage system is needed. A drain hole is a part of a drainage system which utilises gravity to drain groundwater. Drain hole installation in fractured media requires the determination of the number, location, length and other parameters of the drain holes. Drain holes are frequently installed in uniform configurations or in layouts with uniform spacing, which are often ineffective and uneconomical, as some holes are not in the right positions or directions within the fractured media. This paper attempts to develop a conceptual model of an optimised configuration of drain holes by setting the drain hole parameters, or decision variables, such as number, location and length, in such a way that it produces the most effective and efficient outcome by maximising groundwater lowering and minimising cost. The optimisation is supported by the multi-stage genetic algorithm method in combination with a groundwater simulator, hereafter called the multi-stage GWSim-GA SO method. The procedure of the conceptual model will be further developed and used as a framework in the groundwater management of fractured media of an open pit mine slope.     

砂墙地基二维固结自由应变解

将含竖向排水体地基的三维固结变形问题等效为平面应变问题进行数值分析时,砂墙地基二维固结解析解答是合理确定其等效固结计算参数的重要依据。为辨析现有砂墙地基等应变固结近似解答的适用性,针对微单元土体严格的二维固结微分方程,考虑对地基固结有重要影响的井阻作用,以及涵盖完全透水和不完全透水的更一般边界面排水条件,推求得到了其自由应变解答。并与现有解答进行对比分析,同时,分析了泊松比效应以及水平和竖向排水对地基固结的影响。结果表明,现有砂墙地基的等应变固结解答虽然近似,但已有足够精确;砂墙地基以水平向固结为主,竖向固结几乎可以忽略不计;地基固结速率随着泊松比的增大而增大,在将竖向排水体等效为砂墙时,应考虑其作用影响。     

考虑影响区真实形状的竖向排水井地基固结解

针对现有竖向排水井地基固结解析理论对影响区一律采用圆形等效假定的缺陷,研究了影响区真实形状为正六边形的按梅花形布置的竖向排水井地基的固结问题。通过建立新固结方程和引入新的边界条件,并考虑土体水平渗透系数变化,得到了相应的解析解。对于土体水平渗透系数的3种变化模式,分别给出了各种模式下的特殊解。在此基础上,分析了3种模式下3个主要的无量纲参数对地基固结性状的影响,并比较了计算结果和现有理论结果。分析结果表明,影响区和涂抹扰动区范围越大,固结越慢;土体的最大与最小水平渗透系数之比越小,固结越快;在相同条件下,考虑扰动区渗透系数线性变化的模式2固结最快,而假定扰动区渗透系数不变的模式1的解与现有理论解相当接近,验证了现有竖向排水井地基固结解析理论中对影响区采用圆形等效假定的合理性     

Consolidation of vertical drain with depth-varying stress induced by multi-stage loading

An explicit analytical solution is developed for the consolidation of vertical drain with both radial and vertical drainage by adopting a depth-varying stress induced by multi-stage loading. The well resistance and smear effect are also considered. The smear effect is described by three decay patterns of horizontal permeability towards drains within the smeared zone, including a reduced constant pattern, a linear decay pattern and a parabolic decay pattern. A parameter analysis is performed to investigate the consolidation behavior of the vertical drain. The convergence of the proposed series solution is discussed.     

Probabilistic analyses of soil consolidation by prefabricated vertical drains for single‐drain and multi‐drain systems

Natural soils are one of the most inherently variables in the ground. Although the significance of inherent soil variability in relation to reliable predictions of consolidation rates of soil deposits has long been realized, there have been few studies that addressed the issue of soil variability for the problem of ground improvement by prefabricated vertical drains. Despite showing valuable insights into the impact of soil spatial variability on soil consolidation by prefabricated vertical drains, available stochastic works on this subject are based on a single‐drain (or unit cell) analyses. However, how the idealized unit cell solution can be a supplement to the complex multi‐drain systems for spatially variable soils has never been addressed in the literature. In this study, a rigorous stochastic finite elements modeling approach that allows the true nature of soil spatial variability to be considered in a reliable and quantifiable manner, both for the single‐drain and multi‐drain systems, is presented. The feasibility of performing an analysis based on the unit cell concept as compared with the multi‐drain analysis is assessed in a probabilistic context. It is shown that with proper input statistics representative of a particular domain of interest, both the single‐drain and multi‐drain analyses yield almost identical results. Copyright © 2016 John Wiley & Sons, Ltd.     

涂抹区重叠竖井地基固结特性研究

在软基处理工程中,经常出现竖井打设变密而地基固结效率降低的现象。鉴于此,建立了重叠涂抹区内土体水平向渗透系数的分布函数,给出了涂抹区重叠时竖井地基超静孔压和平均固结度的解析解。通过分析不同工况下竖井地基固结度随竖井间距的变化情况,探究了竖井间距减小而地基固结效率不增反减的成因。最后,探讨了涂抹作用和井阻作用对竖井最小临界间距的影响。结果表明：相邻竖井涂抹区重叠是竖井地基中出现竖井最小临界间距的根本原因。涂抹作用越大,则竖井最小临界间距越大;具体表现为当地基扰动程度增大时或涂抹区半径增大时,竖井最小临界间距随之增大。井阻作用越大,则竖井最小临界间距越小;具体表现为当竖井渗透系数减小时、竖井长度增大时或竖井半径减小时,竖井最小临界间距随之减小。     

Risk analysis of landslides – A case study

The effects of uncertainty due to the variability of soil parameters on the risk of landsliding in the Himalayan region are investigated using a random field model combined with slope stability analyses. Effects of spatial variability both in horizontal and vertical directions, number of test samples, variations in piezometric level and the influence of earthquake on the reliability of a typical slope in a slide area are investigated. The results show that the reliability of slopes in the slide area is significantly affected by the coefficients of variation of soil parameters, spatial variations of soil parameters, number of test samples and piezometric variations. The results also show that the assumption of isotropic variations to assess slope reliability isconservative. The results of the study are useful in providing guidelines and pointing to remedial measures in the form of sub-surface drainage to improve slope reliability in the area.     

Numerical investigation of small- and medium-diameter drain wells to stabilise deep landslides

The stabilisation of deep landslides is still a challenge for geotechnical engineers, mainly due to the high cost of structural control works that generally lead engineers to opt for drain systems. Unfortunately there are operative difficulties affecting excavation of deep drain trenches in soils dislocated by landslides (especially as regards the provisional support of the excavation walls). Small- and medium-diameter wells are a valid alternative in deep landslides, being less expensive than large-diameter wells equipped with horizontal pipes and simpler to construct than deep trenches. However, no technical procedures for their proper design are reported in the literature: design criteria commonly used in practice are derived from pumping problems and are largely inadequate, being based on Dupuit’s hypothesis that presumes stream lines to be horizontal. This paper presents numerical solutions obtained from three-dimensional seepage and consolidation analyses of a slope drained by small- and medium-diameter wells, arranged according to various positions, showing that the efficiency of the well system decreases as the depth of the landslide slip surface increases. Comparison is also made between well systems and deep trenches occupying the same draining volume in the landslide body, showing that the former attains much greater efficiency than the latter. Non-dimensional abaci for the square grid of wells (which is the most effective arrangement) are reported herein to be used for practical purposes.

     

成层竖向排水井地基固结分析

实际工程中竖井地基具有成层性,有时竖井也并未完全打穿软土层。在竖井打设区满足竖井等应变固结理论、下卧层满足一维太沙基固结理论假设的基础上,将现有竖井地基固结理论推广到成层未打穿竖井地基情况。利用边界条件和竖直向连续条件,确定该系统的正交关系,并给出了其固结解答,该解具有广泛的适用性。通过对竖井打设区和下卧层层数的变化,即可获得现有关于简单未打穿竖井地基的固结解答。将该解答编制成应用程序,对一算例进行了分析。结果表明,平均固结度按孔压定义和按变形定义是不相同的,硬表层的存在会加快其下土层的固结。     

Consolidation of sensitive clay with vertical drain

The coefficient of consolidation is one of the most important parameters that control the rate of consolidation. Conventional consolidation theories assume that the coefficient of consolidation is constant during the whole consolidation process. In the case of sensitive clay, the coefficient of consolidation is strongly dependent on the level of effective stress of clay. With the dissipation of pore water pressure and the increase of effective stress, the soil structure of the upper subsoil is gradually destroyed downwards and its coefficient of consolidation becomes smaller. At the same time, the coefficient of permeability of the vertical drains drops down because of the kinking or bending effect. The destructured upper subsoil and the kinking of the vertical drain hinder the dissipation of the pore pressure in the lower subsoil. This paper presents a model to describe the above important phenomena during the consolidation of sensitive clay with vertical drain. The solution for proposed model can be obtained by extending the closed‐form solution of the consolidation of double‐layered ground with vertical drain by the interactive method introducing the concept of the moving boundary and the reduction of discharge capacity of vertical drain. The numerical results obtained from the finite element method package PLAXIS (Ver. 7.2) are adopted to compare those obtained from the present algorithm. Moreover, the rationality of the moving boundary is explained by the distributions of the excess pore water pressure in natural soil zone along the radial direction. Wenzhou airport project is taken as a case study in this paper. The results for the sensitive soil with decaying sand drain agree very well with the in situ measured data. The calculated results can properly explain two general phenomena observed in the consolidation of soft sensitive soil ground with vertical drains: one is that the time to achieve the same consolidation degree is much longer under heavy loading than that under light loading; the other is that the consolidation speed is much slower in the lower subsoil than in the upper subsoil. Finally, it is indicated that the vertical drains can decrease the hindrance effect of the destructured subsoil. Copyright © 2007 John Wiley & Sons, Ltd.     

Contribution of the Root to Slope Stability

Land sliding is a geotechnical event that includes a wide range of ground movements such as rockfalls, deep failure of slopes and shallow debris flows, and it can cause various problems in varied civil fields such as roads and dams. Since most conventional methods are neither inexpensive nor applicable everywhere, attention has nowadays been drawn to soil bioengineering using vegetation as the environment-friendly method for slope stabilization. Soil bioengineering or using vegetation in civil engineering design is mostly applicable to shallow slope stabilization projects characterized by unstable slopes with surface movement. Vegetation has both a silent effect on soil improvement to predict the landslide and a mechanical role to increase shear and pulling-out stress on the soil. During the last decade, many researches have been carried out to clarify the effect of vegetation on slope stability, but many questions still remain to be answered.     

复杂荷载作用下考虑下卧层三维渗流的未打穿竖井地基固结分析

针对任意复杂变荷载作用下未打穿的竖井地基,通过在竖井底面以下土层中设置虚拟竖井,使其能够合理考虑下卧层土体三维渗流问题,运用Laplace变换,求得频域内竖井地基的固结解。通过Laplace逆变换,得到了任意荷载作用下竖井地基的平均固结度、孔压消散曲线、沉降曲线。结合具体算例,对影响竖井地基固结的主要影响因素进行了详细分析,并将现有未打穿竖井地基平均固结度近似计算方法的精度和适用的范围进行了对比,得到了一些有益于工程实践的结论。     

Dissipation Testing of Singapore Marine Clay by Piezocone Tests

In situ dissipation tests provide a means of evaluating the in situ coefficient of consolidation due to horizontal flow and hydraulic conductivity in horizontal direction in marine clays formation. Dissipation tests by means of piezocone were utilised in the characterisation of the coefficient of consolidation due to horizontal flow and the hydraulic conductivity in horizontal direction of Singapore marine clay at Changi. Piezocone dissipation tests were carried out prior to reclamation as well as after ground improvement with vertical drains to compare the changes in the coefficient of consolidation due to horizontal flow and hydraulic conductivity in horizontal direction prior to and after ground improvement. The quasi-static piezometric pressures from the dissipation tests were compared with piezometric pressures from piezometers to determine their possibility of future use as an alternative to piezometers. Post-improvement CPTU dissipation tests were carried out in the treated “Vertical Drain Area” as well as in an adjacent untreated “Control Area” for comparison purposes. This study provides support for the use of piezocone dissipation testing methods for the determination of the coefficient of consolidation due to horizontal flow and hydraulic conductivity in horizontal direction of marine clays in the region as well as an alternative to piezometer instrumentation for monitoring of piezometric pressure during consolidation.     

降雨条件下滑坡排水沟排水数值模拟

地表排水沟是滑坡治理常见措施之一。在降雨入渗与坡面径流有限元耦合模型中,通过调整径流方程中的坡度参数,实现地表排水沟排水模型。模型具有易于理解、实现简单的优点。以地表排水模型为基础,对5种典型滑坡在设与不设排水沟情况下坡体渗流场、坡面径流场、坡体入渗量和入渗过程进行了数值模拟。结果表明,当降雨强度相对土体渗透性较小时,排水沟设置在坡体渗透性由小变大的位置,才能有效地截断上游径流,减小入渗量;而当降雨强度相对土体渗透性较大时,排水沟排水效果并不明显。     

Analysis of soil consolidation by vertical drains with double porosity model

The soil around a drain well is traditionally divided into smeared zone and undisturbed zone with constant hydraulic conductivity. In reality, hydraulic conductivity of the soil changes continuously and it may not be always appropriate to approximate its distribution with two zones. In this study, the horizontal hydraulic conductivity of the soil is described by an arbitrary function of radial distance. The horizontal flow under equal strain condition is analysed for a soil–drain system with a circular or regular polygonal boundary. It is found that the horizontal flow can be generally characterized with a linear equation in which the flow rate of water through soil–drain interface is proportional to the difference between the average excess pore pressure in the soil and the excess pore pressure in the drain well. The water exchange between the drain and the soil is analogous to that between fractures and matrix in a double porosity system, a popular conceptual model of fracture rocks. On the basis of this characterization, a simplified approach to analyse soil–drain systems is developed with one‐dimensional double porosity model (DPM). Analytical solutions for both fully and partially penetrating drains are derived. The solution for partially penetrating drains is compared with both numerical and approximate analytical results in literature. Copyright © 2004 John Wiley & Sons, Ltd.     

Analytically computed rates of seepage flow into drains and cavities

The known formulae of Freeze and Cherry, Polubarinova–Kochina, Vedernikov for flow rate during 2-D seepage into horizontal drains and axisymmetric flow into cavities are examined and generalized. The case of an empty drain under ponded soil surface is studied and existence of drain depth providing minimal seepage rate is presented. The depth is found exhibiting maximal difference in rate between a filled and an empty drain. 3-D flow to an empty semi-spherical cavity on an impervious bottom is analysed and the difference in rate as compared with a completely filled cavity is established. Rate values for slot drains in a two-layer aquifer are ‘inverted’ using the Schulgasser theorem from the Polubarinova–Kochina expressions for corresponding flow rates under a dam. Flow to a point sink modelling a semi-circular drain in a layered aquifer is treated by the Fourier transform method. For unsaturated flow the catchment area of a single drain is established in terms of the quasi-linear model assuming the isobaric boundary condition along the drain contour. Optimal shape design problems for irrigation cavities are addressed in the class of arbitrary contours with seepage rate as a criterion and cavity cross-sectional area as an isoperimetric restriction. © 1998 John Wiley & Sons, Ltd.