Seismic rock slope stability charts based on limit analysis methods

Earthquake effects are commonly considered in the stability analysis of rock slopes and other earth structures. The standard approach is often based on the conventional limit equilibrium method using equivalent Mohr–Coulomb strength parameters (c and ?) in a slip circle slope stability analysis. The purpose of this paper is to apply the finite element upper and lower bound techniques to this problem with the aim of providing seismic stability charts for rock slopes. Within the limit analysis framework, the pseudo-static method is employed by assuming a range of the seismic coefficients. Based on the latest version of Hoek–Brown failure criterion, seismic rock slope stability charts have been produced. These chart solutions bound the true stability numbers within ±9% or better and are suited to isotropic and homogeneous intact rock or heavily jointed rock masses. A comparison of the stability numbers obtained by bounding methods and the limit equilibrium method has been performed where the later was found to predict unconservative factors of safety for steeper slopes. It was also observed that the stability numbers may increase depending on the material parameters in the Hoek–Brown model. This phenomenon has been further investigated in the paper.     

Parametric Monte Carlo studies of rock slopes based on the Hoek–Brown failure criterion

Probabilistic evaluation of slope failures is increasingly seen as the most appropriate framework for accounting for uncertainties in design. This paper performs reliability assessments for rock slopes based on the latest version of the Hoek–Brown failure criterion. The purpose of this study is to demonstrate the use of a new form of stability number for rock slope designs that has been recently developed from finite element upper and lower bound limit analysis methods, and to provide guidance for its use in probabilistic assessments. The analyses show that by using this newly proposed stability number, the probability of failure (P_f) obtained from case studies agrees well with the true state of the slope. In addition, this paper details a procedure to determine the magnitude of safety factor required for rock slope design.     

Engineering characteristics of Ankara Greywacke under the foundation of the Beytepe open air theatre,Ankara, Turkey

The construction of a large open air theatre having with an audience capacity of 7,000 is planned at the Beytepe Campus of Hacettepe University located near Ankara, Turkey, in the heart of Anatolia. The foundation of the open air theatre is composed of weak and heavily jointed Ankara Greywacke. An estimation of the strength and deformation of the Ankara Greywacke was required for assessments of short- and long-term stability. Accordingly, rock mass characterization of the Ankara Greywacke was investigated in detail by scan-line surveys and back-analyses of in situ tests performed on the excavated surface of the rock mass. The final version of the Hoek and Brown Criterion (Hoek et al., In: Proceedings of the north American rock mechanics society meeting, Toronto, Canada, pp 1–6, 2002) together with and improvements proposed by Sonmez and Gokceoglu (Int J Rock Mech Min Sci, 43:671–676, 2006) were considered together for the back analyses of small slope benches subjected to plate loading test loaded to failure. In addition, the plate loading test data were used with some well-known empirical equations for predicting of deformation modulus of rock masses to calculate ranges of values of the Geological Strength Index (GSI) The static and pseudostatic slope stabilities of the audience seating structures to be supported by benches excavated into the rock were also analyzed. The stability assessments revealed the unlikelihood of large rock mass failures for the short-term construction stages or for the long-term, as-constructed conditions under static or pseudo-static conditions. Additionally, the analyses showed that there was no need for anchors between the concrete seating structures and greywacke rock mass.     

Pseudo-dynamic stability of rock slope considering Hoek–Brown strength criterion

Rock slopes with planar joints or weak structural planes are vulnerable in nature, especially suffering from the natural hazards, instabilities of slopes are more prone to occur. Therefore, concerning to the influence of earthquakes, this paper performs a new procedure to evaluate slope stability in a geomaterial governed by Hoek–Brown strength criterion. A rotational failure mechanism determined by 21 dependent angle variables is introduced to respect the Hoek–Brown strength criterion. The earthquake load is characterized by a modified pseudo-dynamic method that does not violate the zero boundary condition and considers the damping properties of geomaterials. A slice approach is adopted to calculate the earthquake-induced inertial force work rate. The stability number of rock slope is considered to measure the safety. The stability number is formulated as a classical optimization problem controlled by 21 dependent angle variables and a time variable which need to be optimized by the genetic algorithm toolbox. Comparisons with the literature are made to prove rationality and accuracy of the proposed procedure. Parametric study is carried out to reveal the influence of dynamic properties. For engineering application, stability charts are provided for a quick assessment of slope safety.

     

Effect of rock mass disturbance on the stability of rock slopes using the Hoek–Brown failure criterion

The process of creating man made or “cut” slopes in rock invariably leads to stress relief within the rock mass which in turn induces a certain degree of fracturing and disturbance. The level of disturbance can be particularly significant when the slope is formed using blasting techniques. However, the effects of this disturbance on the overall rock slope stability have not been investigated thoroughly in the current literature. In order to account for rock mass disturbance during construction, a disturbance factor has been included in the Hoek–Brown failure criterion [1]. This paper uses finite element upper and lower bound limit analyses to estimate rock slope stability based on the Hoek–Brown failure criterion whilst including the effect of rock mass disturbance. A rigorous set of analyses have been performed where the level of disturbance is considered as constant or linearly varying throughout the slope. The results are then compared to a number of reported case histories for verification purposes. From the results of this study, the disturbance factor was found to have significant influence on the rock slope stability assessment, especially for poorer quality rock masses. Hence, cautious engineering judgement must be exercised when estimating the level of disturbance. In addition, utilising stability charts to estimate the stability of cut rock slopes without considering the rock mass disturbance may lead to significant overestimations.     

An Empirical Failure Criterion for Intact Rocks

The parameter m _i is an important rock property parameter required for use of the Hoek–Brown failure criterion. The conventional method for determining m _i is to fit a series of triaxial compression test data. In the absence of laboratory test data, guideline charts have been provided by Hoek to estimate the m _i value. In the conventional Hoek–Brown failure criterion, the m _i value is a constant for a given rock. It is observed that using a constant m _i may not fit the triaxial compression test data well for some rocks. In this paper, a negative exponent empirical model is proposed to express m _i as a function of confinement, and this exercise leads us to a new empirical failure criterion for intact rocks. Triaxial compression test data of various rocks are used to fit parameters of this model. It is seen that the new empirical failure criterion fits the test data better than the conventional Hoek–Brown failure criterion for intact rocks. The conventional Hoek–Brown criterion fits the test data well in the high-confinement region but fails to match data well in the low-confinement and tension regions. In particular, it overestimates the uniaxial compressive strength (UCS) and the uniaxial tensile strength of rocks. On the other hand, curves fitted by the proposed empirical failure criterion match test data very well, and the estimated UCS and tensile strength agree well with test data.     

Stability analysis of rock slopes with a modified Hoek–Brown failure criterion

The original Hoek–Brown (HB) failure criterion was used to analyse the stability of rock slopes. For highly fractured rock, the original HB failure criterion has been modified, but its effect on the stability of rock slopes has not been studied. Within the framework of the kinematical approach of limit analysis, this paper computes the rigorous upper bounds of stability factors of homogeneous rock slopes with the modified HB failure criterion under the plane strain condition, by employing a ‘generalized tangential’ technique. In such technique, instead of using the modified HB failure criterion, a series of linear failure surfaces tangent to the actual non-linear failure surface are utilized to derive the upper bound solutions, incorporating a new parameter n ranging from 0.5 to 0.65. The numerical results are compared with other published solutions for the case of n=0.5. The effects of the n on the stability factors of rock slopes are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

桩锚挡墙联合支护残积土边坡离心模型试验研究

利用土工离心机分别对钢轨桩、锚杆联合重力式挡土墙支护土质边坡的效果进行模型对比试验研究,分析了钢轨桩和锚杆在重力式挡土墙支护土质边坡中的作用。试验结果表明,强降雨诱发重力式挡土墙支护下的残积土边坡产生滑动变形,对边坡稳定构成威胁;挡土墙下打入钢轨桩联合支护土质边坡会大大降低因降雨产生的墙体偏移,但墙顶上部坡体的局部浅层滑动仍不可避免;植入墙顶上部坡体内并锚固于墙身的锚杆对边坡局部浅层滑动起到了很好的抑制作用。在不增加挡墙自重前提下,钢轨桩下延作用以及锚杆锚固作用提升了挡土墙的抗倾覆能力和边坡浅层抗滑塌能力,从坡体内部和浅层同时改善了重力式挡土墙的支护效果;钢轨桩和锚杆的使用均布了挡土墙背部土压力,有效避免了局部应力集中。     

Slope stability analyses for materials with a non-linear failure envelope

Upper bound techniques are used to analyse the stability of slopes of material failing according to a non-linear failure criterion, such as closely jointed rocks. The global, extremal nature of upper bound calculations is discussed, as is the inverse use of such procedures for obtaining safe lower bound estimates for material strength properties in back analyses. Specific results are presented for the material model proposed by Hoek and Brown.     

The Stability of Upper Bound Analysis of Soft Rock Tunnel Faces Under Different Underground Water Levels

The effect of underground water levels on the stability of soft rock tunnel faces was analyzed in this paper. The underground water levels was divided into three cases, and the Hoek–Brown failure criterion was introduced into the kinematic approach by "tangent method", then three kinds of stability analysis model of tunnel faces under different underground water levels was constructed. Based on the principle of virtual power, the expressions of supporting force on the tunnel faces of soft rock under different underground water levels were derived. Moreover, the optimal upper limit solution of the supporting force on tunnel faces was obtained by using the sequential quadratic programming algorithm with Matlab software. After that, the effect of underground water levels on the supporting force of tunnel faces was analyzed, and the damage range of tunnel faces under different underground water levels was given. This paper provides some reference value for setting parameters of shield tunneling in water-rich section.

     

Limit equilibrium analysis of seismic stability of slopes reinforced with a row of piles

An approach based on the category of limiting equilibrium analysis is proposed to consider the reinforcing effect of one row of vertical piles on slope under seismic conditions. The approach is based on an uncoupled formulation in which the pile response and slope stability are considered separately. Closed‐form equations are derived, allowing the yield acceleration coefficient to be determined for giving pile characteristics. Results were compared with those obtained using another limit equilibrium method. The effects of pile location on the effectiveness of increasing seismic stability of the slope–pile system were elucidated. It was found out that the piles should be installed in the middle–upper part of the slope to achieve greatest safety, but the pile length and other possible failure modes should be checked carefully in design. Copyright © 2015 John Wiley & Sons, Ltd.     

Back analysis of an excavated slope failure in highly fractured rock mass: the case study of Kargar slope failure (Iran)

This paper examines the failure of Kargar cut slope located at the south part of Esfahan subway using analytical and numerical back analysis methods. The excavated trench has 27 m depth with near vertical walls due to the space limitation around it. The geology of the area comprises weathered and heavily jointed shale and sandstone overlaid by alluvium deposits. Despite the slope being supported by shotcrete and fully grouted rock bolts, a catastrophic failure occurred at the east wall. Due to the uncertainty about the causes of failure initiation, back analyses have been performed via both the limit equilibrium and numerical method for considering various probable mechanisms. In the back analysis with limit equilibrium method, the rock mass is assumed as an equivalent continuum and Hoek–Brown failure criterion and geological strength index (GSI) are applied to calculate the shear strength parameters. The results show that GSI value was 33 in the failed mass. In the numerical back analysis, the distinct element method is applied to study the contribution of rock joints to the failure and progressive rock mass strength degradation until failure. The results show that threshold values of joint cohesion and friction were 0.2 MPa and 30°, respectively. Also the modeled slip surface being step-shaped agrees with the observed one.     

Stability analysis and supporting system design of a high-steep cut soil slope on an ancient landslide during highway construction of Tehran–Chalus

The stability of both natural and cut slopes in mountainous areas is a great challenge to highway constructions and operations. This paper presents a successful case study of stability analyses and protection treatments for high-steep cut soil slopes in an ancient landslide zone which was located at Km12+700 to Km15+000 along the Tehran?CChalus highway. This report has three parts. First, geotechnical investigations of in situ direct shear test, SPT tests and laboratory tests were implemented to get the subsurface profiles and the mechanical properties of the soil mass. Second, finite difference analysis was carried out to evaluate the stability of both the natural and cut slopes. Minimum safety factors and potential failure modes of cut slopes were obtained under both static and dynamic conditions. These results indicated that the ancient landslide could not be reactivated under the present climatic and morphological conditions, but there were some potential shallow failures in some cut soil slopes (failure actually occurred during excavation). Protection treatments and reinforcements were thus necessary. Third, the stability of the cut slopes was re-assessed by simplified Bishop limit equilibrium analysis (using Slide 5.0). Some potential failure zones were designed to be protected by back-anchored concrete retaining wall at the slope toe, rock bolts and frame beams on the slope face and planting grass on the slope face. Numerical analysis indicated that these protection measures could stabilize this remedial slope. These practical experiences may be of benefit for similar highway construction projects.     

桩锚支护结构设计及支护结构变形监测分析

结合北京一个基坑支护工程,从设计角度就桩锚支护结构在基坑支护中的应用及变形控制进行了阐述。根据受力情况,护坡桩主筋配筋采用不均匀布置方式,结合工程、支护结构特点分段配筋;为了满足基坑安全及现场施工用地,砖墙设计时,在砖墙中部增设混凝土腰梁;护坡桩施工中,运用不同的施工工艺,保证了护坡范围内古树的生命安全。从基坑开挖监测角度,对支护结构顶部水平位移进行了监测,对周边建（构）筑物进行了沉降监测,同时对锚杆进行了检测与监测。结果分析表明,基坑水平及垂直变形量均在设计控制范围内,基坑整体稳定,桩锚支护结构对变形起到了有效的控制作用。     

Seismic bearing capacity of shallow foundations near rock slopes using the generalized Hoek–Brown criterion

The seismic bearing capacity of shallow foundations resting on a modified Hoek–Brown rock mass is investigated within the framework of the kinematic approach of limit analysis theory. The analysis focuses on evaluating the reduction in bearing capacity induced by seismic loading and by the proximity of a rock slope. A pseudo‐static approach is adopted to account for the earthquake effects for the seismic bearing capacity evaluations. At the rock material level, the closed‐form expressions previously obtained for the support functions of the rock failure criterion allow the implementation of different failure mechanisms families, and thus to derive rigorous upper bounds estimates of the load‐bearing capacity in both static and seismic conditions. The effects of geometrical, strength and loading parameters are assessed through a large number of parametric computations. Finally, design tables are presented for practical use in rock engineering. Copyright © 2010 John Wiley & Sons, Ltd.     

Probabilistic analysis of three-dimensional tunnel face stability in soft rock masses using Hoek–Brown failure criterion

This paper investigates tunnel face stability in soft rock masses via coupled limit and reliability analyses. Specifically, a 3D face collapse mechanism was first constructed. Then the Hoek–Brown failure criterion was introduced into the limit analysis via the tangential technique. Taking the variability of rock mass parameters and loads into consideration, a reliability model was established. The collapse pressure and failure range of tunnel faces were determined. In addition, the required factor of safety (FS) and supporting pressure under three safety levels were obtained, and the corresponding safety level graphs for support design were presented. Comparison of the obtained results with previous work demonstrates the rationality of the 3D collapse mechanism and the validity of the results. A decrease in the geological strength index, Hoek–Brown parameter m_i, and uniaxial compressive strength or an increase in the disturbance factor results in a nonlinear increase of the collapse pressure and an enlargement of the failure zone. Such changes also lead to a nonlinear increase of the required support pressure under a certain safety level. By contrast, the FS does not exhibit any obvious change when these parameters vary. Therefore, when a rock mass is of poor quality or heavily disturbed, the advance support should be enlarged from upper front to right above the tunnel face. Moreover, as the safety level increases, both the required FS and supporting pressure of the tunnel face increase nonlinearly at a higher rate.     

LNG储罐高低承台桩基础抗震性能对比分析

目前全容式LNG储罐基础常采用低承台和高承台桩基2种形式。采用弹性振动理论,并考虑壳液耦联振动效应,对全容式储罐高、低承台桩基的抗震性能进行对比分析,给出了2种桩基础形式下全容式LNG储罐结构与基础的震动特性,包括自振周期、单桩水平地震力、抗倾覆性能、罐底周边单位长度上的提离力、储液晃动周期以及晃动波高等。分析表明,高承台桩基的水平地震响应大于低承台8.69%、垂直地震响应大于6.34%;低承台桩基的抗倾覆能力比高承台高12.11%,抗提离能力高于高承台储罐11.42%;高承台的自振周期高于低承台;低承台基础结构的抗震能力要优于高承台基础结构。其结论对桩基础全容式LNG储罐的设计与施工具有一定的参考价值。     

A Comparative Study of Different Approaches for Factor of Safety Calculations by Shear Strength Reduction Technique for Non-linear Hoek–Brown Failure Criterion

The shear strength reduction technique is becoming more and more popular to determine the factor-of-safety for geotechnical constructions, especially for slopes. At present, two in principal different procedures are used to apply the numerical shear strength reduction technique for materials characterised by non-linear failure envelopes, like the Hoek–Brown criterion. One procedure is based on the determination on local stress and strength values, whereas the other is based on a global linearization of the non-linear failure envelope. This article shortly describes and discusses these two different procedures and compares results for a broad spectrum of parameter constellations based on slope stability calculations. The local approach is physically more correct. The global approach can be considered as a first approximation. A comparison of both methods reveal that the global approach in comparison to the local approach, can leads to a deviation of up to 15?% in both directions. If one considers the local approach as the ‘correct’ one, depending on the parameters the results of the global approach can lie on the safe or unsafe site. The practical conclusion is that evaluation of slope stability using the global approach can result in uneconomic slope design or overestimation of safety margin. The use of the local approach instead of the global should be preferred. In case of small safety margins (e.g. 20?% or less) the use of the local approach is strictly recommended.     

软岩陡坡椅式桩支挡结构受力变形模型试验研究

对软岩陡坡椅式桩（CSP）支挡结构,通过大比例模型试验研究路基面分级荷载作用下其内力变形规律、结构-岩土体相互作用,根据试验条件和结构受力状态,提出了其设计计算方法。结果表明,椅式桩的空间结构特性可有效控制结构变形和减小桩身内力;主副桩桩身弯矩大小接近,最大弯矩位于坡面处,桩侧岩石压力主要跟桩基变形与岩石变形模量有关;椅式桩一般不会出现结构倾倒破坏,软岩边坡则以浅层破坏为主;基于弹性地基梁的分析解,可较好地描述椅式桩的内力变化及其分布规律。研究结果对正确分析椅式桩支挡结构的抗滑机制和设计计算具有较好的参考价值。