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1.
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. 相似文献
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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. 相似文献
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Jiahua Zhang Lianyang Zhang Weijun Wang Daobing Zhang Biao Zhang 《国际地质力学数值与分析法杂志》2020,44(11):1601-1616
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 mi, 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. 相似文献
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A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes 
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下载免费PDF全文 Apostolos Vrakas 《国际地质力学数值与分析法杂志》2017,41(7):1077-1090
This paper generalizes the finite strain Coulomb solution of Vrakas and Anagnostou (Int J Numer Anal Meth Geomech 2014; 38(11): 1131–1148) for the classic tunnel mechanics problem of the ground response curve to elastoplastic grounds satisfying a non‐linear Mohr's failure criterion. A linear (Coulomb‐type) plastic potential function is used, leading to a non‐associated flow law, and edge plastic flow is considered in the plastic zone. The solution for a general non‐linear Mohr's failure criterion is semi‐analytical in that it requires the evaluation of definite integrals. In the special case of the Hoek–Brown criterion, however, these integrals are calculated analytically, resulting in a rigorous closed‐form series solution. The applicability of the derived solution is illustrated through the example of the Yacambú‐Quibor tunnel, where very large deformations were observed when crossing of weak graphitic phyllites. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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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.
相似文献7.
Zhang Dao-bing Jiang Jin Zhang Jia-hua 《Geotechnical and Geological Engineering》2021,39(6):4393-4404
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.
相似文献8.
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. 相似文献
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Fitting strength criteria to intact rock 总被引：2，自引：0，他引：2
B. J. Carter E. J. Scott Duncan E. Z. Lajtai 《Geotechnical and Geological Engineering》1991,9(1):73-81
Summary Rock strength data covering the full range of possible stress conditions are presented for three rocks: a granite, a limestone and a salt rock. The Hoek and Brown square root parabola and the Johnston criteria are fitted to the strength data coming from around 500 laboratory tests. The fitting procedure is facilitated by a specially built PC code, ROCKER, which is available to anyone on request.The Hoek and Brown criterion is modified through the inclusion of a third parameter to account for the low tensile strength of the salt rock. A new criterion, the Rocker function is formulated to follow strength data closely in the tension-low confining pressure region. 相似文献
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An Empirical Failure Criterion for Intact Rocks 总被引：1，自引：1，他引：0
Jun Peng Guan Rong Ming Cai Xiaojiang Wang Chuangbing Zhou 《Rock Mechanics and Rock Engineering》2014,47(2):347-356
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. 相似文献
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考虑坡顶均布荷载和地震效应典型情况下,将边坡滑体进行任意斜条块划分,建立了具有倾斜界面的多块体破坏模型。基于极限分析上限法和非线性摩尔-库仑破坏准则,考虑岩体内正应力的不均匀性,引入多点切线法和强度折减法推导得出边坡临界破坏状态下的安全系数Fs通用计算公式。采用序列二次规划法对安全系数Fs的目标函数进行最优化计算,并与既有研究成果进行对比分析,其结果具有较好的一致性,相对误差不超过3.565%,表明了该方法的正确性。同时对比传统单点切线法计算结果,多点切线法较单点切线法获得的边坡安全系数值偏小,表明了多点切线斜条分法偏于保守,是安全的。参数分析表明坡顶均布荷载、地震效应和非线性参数均对边坡安全系数及潜在临界滑裂面有重要影响。多点切线法引入非线性摩尔-库仑破坏准则对边坡进行稳定性极限分析,为相关研究人员提供了一种新的思路与方法。 相似文献
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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. 相似文献
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Slope Stability Problems and Back Analysis in Heavily Jointed Rock Mass: A Case Study from Manisa, Turkey 总被引：1，自引：1，他引：0
Mutluhan Akin 《Rock Mechanics and Rock Engineering》2013,46(2):359-371
This paper presents a case study regarding slope stability problems and the remedial slope stabilization work executed during the construction of two reinforced concrete water storage tanks on a steep hill in Manisa, Turkey. Water storage tanks of different capacities were planned to be constructed, one under the other, on closely jointed and deformed shale and sandstone units. The tank on the upper elevation was constructed first and an approximately 20-m cut slope with two benches was excavated in front of this upper tank before the construction of the lower tank. The cut slope failed after a week and the failure threatened the stability of the upper water tank. In addition to re-sloping, a 15.6-m deep contiguous retaining pile wall without anchoring was built to support both the cut slope and the upper tank. Despite the construction of a retaining pile wall, a maximum of 10 mm of displacement was observed by inclinometer measurements due to the re-failure of the slope on the existing slip surface. Permanent stability was achieved after the placement of a granular fill buttress on the slope. Back analysis based on the non-linear (Hoek–Brown) failure criterion indicated that the geological strength index (GSI) value of the slope-forming material is around 21 and is compatible with the in situ-determined GSI value (24). The calculated normal–shear stress plots are also consistent with the Hoek–Brown failure envelope of the rock mass, indicating that the location of the sliding surface, GSI value estimated by back analysis, and the rock mass parameters are well defined. The long-term stability analysis illustrates a safe slope design after the placement of a permanent toe buttress. 相似文献
14.
In this study, upper bound finite element (FE) limit analysis is applied to stability problems of slopes using a nonlinear criterion. After formulating the upper bound analysis as the dual form of a second-order cone programming (SOCP) problem, the stress field and corresponding shear strength parameters can be determined iteratively. Thus, the nonlinear failure criterion is represented by the shear strength parameters associated with stress so that the analysis of slope stability using a nonlinear failure criterion can be transformed into the traditional upper bound method with a linear Mohr–Coulomb failure criterion. Comparison with published solutions illustrates the accuracy and feasibility of the proposed method for a simple homogeneous slope stability problem. The proposed approach is also applied to a seismic stability problem for a rockfill dam to study the influence of different failure criterions on the upper bound solutions. The results show that the seismic stability coefficients obtained using two different nonlinear failure criteria are similar but that the convergence differs significantly. 相似文献
15.
Considerations on strength of intact sedimentary rocks 总被引：12，自引：0，他引：12
This study presents the results of laboratory testing of sedimentary rocks under point loading as well as in uniaxial and triaxial compression. From the statistical analysis of the data, different conversion factors relating uniaxial compressive and point loading strength were determined for soft to strong rocks. Additionally, the material constant mi, an input parameter for the Hoek and Brown failure criterion, was also estimated for different limestone samples by analysing the results from a series of triaxial compression tests under different confining pressures. The uniaxial compressive strength (UCS) of intact rocks, as estimated from the point load index using conversion factors, together with the Hoek–Brown constant mi, and the Geological Strength Index (GSI) constitute the parameters for the calculation of the strength and deformability of rock masses. 相似文献
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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. 相似文献
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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 (Pf) 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. 相似文献
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This study focuses on the stress and displacement of a circular opening that is excavated in a strain-softening rock mass incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness. It follows the generalized Hoek–Brown failure criterion. Moreover, an improved numerical approach and stepwise procedure are proposed. This approach considers the deterioration of the strength, deformation, and dilation angle and the variation of elastic strain in the plastic region considering the effect of the hydraulic–mechanical coupling and the rockbolts effectiveness. The presented solutions were validated by FLAC results. Several examples are conducted to demonstrate the validity and accuracy of the proposed solution through MATLAB programming. Parametric studies are also conducted to highlight the influences of hydraulic–mechanical coupling and rockbolts effectiveness on stress and displacement. Results show that stress and displacement, incorporating the effects of hydraulic–mechanical coupling and rockbolts effectiveness, are between those when hydraulic–mechanical coupling or rockbolts effectiveness is considered separately. However, this theory needs more verification from practical engineering. 相似文献
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Tamara Al-Bittar Abdul-Hamid Soubra 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2017,11(2):215-229
This paper presents a probabilistic analysis to compute the probability density function of the bearing capacity of a strip footing resting on a spatially varying rock mass. The rock is assumed to follow the generalised Hoek–Brown failure criterion. The uniaxial compressive strength of the intact rock (σc) was considered as a random field and the geological strength index was modelled as a random variable. The uncertainty propagation methodology employed in the analysis is the sparse polynomial chaos expansion. A global sensitivity analysis based on Sobol indices was performed. Some numerical results were presented and discussed. 相似文献