Small-scale modelling of plant root systems using 3D printing,with applications to investigate the role of vegetation on earthquake-induced landslides

Vegetation has been previously proposed as a method for protecting artificial and natural slopes against shallow landslides (e.g. as may be triggered by an earthquake); however, previous research has concentrated on individual root soil interaction during shear deformation rather than the global slope behaviour due to the extreme expense and difficulty involved in conducting full-scale field tests. Geotechnical centrifuge modelling offers an opportunity to investigate in detail the engineering performance of vegetated slopes, but its application has been restricted due to the lack of availability of suitable root analogues that can repeatably replicate appropriate mechanical properties (stiffness and strength) and realistic 3D geometry. This study employed 3D printing to develop a representative and repeatable 1:10 scale model of a tree root cluster (representing roots up to 1.5 m deep at prototype scale) that can be used within a geotechnical centrifuge to investigate the response of a vegetated slope subject to earthquake ground motion. The printed acrylonitrile butadiene styrene (ABS) plastic root model was identified to be highly representative of the geometry and mechanical behaviour (stiffness and strength) of real woody root systems. A programme of large direct shear tests was also performed to evaluate the additional strength provided by the root analogues within soil that is slipping and investigate the influence of various characteristics (including root area ratio (RAR), soil confining effective stress and root morphology) on this reinforcing effect. Our results show that root reinforcement is not only a function of root mechanical properties but also depends on factors including surrounding effective confining stress (resulting in depth dependency even for the same RAR), depth of the slip plane and root morphology. When subject to shear loading in soil, the tap root appeared to structurally transfer load within the root system, including to smaller and deeper roots which subsequently broke or were pulled out. Finally, the root analogues were added to model slopes subjected to earthquake ground motion in the centrifuge, where it was revealed that vegetation can substantially reduce earthquake-induced slope deformation in the soil conditions tested (76% reduction on crest permanent settlement during slippage). Both the realistic 3D geometry and highly simplified root morphologies, as characterised mechanically by the shear tests, were tested in the centrifuge which, despite exhibiting very different levels of additional strength in the shear tests, resulted in very similar responses of the slopes. This suggests that once a certain minimum level of reinforcement has been reached which will alter the deformation mechanism within the slope, further increases of root contribution (e.g. due to differences in root morphology) do not have a large further effect on improving slope stability.     

降雨条件下土坡饱和-非饱和渗流及稳定性分析

基于非饱和土力学理论,利用有限元法对降雨条件下边坡的饱和-非饱和渗流及稳定性进行了探讨。数值分析表明,雨水入渗使边坡非饱和区土体的基质吸力减小,是导致边坡稳定性降低的主要因素。进而考察了基质吸力的不同取值及裂隙的不同位置对边坡稳定性的影响,结果表明：在降雨初期基质吸力取值越大,得到的边坡安全系数越高,但经过长时间降雨即边坡土体基本达到饱和后,基质吸力的取值不同对边坡安全系数基本上没有影响;裂隙的存在为雨水入渗提供了良好的通道,因而导致边坡稳定性相对于无裂隙状态来说有所降低。降雨初期下游裂隙使边坡稳定性降低较快,但随着降雨历时的增加,即下游土体逐渐变为饱和状态后,边坡的稳定性变化则主要由上游裂隙控制。     

土质斜坡存在唯一最小安全系数的数据作图论证及原因分析

本文通过数据作图法揭示了土体黏聚力和内摩擦角对斜坡安全系数作用的不同规律,并论证了一般土质斜坡存在唯一最小安全系数及其原因。本文在土质斜坡中划分了大量的潜在滑移面,并定义了每一个潜在滑移面所拥有的4类安全系数FOSc×φ、FOSc、FOSφ和FOSc+φ。基于极限平衡的条分法计算了滑移面的4类安全系数,并使用数据作图法揭示和确定了这4类安全系数值随潜在滑移面深度d变化的4条特征和规律。由土体黏聚力和内摩擦角共同作用的安全系数FOSc×φ包络线随d的增加先单调下降,到达一段最小值区间后,再单调上升。因此,它必然存在一个总体最小值。仅由土体黏聚力贡献的FOSc包络线随d的增加先快速、再缓慢单调下降。仅由土体内摩擦角贡献的安全系数FOSφ包络线随d的增加线性上升。FOSc与FOSφ之和FOSc+φ数值几乎等同于FOSc×φ数值。这4条规律揭示了土体黏聚力和内摩擦角对斜坡安全系数作用的不同规律,并论证了一般斜坡存在最小安全系数及其原因。本文进一步论证和揭示了这4条特征和规律适用于5种经典有限条分法的计算结果,适用于考虑地下孔隙水压强作用的计算结果,和考虑斜坡土体分层不均质影响的计算结果。特别地,地下孔隙水会加深拥有最小安全系数的潜在滑移面深度。土体黏聚力对斜坡安全系数贡献随潜在滑移面深度增大而减小,土体内摩擦角对斜坡安全系数贡献随潜在滑移面深度增大而增大。这两种强度随深度的相反贡献规律导致了一般土质斜坡存在唯一最小安全系数。     

A resilience framework for safety management of fossil fuel power plant

In the present study, cut slope stability assessment along ghat road section of Kolli hills was carried out by using various geotechnical parameters of rock and soil slope sections and structural kinematics of major discontinuities is presented. The rock slope (RS) stability assessment was carried out using Rock Mass Rating basic (RMR_basic) and Slope Mass Rating (SMR) classification systems. The type of failure and their Factor of Safety (FOS) for individual RS was calculated using Hoek and Bray method. In the case of soil slopes (SS), the FOS was calculated using Circular Failure Chart (CFC) and Limit Equilibrium (LE) methods. The input data for the slope stability analyses were collected through extensive field work followed by stereonet plotting and laboratory test. There are six rock slope sections, and five soil slope sections were taken into consideration for the cut slope stability analyses. The area depicts class II (RS-1, 2, & 6) and class III (RS-3, 4, & 5) of RMR classes. The SMR result depicts for RS-1, RS-2, and RS-6 are 64.40, 60.02, and 60.70, respectively, and falls in class II stable condition. The SMR values of RS-3 and RS-5 were 44.33 and 57, respectively, and come under the class III partially stable condition. The RS-4 with SMR value of 17.33 falls under the class I completely unstable condition. The FOS of planar failure case indicates that RS-3 (FOS = 0.22) is more unstable, while all other sections are having greater than 1 FOS. The calculated FOS values using CFC method reveals that the FOS is very close to 1 for all the SS sections that fall under completely saturated condition which indicates that these slope sections may fail during heavy rainfall. In LE method, the sections SS-3 and SS-4 are unsafe under partially and completely saturated (natural slope) condition. In average slope condition, all the SS sections are unsafe under partially or completely saturated conditions. The facets 2, 3, 4, and 5 required mitigation measures, to improve the stability of slopes. Site-specific mitigation measures were suggested for partially or completely unstable rock and soil cut slopes.     

香根草固土护坡工程特性初步研究

香根草的根系长度和抗拉力或强度都较大,单根的抗拉力或强度的平均值为12.4N或69.7MPa,而且群根效应显著,对边坡起着“活着的土钉”作用。深扎广布于坡体中的根系网,显著改善边坡土体的物理力学性质,明显提高边坡土体的强度及稳定性,可较大幅度地降低作用于护坡挡墙上的主动土压力强度(总主动土压力的减少值大于15%);浓密成丛的香根草可分散径流和减少径流量,有效降低降雨与径流对坡面的冲击力及侵蚀量,对坡面起到较好的防护作用;此外,光合作用强、速生快长的香根草及其发达根系网的吸收与蒸腾作用,可降低边坡土体中的含水量及孔隙水压力,增强土中吸力,进而提高边坡土体的强度,增强边坡的稳定性;穿扎广布于坡体土中的香根草根系网系统,类似“活性钢筋网”,与边坡体固结共同作用、融合胶结构成类似原位复合的重力墙,可较好地防止及控制边坡位移或失稳的发生。初步研究表明;香根草护坡的力学效果较为理想,且具有较强的经济效益及环境效益优势。     

水位下降条件下黏性土边坡稳定性的图表法

库（河）岸边坡由于坡体迎水面水位下降经常造成坡体稳定性降低,建立快速评估水位变化条件下的边坡稳定性分析方法具有重要的工程实用价值。基于库（河）水位下降过程及坡体内非稳定渗流条件,通过对ABAQUS程序进行二次开发,发展了考虑地表水-地下水联动作用下的黏性土边坡强度折减有限元分析方法;在分析边坡土性参数、相对渗透比值、边界条件对边坡稳定性影响的基础上,建立了考虑土性参数、相对渗透比值、库水位下降比、坡角等一体化的相对稳定安全系数综合图表表示方法。该方法能够简便、快捷地查出实际涉水边坡在不同工况下的稳定安全系数及设计边坡坡比,可作为现有图表法的有益补充。     

Partial Saturation and Seismicity on Steep Reclaimed Slopes

While traditional mine reclamation methods emphasize compaction to increase the strength of the materials and ensure stability of the restored slope, high compaction restricts the successful reforestation of reclaimed mine sites. The Forest Reclamation Approach (FRA), which uses low compaction in the uppermost 1.2–1.5 m of the surface has been shown to facilitate the establishment of healthy native forests. Stability analyses of three steep FRA slopes from the southern Appalachian region have shown that the long-term static stability is not compromised, and that the infinite slope method provides a rational method to evaluate the stability of steep FRA slopes. In this article, modifications of the infinite slope equation are utilized to (a) include the effects of matric suction due to unsaturated soil conditions and (b) evaluate the seismic performance of FRA slopes based on spectral accelerations. Monthly variation of the water content at three research sites demonstrated the seasonal stability variation of FRA slopes due to matric suction, while seismic analyses illustrated the conditions under which instability may occur.     

Evaluation of factor of safety for vegetated and barren soil slopes with limit equilibrium computations

Limit equilibrium method (LEM) is the most conventional and popular technique in slope stability analysis. Location of the unique failure surface and the determination of corresponding critical factor of safety (critical-FOS) of the soil slope requires a lot of trial and research. With this amount of trial and research results, we evaluate the field of factor of safety (FOS-field), which represents the critical-FOS at a point within the domain of all possible failure surfaces. Such a field can be very important for the precise judgment of the most critical-FOS of the slope and its perturbation. This paper also presents the evaluation of the FOS-field of vegetated slopes, thus providing an analytical way to examine the effect of vegetation on the soil slope stability. We evaluated the stability of vegetated and barren soil slopes under dry and fully saturated conditions. With dry and fully saturated conditions, the behaviour of slopes in most favourable and worst conditions can be simulated. Evaluation of FOS-field for various slope geometries and conditions show that the more unstable the slope becomes, the more difficult it will be to pinpoint the location of the critical failure surface with the unique least FOS. We verified the LEM codes with finite element method (FEM) and spectral element method (SEM) codes considering a sample problem from Smith and Griffiths’ book (Smith and Griffiths 2003).     

3D stability of unsaturated soil slopes with tension cracks under steady infiltrations

Most classical approaches for evaluating the stability of soil slopes with cracks are performed under two-dimensional (2D) condition. Three-dimensional (3D) effect and suction-induced effect of unsaturated soils are generally neglected in assessing the slope stability. This paper develops a 3D limit analysis method to evaluate the stability of an unsaturated soil slope with tension cracks under steady infiltrations. The boundary-value problem is formulated based on the 3D rotational failure mechanism by taking the effects of suction, effective unit weight, and tension crack into account. A simplified method is proposed to calculate the work rate of unsaturated soil weight. A layer-wise summation method is developed based on the divergence theorem to calculate the internal energy dissipation rate. Detailed discussions are conducted to investigate the effects of suction and Poisson's ratio on the stability of unsaturated soil slopes. Examples are given to illustrate the 3D effect, the suction-induced effect as well as the effects of infiltration and water in cracks on the slope stability.     

青藏铁路沱沱河段路基边坡植物护坡根系力学强度试验研究

以青藏铁路沱沱河段路基边坡作为试验区,且在试验区路基边坡两侧种植了乡土护坡草本植物垂穗披碱草,通过对种植在试验区路基阴坡、阳坡生长5年的垂穗披碱草,做了野外原位根系拉拔试验,获得了垂穗披碱草根系抗拔力。研究表明:种植在阳坡的垂穗披碱草根系抗拔力为3088N,阴坡抗拔力为2352N,即种植在阳坡的垂穗披碱草根系抗拔力显著大于阴坡,影响其抗拔力大小的主要因素与土壤含水量及其变化有密切关系,试验区阳坡接受光照时间、程度均强于阴坡,试验区阳坡坡面土壤水分蒸发量大于阴坡这种差异形成阴坡、阳坡坡体土壤含水量不同的主要原因;垂穗披碱草根系抗拔力大小与须根数量、根径、根长、株高、根表面积、分蘖数之间均呈线性关系,其中抗拔力与须根数量之间呈显著性线性相关,阳坡垂穗披碱草抗拔力随根系数量增加的幅度显著大于阴坡,即当须根数量为40～60条时,阳坡垂穗披碱草的抗拔力集中分布在11～25N,阴坡抗拔力分布在8～15N;当须根数量为60～140条时,阳坡垂穗披碱草的抗拔力分布在30～70N,阴坡抗拔力为20～50N。根据路基边坡阴坡、阳坡垂穗披碱草根系抗拔力试验结果,评价了阴、阳两种坡向条件下垂穗披碱草根系护坡力学贡献,这对青藏铁路路基边坡种植草本植物实现该边坡与周边自然生态环境之间的协调发展具有理论指导意义。     

Prediction of slope stability using multiple linear regression (MLR) and artificial neural network (ANN)

The stability problem of natural slopes, filled slopes, and cut slopes are commonly encountered in Civil Engineering Projects. Predicting the slope stability is an everyday task for geotechnical engineers. In this paper, a study has been done to predict the factor of safety (FOS) of the slopes using multiple linear regression (MLR) and artificial neural network (ANN). A total of 200 cases with different geometric and shear strength parameters were analyzed by using the well-known slope stability methods like Fellenius method, Bishop’s method, Janbu method, and Morgenstern and Price method. The FOS values obtained by these slope stability methods were used to develop the prediction models using MLR and ANN. Further, a few case studies have been done along the Jorabat-Shillong Expressway (NH-40) in India, using the finite element method (FEM). The output values of FEM were compared with the developed prediction models to find the best prediction model and the results were discussed.     

Rainfall-induced landslides by deficit field matric suction in unsaturated soil slopes

Landslides are mainly triggered by decrease in the matric suction with deepening the wetting band by rainfall infiltrations. This paper reports rainfall-induced landslides in partially saturated soil slopes through a field study. A comprehensive analysis on Umyeonsan (Mt.) landslides in 2011 was highlighted. The incident involves the collapse of unsaturated soil slopes under extreme-rainfall event. Fundamental studies on the mechanism and the cause of landslides were carried out. A number of technical findings are of interest, including the failure mechanism of a depth of soil and effect of groundwater flow, the downward movement of wetting band and the increase of groundwater level. Based on this, an integrated analysis methodology for a rainfall-induced landslide is proposed in this paper that incorporates the field matric suction for obtaining hydraulic parameters of unsaturated soil. The field matric suction is shown to govern the rate of change in the water infiltration for the landslide analysis with respect to an antecedent rainfall. Special attention was given to a one-dimensional infiltration model to determine the wetting band depth in the absence of the field matric suction. The results indicate that landslide activities were primarily dependent on rainfall infiltration, soil properties, slope geometries, vegetation, and groundwater table positions. The proposed methodology has clearly demonstrated both shallow and deep-seated landslides and shows good agreement with the results of landslide investigations.     

高寒矿区排土场植被恢复对边坡土体物理力学性质影响研究

本项研究针对高寒干旱环境下矿山排土场边坡植物增强土体强度和提高边坡稳定性作用贡献,以青海北部木里煤田江仓矿区作为研究区,通过采用组合种植草本垂穗披碱草(Elymus nutans Griseb.)+冷地早熟禾(Poa crymophila Keng)的方式,开展了组合种植植物根-土复合体与不含根系素土物理力学性质指标试...     

The role of infiltration processes in steep slope stability of pyroclastic granular soils: laboratory and numerical investigation

Rainfall-induced landslides on steep slopes are a common feature in much of Italy’s mountain areas covered by shallow-pyroclastic deposits. Generally, these deposits are unsaturated and have a slope angle higher than 40°–50°; hence their stability is due to the positive effect of matric suction on soil shear strength. During rainfall, rainwater infiltration causes a decrease in suction, which in turn causes changes in soil mechanical and hydraulic properties, leading towards an instability process. However, the response of pyroclastic soil slopes to rainwater infiltration is not fully understood. The aim of this study is to link slope instability to the infiltration process on the basis of advanced geotechnical characterization, in situ monitoring and numerical analysis calibrated through a back-analysis of well-instrumented flume tests.     

挡墙加固非饱和土边坡整体稳定性分析

在对挡墙加固边坡进行设计和评价时应综合考虑基质吸力和挡墙对边坡整体稳定性的影响。应用可以考虑基质吸力的弹塑性强度折减有限元程序,分析了挡墙加固非饱和土边坡的整体稳定性,揭示了基质吸力对加固边坡整体稳定性的影响程度,同时亦分析了整体潜在滑动面位置的变化情况,并进行了关于吸力摩擦角的敏感性分析。     

Contours of saturated and unsaturated overhanging slopes at limiting equilibrium condition

Overhangs are frequently observed in riverbanks, coastal headlands, and rock formations. The geometry of an overhang is an input into most slope stability analyses and is often idealised or back-calculated from empirical data. This study investigates the geometries of overhang slopes, which exist while in limiting conditions satisfying static equilibrium with soil strength governed by the Mohr-Coulomb failure criterion. The overhanging contour is formulated as the unknown in a boundary value problem and solved for using the slip line theory. Analyses consider nonhomogeneous soils, where cohesion and, if unsaturated, the contribution of suction to the effective stress vary linearly with depth. The solutions are presented in general dimensionless charts. Applications of the charts are illustrated via examples. It has been observed that soil with varying amounts of friction and cohesion could develop overhanging arches of different sizes and shapes. This study shows that the curvature of an overhang becomes more pronounced for small values of φ′ . It is also demonstrated that changing the contribution of suction to the effective stress has a direct impact on the size of an unsaturated soil overhang. Overhanging slope shapes observed in reality may be different from the idealised subset studied in this paper since real slopes are not necessarily at impending failure. The real shapes may be influenced by various physical processes such as weathering, stress variations caused by cycles of wetting-drying. Even so, the results presented in the paper indicated how key soil properties influence slope shapes, albeit it while in limiting conditions.     

Rain-triggered slope failure of the railway embankment at Malda,India

The common slope stability analysis is incapable of accurately forecasting shallow slides where suction pressures play a critical role. This realization is used for elaborate stability analyses which include soil suction to better predict rainfall-induced slides at railway embankment at Malda where three known cases of slope failures and train derailments occurred after heavy rainfall. The relationship between the soil–water content and the matric suction is established for the embankment soil. It is then used in the coupled analyses of seepage and slope stability to estimate performances of the embankment at different intensity and duration of rainfall. The numerical simulations are performed with the FE code Geo-Studio. The numerical results show significant reduction in the factor of safety of the railway embankment with the increase in the intensity and duration of rainfall. The effectiveness of the proposed mitigation measures including placement of 2 m-wide free draining rockfill across the slopes and drilling 5-m-long sheet pile wall at the toe of the embankment is studied numerically. The study confirms that the proposed mitigation measures effectively increase the factor of safety of the embankment and stabilizing it even in case of a heavy rainfall of 25 mm/h over 12 h.     

基于SWCC试验数据的坝体非饱和非稳态渗流与稳定性研究

饱和-非饱和状态是土存在于自然界的真实状态,描述和解释这种状态的非饱和土力学理论在土石坝渗流、污染物传输、冻土渗流相变、边坡和路基稳定性分析等领域有着广泛的应用。非饱和土的土水特征曲线(SWCC)是非饱和土力学研究的基本内容之一,对非饱和土体渗流和稳定性分析至关重要。采用Python语言开发了非饱和渗流与稳定性分析软件包USSA和非饱和土土水特征曲线试验数据处理和模型拟合界面。对非饱和土的土水特征曲线数据进行处理,以模型拟合参数作为基本输入进行非饱和渗流场的模拟,再到非饱和土的稳定性分析,详细呈现了非饱和土渗流与稳定性分析及软件开发的全过程。基于SWCC模型的拟合参数对坝体渗流稳定性进行了分析,分析结果表明水位变化过程中坝体两侧斜坡具有明显不同的稳定性演化规律。当采用有限元强度折减法进行非饱和土斜坡稳定性分析时,最终安全系数为所有边坡安全系数演化曲线的最低包络线。     

Design Charts for the Stability Analysis of Unsaturated Soil Slopes

Simple limit equilibrium analyses can be performed to determine the Factor of Safety (FOS) against slope failure of unsaturated soil slopes. However, many of the input parameters needed for these analyses are highly variable, and the FOS value obtained is critically dependent on assumptions made by the designer. This paper describes a suite of reliability analyses on unsaturated soil slopes performed using an invariant reliability model. The results are presented in design charts from which a designer can choose the FOS value required to ensure a given target reliability index for a slope. The approach ensures that despite the variability of input parameters the slope will have a probability of failure of 2.23% or less.     

根系和裂隙对土体水力和力学特性影响数值模拟

为探究根系和裂隙对土体水力及力学特性的影响,利用有限元软件计算降雨过程中裂隙和根土间隙对渗流场的影响,并以渗流计算结果为基础,分析降雨对根系固土作用的影响,采用分区强度折减法对降雨前后根?土复合体进行直剪试验模拟,同时考虑了侧根倾角的影响。结果表明,裂隙和根土间隙为雨水入渗提供优先通道,降雨影响深度随裂隙深度增加而增加;有根系时降雨影响深度由主根深度决定,侧根倾角对其影响较小,考虑根土间隙影响的降雨影响深度相较于无根系工况增加了93.3%;根系能显著提高土体的抗剪强度,相对于垂直主根方向的不同倾角,侧根增加土体抗剪强度由大至小依次为60o、45o、30o侧根和无根系;雨水入渗降低了土体强度,同时削弱了根系固土作用,使得降雨后根-土复合体抗剪强度大幅降低,是许多植被覆盖边坡仍发生浅层滑动原因之一。