Uncertainty of rainfall-induced landslides considering spatial variability of parameters

A cross-correlation analysis is conducted to determine the impacts of the heterogeneity of hydraulic conductivity K_s, soil cohesion c′ and soil friction angle (tan φ′) on the uncertainty of slope stability in time and space during rainfall. We find the relative importance of tan φ′ and c′ depends on the effective stress. While the sensitivity of the stability to the variability of K_s is small, the large coefficient of variation of K_s may exacerbate the variability of pore-water pressure. Therefore, characterizing the heterogeneity of hydraulic properties and pore-water distribution in the field is critical to the stability analysis.     

External seismic stability of vertical geosynthetic-reinforced soil walls using pseudo-static method

Analysis of external stability of vertical geosynthetic-reinforced soil (GRS) walls is very important in the seismic prone zone. The scope of this paper is to obtain required minimum reinforcement length, L _min, for external seismic stability of vertical GRS walls by pseudo-static limit equilibrium method. Then, L _min can be calculated to resist sliding, eccentricity, and bearing capacity failure modes. The parameters considered include both horizontal and vertical seismic coefficients (k _h and k _v ), surcharge load (q), wall height (H) and the properties of retained backfill, GRS, and foundation soil. Results show that L _min against sliding failure mode, L _min,S , increases more quickly than that against the other two failure modes with the increase in k _h , q, or unit weight of retained backfill, γ _b , while L _min,S decreases more quickly than that against the other two failure modes with increase in friction angle of retained backfill, ? _b , or unit weight of GRS, γ _r . For the different failure modes, the effect of k _v on L _min is not identical with the change of k _h , and in addition, L _min/H will tend to remain unchanged with the increase in H. In general, L _min against bearing capacity failure mode, L _min,BC, is larger than L _min against the other two failure modes. However, L _min,BC will be less than L _min against eccentricity failure mode, L _min,E , for k _h exceeding 0.35, or friction angle of foundation soil, ? _f , exceeding 37°, and L _min,BC will also be less than L _min,S for friction angle of GRS, ? _r , being no more than 26°.     

Risk assessment and prediction of safety factor for circular failure slope using rock engineering systems

Circular failure is generally observed in the slope of soil, highly jointed rock mass, mine dump and weak rock. Accurate estimation of the safety factor (SF) of slopes and their performance is not an easy task. In this research, based on rock engineering systems (RES), a new approach for the estimation of the SF is presented. The introduced model involves six effective parameters on SF [unit weight (γ), pore pressure ratio (r _u), height (H), angle of internal friction (φ), cohesion (C) and slope angle (\(\beta\))], while retaining simplicity as well. In the case of SF prediction, all the datasets were divided randomly to training and testing datasets for proposing the RES model. For comparison purposes, nonlinear multiple regression models were also employed for estimating SF. The performances of the proposed predictive models were examined according to two performance indices, i.e., coefficient of determination (R ²) and mean square error. The obtained results of this study indicated that the RES is a reliable method to predict SF with a higher degree of accuracy in comparison with nonlinear multiple regression models.     

Reliability analysis for bearing capacity of surface strip footing using fuzzy finite element method

ABSTRACT

This paper presents the reliability analysis on the basis of the foundation failure against bearing capacity using the concept of fuzzy set theory. A surface strip footing is considered for the analysis and the bearing capacity is estimated using the conventional Finite Element Method (FEM). The spatial variability of the variables is taken into consideration to capture the physical randomness of the soil parameters for an isotropic field. A variation of the probability of failure (P_f) against a varying limiting applied pressure (q) is presented for different Coefficient of Variation (COV) of the variables and different scale of fluctuation (θ). The results reveal that the friction angle of soil (?) is the most influencing parameter among the other variables. Further, the influence of the scale of fluctuation (θ) on the probability of failure (P_f) is also examined. It is observed that for a particular COV of ?, higher value of θ predicts higher P_f whereas, P_f increases as COV of ? increases for a particular θ value. Later, a comparison study is accomplished to verify the viability of the present method and it can be noticed that the present method compares well with the other reliability method (First Order Reliability Method) to a reasonably good extent.     

Seismic Bearing Capacity of Shallow Strip Footing with Coulomb Failure Mechanism using Limit Equilibrium Method

In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (q_uE) is expressed in terms of single coefficient N_γE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (d_f/B₀), seismic acceleration (k_h, k_v) are studied on the variation of seismic bearing capacity co-efficients.     

Dynamic active earth pressure on cantilever retaining walls

In normal practice, the active earth pressure on cantilever retaining wall is evaluated with different procedures relating to an ideal vertical plane passing through the heel of the wall. If the wall presents a long heel, failure planes do not interfere with the vertical stem, so that the limit Rankine conditions can develop freely in the backfill. The inclination of lateral actions along the ideal plane is assumed to be constant and depends on the geometry of the ground level and on the friction angle φ. The Authors recently proposed a new method to evaluate the active earth pressure coefficient due to seismic loading with a pseudo-static stress plasticity solution. The present paper describes the application of this method to a retaining wall supporting a φ soil backfill with an irregular surface. For two different configurations of wall-soil system, the behaviour is also studied by continuum FDM dynamic analyses, utilising four Italian accelerometric time-histories scaled at the same peak ground acceleration. The comparison between different procedures is also analysed.     

Efficient stochastic analysis of unsaturated slopes subjected to various rainfall intensities and patterns

Rainfall infiltration poses a disastrous threat to the slope stability in many regions around the world. This paper proposes an extreme gradient boosting (XGBoost)-based stochastic analysis framework to estimate the rainfall-induced slope failure probability. An unsaturated slope under rainfall infiltration in spatially varying soils is selected in this study to investigate the influences of the spatial variability of soil properties (including effective cohesion c′, effective friction angle φ′ and saturated hydraulic conductivity k_s), as well as rainfall intensity and rainfall pattern on the slope failure probability. Results show that the proposed framework in this study is capable of computing the failure probability with accuracy and high efficiency. The spatial variability of k_s cannot be overlooked in the reliability analysis. Otherwise, the rainfall-induced slope failure probability will be underestimated. It is found that the rainfall intensity and rainfall pattern have significant effect on the probability of failure. Moreover, the failure probabilities under various rainfall intensities and patterns can be easily obtained with the aid of the proposed framework, which can provide timely guidance for the landslide emergency management departments.     

Enhancement of random finite element method in reliability analysis and risk assessment of soil slopes using Subset Simulation

Random finite element method (RFEM) provides a rigorous tool to incorporate spatial variability of soil properties into reliability analysis and risk assessment of slope stability. However, it suffers from a common criticism of requiring extensive computational efforts and a lack of efficiency, particularly at small probability levels (e.g., slope failure probability P _f ?<?0.001). To address this problem, this study integrates RFEM with an advanced Monte Carlo Simulation (MCS) method called “Subset Simulation (SS)” to develop an efficient RFEM (i.e., SS-based RFEM) for reliability analysis and risk assessment of soil slopes. The proposed SS-based RFEM expresses the overall risk of slope failure as a weighed aggregation of slope failure risk at different probability levels and quantifies the relative contributions of slope failure risk at different probability levels to the overall risk of slope failure. Equations are derived for integrating SS with RFEM to evaluate the probability (P _f ) and risk (R) of slope failure. These equations are illustrated using a soil slope example. It is shown that the P _f and R are evaluated properly using the proposed approach. Compared with the original RFEM with direct MCS, the SS-based RFEM improves, significantly, the computational efficiency of evaluating P _f and R. This enhances the applications of RFEM in the reliability analysis and risk assessment of slope stability. With the aid of improved computational efficiency, a sensitivity study is also performed to explore effects of vertical spatial variability of soil properties on R. It is found that the vertical spatial variability affects the slope failure risk significantly.     

River bank erosion control by soil nailing

A study has been done for analysing soil nailed cuts with circular type wedge failure by friction circle method. Various parameters such as nail length, nail diameter, nail inclination, wall inclination and angle of internal friction of soil have been considered to determine the factor of safety of nailed open cuts. The study shows that for cohesionless soil nailed cut, factor of safety increase with increase of parameters like angle of internal friction of soil, length of nail (L) versus height of cut (H) ratio, cohesion of soil and nail inclination (upto 15°) with horizontal. The study revealed that nails grouted with cement perform better than driven nails. A case study further confirms the analytical findings. Received 7 October     

Instantaneous Friction Angle and Cohesion of 2-D and 3-D Hoek–Brown Rock Failure Criteria in Terms of Stress Invariants

The Mohr–Coulomb (M–C) failure criterion is one of the most widely used failure criteria in rock mechanics, although it has a number of shortcomings such as neglecting the nonlinear strength observed in rock or the effect of the intermediate principal stress σ ₂. Other failure criteria have been proposed to effectively include in the predictions of failure the non-linear response of rock to confinement or the effects of the intermediate principal stress. The M–C criterion is still widely used, and it is arguably the criterion most used in practice. For example, stability evaluations of shallow rock structures such as slopes and foundations are routinely carried out by estimating a friction angle and a cohesion of the rock mass. To include the dependency of cohesion and friction angle on stresses, efforts are being made to estimate equivalent values of the M–C parameters for the range of stresses applicable to a particular design. The paper suggests a new and convenient approach to find the equivalent friction angle and cohesion from any failure criterion that can be expressed in terms of the Nayak and Zienkiewicz’s stress invariants. To demonstrate the capabilities and application of the methodology, the new approach is applied to two failure criteria: the Hoek–Brown (H–B) criterion and the Hoek–Brown and Willam–Warnke (HB–WW) criterion, 2-D and 3-D failure criteria, respectively. Results from the new method, in terms of equivalent friction and cohesion for the H–B criterion, are exactly the same as the results obtained from Balmer’s theory, which confirms the validity of the new method. The predicted equivalent friction and cohesion for the HB–WW criterion show a dependency on σ ₂, which does not occur for a 2-D failure criterion.     

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross‐correlated non‐Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non‐intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd.     

Piles shaft capacity from CPT and CPTu data by polynomial neural networks and genetic algorithms

Cone penetration test (CPT) is one of the most common in situ tests which is used for pile design because it can be realized as a model pile. The measured cone resistance (q_c) and sleeve friction (f_s) usually are employed for estimation of pile unit toe and shaft resistances, respectively. Thirty three pile case histories have been compiled including static loading tests performed in uplift, or in push with separation of shaft and toe resistances at sites which comprise CPT or CPTu sounding. Group method of data handling (GMDH) type neural networks optimized using genetic algorithms (GAs) are used to model the effects of effective cone point resistance (q_E) and cone sleeve friction (f_s) as input parameters on pile unit shaft resistance, applying some experimentally obtained training and test data. Sensitivity analysis of the obtained model has been carried out to study the influence of input parameters on model output. Some graphs have been derived from sensitivity analysis to estimate pile unit shaft resistance based on q_E and f_s. The performance of the proposed method has been compared with the other CPT and CPTu direct methods and referenced to measured piles shaft capacity. The results demonstrate that appreciable improvement in prediction of pile shaft capacity has been achieved.     

Bearing capacity of foundations on slopes

By applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, N_c, N_q and N_γ, due to the components of cohesion, surcharge and unit weight, respectively, have been estimated for a horizontal strip footing placed along a sloping ground surface. The variation of N_c, N_q and N_γ with changes in slope angle (β) for different soil friction angle (φ) have been computed for smooth as well as rough strip footings. The analysis reveals that along a sloping ground surface, in addition to N_γ, the factors N_c and N_q also vary considerably with changes in footing roughness. Compared to the smooth footing, the extent of the plastic zone around the footing becomes greater for the rough footing. The results obtained from the analysis are found to compare well with those previously reported in literature.     

Residual and Fully Softened Strength Evaluation of Soils using Artificial Neural Networks

A backpropagation artificial neural network (ANN) model is developed to predict the secant friction angle of residual and fully softened soils, using data reported by Stark et al. (J Geotech Geoenviron Eng ASCE 131:575–588, 2005). In the ANN model, index properties such as liquid limit, plastic limit, activity, clay fraction and effective normal stress are used as input variables while secant residual friction angle is used as output variable. The model is verified using data that were not used for model training and testing. The results also indicate that the secant residual friction angle of cohesive soils can be predicted quite accurately using liquid limit, clay fraction and effective normal stress as input variables with R ² = 0.93. The sensitivity analysis results indicate that plastic limit and activity have no appreciable effect on ANN predicted secant friction angles. The secant friction angle predictions of the ANN model were also compared with those of Stark’s et al. (2005) curves and the empirical formulas suggested for the same data sets by Wright (Evaluation of soil shear strengths for slope and retaining wall stability with emphasis on high plasticity clays, 2005). The comparison shows that the ANN model predictions are very close to those suggested by the Stark et al. (2005) curves but much better than the prediction of Wright’s (2005) empirical equations. The results also show that ANN is an alternative powerful tool to predict the secant friction angle of soils.     

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。     

放坡状态有限土体刚性挡土墙主动土压力研究

针对现有有限土体刚性挡土墙主动土压力研究大都集中于临近建筑物墙体或地下室外墙的狭窄土体,相邻基坑、路堤与切坡挡土墙形成放坡状态有限土体研究甚少,本文考虑填土黏聚力及墙土间黏结力、墙土间摩擦作用、墙背倾角及填土顶面竖向荷载等的影响,利用刚体极限平衡理论进行研究。根据相邻基坑与边坡挡土墙放坡状有限土体的工程特性,分析挡土墙平动位移模式下平面滑动破裂面的形成特征,建立放坡状态有限土体主动土压力计算模型,并利用数值计算方法可以求解。通过对放坡状有限土体主动土压力进行算例分析与参数分析,表明极限破裂角与宽高比、黏聚力、墙背倾角及墙土间外摩擦角为负相关,不同黏聚力下随着宽高比增大,极限破裂角趋近于考虑黏聚力作用库伦方法得到的极限破裂角值,不同黏聚力下有限土体宽度临界值亦是变化的;主动土压力随黏聚力、墙背倾角及墙土外摩擦角增大而减小,随着宽高比增大而增大并逐步趋近于库伦方法计算的土压力值。最后,通过模型试验验证表明按本文方法计算的极限破裂角与实测破裂角吻合,PIV系统测试得到的临界宽高比与库伦方法的结果一致。     

The critical scale of fluctuation for active lateral forces in spatially variable undrained clays

This study addresses the phenomenon of the critical scale of fluctuation (SOF) for active lateral force (P_a) in undrained clay when there is a spatial variability in the clay. The phenomenon is significant under shear strength (τ_f) random fields but is insignificant under unit weight (γ) random fields. It is found that the phenomenon of the critical SOF is connected to the nature of the spatial averaging, which is “line averaging” under τ_f random fields and is “area averaging” under γ random fields. The former averaging effect (line) is significantly weaker than the latter (area), so the tendency for the critical slip plane to seek for a favorable location is stronger for the τ_f random field than for the γ random field. Hence, the phenomenon of the critical SOF is more pronounced under τ_f random fields than under γ random fields. The underlying mechanisms for the phenomenon of the critical SOF will be explored in this paper.     

Bearing Capacity of the New Composite Foundation with Discrete Material-Concrete Compound Piles

In order to solve the bulging deformation and fracture at the top of widely used gravel piles in treating ground consolidation, a new, optimized composite foundation form was proposed. The composite foundation was constructed using discrete materials and concrete piles. Additionally, various parameters of this new composite foundation were analyzed, including foundation forms, construction technologies, bearing mechanism and failure mode. By applying cavity expansion theory, the Vesic cavity spreading pressure of the discrete material-concrete pile is solved as a polar axis symmetric problem on the basis of Mohr–Coulomb yield criterion. Then the computing formula for the ultimate bearing capacity of the discrete materials-concrete pile is elicited when the internal friction angle of soil in the piles is φ = 0 and φ ≠ 0. Finally, the ultimate bearing capacity value of the composite foundation is acquired through analytic calculation and numerical simulation. Finally, it is found that the calculation result is 14.4% lower than that of the simulated result, which is within the acceptable accuracy range and therefore proves the accuracy of the analytic calculation method for bearing capacity of the new composite foundation.     

基于综合变异系数的地基承载力可靠性分析

采用一次二阶矩法,考虑岩土参量变异系数的试验及历史数据,提出了基于综合变异系数的地基承载力简化可靠性与风险分析方法。利用提出的简化可靠性与风险分析方法,可在传统确定性分析的基础上,采用合理的变异系数,分别得到与地基承载力有关的可靠度、破坏概率和平均期望损失的最可能值及其变化范围,为提出优化的地基基础设计方案和工程决策奠定基础;相对于土重度和黏聚力,地基承载力可靠度对于内摩擦角的变化更加敏感;设计时可以综合考虑所需的安全系数、可靠度和破坏概率,确定合适的基础宽度或基底面积。当地基土的场地勘察统计结果的变异系数权重逐渐增加时,综合变异系数不断减小,其相应的地基承载力的可靠度逐渐增加,而相应的破坏概率逐渐减少。     

Seismic vertical uplift capacity of horizontal strip anchors using pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis to determine the seismic vertical uplift capacity of a horizontal strip anchor using upper bound limit analysis. However, in the literature, the pseudo-static approach was used by few researchers to compute the seismic vertical pullout resistance, where the real dynamic nature of earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of uplift factor f_γE are determined for different magnitudes of soil friction angle, soil amplification, embedment ratio and seismic acceleration coefficients both in the horizontal and vertical directions. It is observed that the uplift factor f_γE decreases significantly with the increase in seismic accelerations and amplification but increases with the increase in embedment ratio. The results are compared with the existing values in the literature and the significance of the present methodology for designing the horizontal strip anchor is discussed. In presence of vertical earthquake acceleration and amplification of vibration, the present values of f_γE compare reasonably well with the existing pseudo-static values obtained by modifying the horizontal acceleration coefficient.