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1.
In this paper, the strength envelope of rock masses is considered to follow a non-linear unified strength criterion that considers the effect of the intermediate principal stress. A unified slip line method for resolving the differential equation system that governs the stress field is established to research the ultimate bearing capacity, which can be adapted for a wide variety of rock masses. Through this new theory, a suitable characteristic method for rock masses of interest can be obtained, and the relationships between different types of characteristic methods are revealed. The characteristic methods are based on different strength criteria, such as the Hoek–Brown criterion, modified Hoek–Brown criterion, or non-linear twin-shear strength criterion; each of these criteria is a special case of the proposed theory. Moreover, a series of new characteristic methods can be easily derived from it. In terms of the proposed theory, the ultimate bearing capacity with the Hoek–Brown criterion forms the lower bound; the ultimate bearing capacity with a non-linear twin-shear strength criterion forms the upper bound; and a series of the ultimate bearing capacities ranging between these two bounds may be derived from a non-linear unified strength criterion. A comparison is made between existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. It is shown that the present results are in good agreement with existing numerical analyses and non-linear finite element analysis solutions with the Drucker–Prager strength criterion. 相似文献
2.
A strain hardening model is proposed for simulation of the shear behavior of rockfills, including the non-linear stress–strain relationship, stress-dependence of stiffness, non-linear strength envelope, and particularly the shearing contraction and dilatancy. This model utilizes the Mohr–Coulomb yield criterion, which is defined by the mobilized friction angle varying with plastic octahedral shear strain. The development of Rowe’s stress dilatancy theory is reviewed, with its limitation for rockfills highlighted. A modified solution is then proposed to derive the mobilized dilatancy angle of rockfills. Compared with large-scale triaxial testing results, it has been demonstrated that this simple model is capable of predicting the shear behavior of rockfills with fair accuracy. 相似文献
3.
Probabilistic analysis of underground rock excavations using response surface method and SORM 总被引：6，自引：0，他引：6
Probabilistic analysis of underground rock excavations is performed using response surface method and SORM, in which the quadratic polynomial with cross terms is used to approximate the implicit limit state surface at the design point. The response surface is found using an iterative algorithm and the probability of failure is evaluated using the first-order and the second-order reliability method (FORM/SORM). Independent standard normal variables in U-space are chosen as basic random variables and transformed into correlated non-normal variables in the original space of random variables for constructing the response surface. The proposed method is first illustrated for a circular tunnel with analytical solutions considering Mohr–Coulomb (M–C) and Hoek–Brown (H–B) yield criteria separately. The failure probability with respect to the plastic zone criterion and the tunnel convergence criterion are estimated from FORM/SORM and compared to those obtained from Monte Carlo Simulations. The results show that the support pressure has great influence on the failure probability of the two failure modes. For the M–C model, the hypothesis of uncorrelated friction angle and cohesion will generate higher non-performance probability in comparison to the case of negatively correlated shear strength parameters. Reliability analyses involving non-normal distributions are also investigated. Finally, an example of a horseshoe-shaped highway tunnel is presented to illustrate the feasibility and validity of the proposed method for practical applications where numerical procedures are needed to calculate the performance function values. 相似文献
4.
L. Zhang 《Rock Mechanics and Rock Engineering》2008,41(6):893-915
Summary Although the Hoek–Brown strength criterion has been widely used in rock mechanics and rock engineering, it does not take account
of the influence of the intermediate principal stress. Much evidence, however, has been accumulating to indicate that the
intermediate principal stress does influence the rock strength in many instances. Therefore, researchers have developed three-dimensional
(3D) versions of the Hoek–Brown strength criterion. In this paper, three existing 3D versions of the Hoek–Brown strength criterion
are reviewed and evaluated. The evaluation shows that all of the three 3D versions of the Hoek–Brown strength criterion have
limitations. To address the limitations, a generalized 3D Hoek–Brown criterion is proposed by modifying the generalized Hoek–Brown
strength criterion. The proposed 3D criterion not only inherits the advantages of the Hoek–Brown strength criterion but can
take account of the influence of the intermediate principal stress. At a 2D stress state (triaxial or biaxial), the proposed
3D criterion will simply reduce to the form of the generalized Hoek–Brown strength criterion. To validate the proposed 3D
strength criterion, polyaxial or true triaxial compression test data of intact rocks and jointed rock masses has been collected
from the published literature. Predictions of the proposed generalized 3D Hoek–Brown strength criterion are in good agreement
with the test data for a range of different rock types. The difference of the proposed generalized 3D Hoek–Brown strength
criterion from and its advantages over the existing 3D versions of the Hoek–Brown strength criterion are also discussed. It
should be noted that the proposed 3D criterion is empirical in nature because it is an extension of the 2D Hoek–Brown strength
criterion, which is empirical. Because of the non-convexity of the yield surface for a biaxial stress state, the proposed
3D criterion may have problems with some stress paths.
Correspondence: L. Zhang, Department of Civil Engineering and Engineering Mechanics, The University of Arizona, Tucson, Arizona
85721, USA 相似文献
5.
The brittle failure behavior of an over-consolidated clay shale (Opalinus Clay) in undrained rapid triaxial compression was
studied. The confining stress levels were chosen to simulate the range of confining stresses relevant for underground excavations
at the Mont Terri Underground Research Laboratory, and to investigate the transition from axial splitting failure to macroscopic
shear failure. Micro-crack initiation was observed throughout the confining stress range utilized in this study at a differential
stress of 2.1 MPa on average, which indicates that friction was not mobilized at this stage of brittle failure. The rupture
stress was dependent on confinement indicating friction mobilization during the brittle failure process. With increasing confinement
net volumetric strain decreased suggesting that dilation was suppressed, which is possibly related to a change in the failure
mode. At confining stress levels ≤0.5 MPa specimen rupture was associated with axial splitting. With increasing confinement,
transition to a macroscopic shearing mode was observed. Multi-stage triaxial tests consistently showed lower strengths than
single-stage tests, demonstrating cumulative damage in the specimens. Both the Mohr–Coulomb and Hoek–Brown failure criteria
could not satisfactorily fit the data over the entire confining stress range. A bi-linear or S-shaped failure criterion was
found to satisfactorily fit the test data over the entire confinement range studied. 相似文献
6.
This paper presents a numerical investigation of shear behavior and strain localization in cemented sands using the distinct element method (DEM), employing two different failure criteria for grain bonding. The first criterion is characterized by a Mohr–Coulomb failure line with two distinctive contributions, cohesive and frictional, which sum to give the total bond resistance; the second features a constant, pressure-independent strength at low compressive forces and purely frictional resistance at high forces, which is the standard bond model implemented in the Particle Flow Code (PFC2D). Dilatancy, material friction angle and cohesion, strain and stress fields, the distribution of bond breakages, the void ratio and the averaged pure rotation rate (APR) were examined to elucidate the relations between micromechanical variables and macromechanical responses in DEM specimens subjected to biaxial compression tests. 相似文献
7.
The strength of frozen soils has been one of the most extensively studied aspects in frozen soil mechanics. When carrying
out deep excavations using freezing methods, high stress states are often encountered. Therefore, the strength of frozen soils
under high confining pressures is of major concern. This paper first reviews the present failure criteria for frozen soils,
especially with regard to the effect of confining pressure on the strength. It is suggested that the strength consists of
two components, cohesion and friction, and can be expressed by the Mohr–Coulomb criterion and in the framework of the Drucker–Prager
criterion. However, these two components are both dependent on the stress state. Duncan’s equation for the friction angle
is extended to frozen soils. A frozen Lanzhou fine sand is taken as study subject. The frozen sand is compressed at a high
strain rate under three different temperatures and under a wide range of confining pressure. Experimental results have confirmed
the generally recognized principle that the strength increases with the confining pressure up to certain value. Thereafter,
it decreases with continued increase in confining pressure. Experimental data from our own tests and literature are fitted
to the new criterion, which shows its validity. 相似文献
8.
9.
The original Hoek–Brown failure criterion was first introduced in 1980. Since then, it has been further developed and used
in different rock mechanics applications. The main advantage of the Hoek–Brown criterion is that its input data are determined
from the uniaxial compressive strength, mineralogy and structural properties of the rock. However, its application in the
petroleum industry has been limited, partly because it does not take account of the intermediate principal stress in a three-dimensional
stress state. In 2005, Priest introduced comprehensive and simplified versions of a new three-dimensional Hoek–Brown yield
criterion, which was developed by combining the two-dimensional Hoek–Brown and three-dimensional Drucker–Prager criteria.
Until now, direct analytical solutions have not been developed to solve the governing equations and numerical solution strategies
have been applied. This paper presents and validates an explicit solution for the comprehensive three-dimensional Hoek–Brown
yield criterion, which can be combined with numerical stress modelling codes. 相似文献
10.
This paper presents a numerical approach to analyse the stability of slopes in soils with strain-softening behaviour. In these materials, a progressive failure can occur owing to a reduction of strength with increasing strain. Such a phenomenon can be analysed using methods that are able to simulate the formation and development of the shear zones in which strain localises. From a computational point of view, this presents many difficulties because the numerical procedures currently used are often affected by a lack of convergence, and the solution may depend strongly on the mesh adopted. In order to overcome these numerical drawbacks, in the present study use is made of a non-local elasto-viscoplastic constitutive model within the framework of the finite element method. The Mohr–Coulomb yield function is adopted, and the strain-softening behaviour of the soil is simulated by reducing the strength parameters with the increasing deviatoric plastic strain. To assess the reliability of the proposed approach, some comparisons with the results obtained using other constitutive models for soils with strain-softening behaviour are presented. Finally, a slope subjected to a prescribed process of weathering is considered, and the effects of this process on the slope stability are discussed. 相似文献
11.
修正有限元强度折减法与失稳判据在边坡稳定分析中的应用 总被引：1，自引：0，他引：1
现有的有限元强度折减法用于边坡稳定性分析,在土体变形特性的认识和失稳判据上有缺陷。基于土体的应力-应变曲线和邓肯-张非线性弹性模型进行有限元强度折减法计算分析,在现有方法仅对强度参数--黏聚力c和内摩擦角φ进行折减的基础上,提出了切线弹性模量Et的折减算法,更全面地体现折减的内涵;提出了以潜在滑动区域的能量积分变化作为判据,根据能量积分与折减系数关系曲线的特征,将其拟合成两段直线,以其交点所对应的折减系数作为边坡的安全系数。比较分析了修正Duncan有限元强度折减法、失稳判据与文献的计算结果,同时分析了边坡滑动区能量积分计算范围对结果的影响,并用于南水北调东线实际工程计算分析。结果表明：修正Duncan有限元强度折减法能较全面考虑土体的变形和强度特性,新的边坡滑动失稳判据可行且具有较好的计算稳定性,能保证工程建设的安全。 相似文献
12.
基于双强度折减策略的边坡稳定性分析方法探讨 总被引：3，自引：0，他引：3
基于能耗分析理论,假定黏聚力和内摩擦角按不同折减系数进行强度折减,采用不同边坡综合安全系数定义方式,根据虚功原理推导了各自综合安全系数的目标函数表达式。采用序列二次规划法和内点法编制了非线性规划迭代程序,对综合安全系数目标函数进行优化求解。依据算例结果探讨了双强度折减技术评价方法对边坡安全系数计算的影响规律。研究结果表明,边坡稳定性影响因素众多,抗剪强度参数c与φ的折减系数之间不存在惟一确定的函数关系,现有预先假定黏聚力和内摩擦角按某一比例进行强度折减的处理方法尚难以完全合理解释;通过强度折减的最短路径来定义边坡综合安全系数的方法物理意义更为明确。研究结论可为工程技术人员加深采用强度折减技术进行边坡稳定性分析的认识提供有益参考。 相似文献
13.
Determination of Shear Strength and Three-dimensional Yield Strength for the Hoek-Brown Criterion 总被引：1，自引：3，他引：1
S. D. Priest 《Rock Mechanics and Rock Engineering》2005,38(4):299-327
Summary. Most currently used techniques for analysing the stability of near surface structures, such as rock slopes, are based on the application of the effective Coulomb shear strength parameters cohesion c′, and the angle of friction φ′ on some known or anticipated shear surface subjected to an effective normal stress σ′n. The most widely used of these techniques are the variants of the method of slices and related upper bound techniques. If the Hoek-Brown criterion is to be used to model the strength of near surface fractured rocks, it is necessary to determine equivalent Coulomb shear strength parameters for the specified level of effective normal stress. Calculation of the equivalent Coulomb parameters for the Hoek-Brown criterion for cases when a ≠ 0.5 is not a straightforward matter. A simple procedure for calculating instantaneous values of c′i and φ′i has been developed based on spreadsheet calculations and the application of a numerical optimisation routine. This procedure can also be applied to calculating the Hoek-Brown envelope plotted in shear stress/normal stress space. A simple closed form solution for c′i and tan φ′i has also been developed for the special case when a = 1. A three-dimensional version of the Hoek-Brown criterion has been developed by combining it with the Drucker-Prager criterion. This new yield criterion has been implemented by numerical solution of the governing equations. A simplification of this three-dimensional yield criterion has been developed by introducing an intermediate principal stress weighting factor. Comparison with published results demonstrates that this simplified criterion has the capacity to model the results of true triaxial tests for a range of different rock types over a wide range of stress levels. The new three-dimensional yield criterion has the advantage that its input parameters can be determined from routine uniaxial compression tests and mineralogical examination. 相似文献
14.
S. D. Priest 《Rock Mechanics and Rock Engineering》2010,43(4):379-389
This article focuses on two broad categories of yield criteria: those based on the Hoek–Brown yield criterion and a range
of other widely used criteria. The first group of criteria source their input data from uniaxial compressive strength, coupled
with mineralogical and structural properties of the rock. The second group of selected criteria, here referred to as ‘frictional
criteria’, source their input data from one or more of the parameters uniaxial compressive strength, cohesion and friction.
Although some authors have attempted to compare the predictions of the wide range of published criteria, the results have
not been entirely satisfactory due to disparities in the input data and the difficulties in extrapolating a two-dimensional
criterion into three-dimensions. This article presents a strategy for achieving a consistent basis for comparing three-dimensional
yield criteria for rock. This strategy is based on using the two-dimensional Hoek–Brown criterion as a single ‘front end’
for calculating the input parameters for the selected frictional criteria. In essence, four amended yield criteria have been
defined: the Hoek–Brown–Drucker–Prager (which is a close approximation to the comprehensive Priest criterion); the Hoek–Brown-Coulomb;
the Hoek–Brown-modified Wiebols and Cook; and the Hoek–Brown-modified Lade. The predictions of these criteria, and also the
comprehensive Zhang-Zhu criterion, can be approximated over a limited range of intermediate principal stress by selecting
a value for the weighting factor w between 0.2 and 0.5 in the simplified Priest criterion to achieve the appropriate sensitivity to the intermediate effective
principal stress. 相似文献
15.
土体的各向异性与沉积环境和应力历史密切相关。以能够考虑土体特性的各向异性不排水抗剪强度公式为基础,利用圆弧滑动方法,并考虑破坏面上强度的折减（ ）,推导各向异性软土基坑抗隆起稳定极限平衡解。对软土基坑抗隆起稳定进行研究,系统分析了开挖深度H、围护结构插入深度D、最下道支撑与坑底相对距离He/H等几何因素及土体有效内摩擦角 、各向异性强度比k及强度沿深度非均质变化的斜率 等强度参数的影响。最后结合工程实例,验证了公式的适用性,为软土基坑工程抗隆起分析提供了新的思路。 相似文献
16.
Modelling of landslides with the material-point method 总被引：2，自引：0，他引：2
A numerical model for studying the dynamic evolution of landslides is presented. The numerical model is based on the Generalized
Interpolation Material Point Method. A simplified slope with a house placed on top is analysed. An elasto-plastic material
model based on the Mohr–Coulomb yield criterion is employed for the soil. The slide is triggered for the initially stable
slope by removing the cohesion of the soil and the slide is followed from the triggering until a state of static equilibrium
is again reached. Parameter studies, in which the angle of internal friction of the soil and the degree of discretisation
are varied, are presented. 相似文献
17.
By incorporating the fabric effect and Lode’s angle dependence into the Mohr–Coulomb failure criterion, a strength criterion for cross-anisotropic sand under general stress conditions was proposed. The obtained criterion has only three material parameters which can be specified by conventional triaxial tests. The formula to calculate the friction angle under any loading direction and intermediate principal stress ratio condition was deduced, and the influence of the degree of the cross-anisotropy was quantified. The friction angles of sand in triaxial, true triaxial, and hollow cylinder torsional shear tests were obtained, and a parametric analysis was used to detect the varying characteristics. The friction angle becomes smaller when the major principal stress changes from perpendicular to parallel to the bedding plane. The loading direction and intermediate principal stress ratio are unrelated in true triaxial tests, and their influences on the friction angle can be well captured by the proposed criterion. In hollow cylinder torsional shear tests with the same internal and external pressures, the loading direction and intermediate principal stress ratio are related. This property results in a lower friction angle in the hollow cylinder torsional shear test than that in the true triaxial test under the same intermediate principal stress ratio condition. By comparing the calculated friction angle with the experimental results under various loading conditions (e.g., triaxial, true triaxial, and hollow cylinder torsional shear test), the proposed criterion was verified to be able to characterize the shear strength of cross-anisotropic sand under general stress conditions. 相似文献
18.
不同于常规土体单元试验中恒定围压的应力路径,进行了减围压（卸载）应力路径下丰浦砂的平面应变压缩试验,研究了初始围压和初始相对密度对砂土的剪切强度和剪切带特性的影响。结合二维数字图像（DIC）相关方法,分析剪切带的形成过程,对剪切带的厚度和倾角及其影响因素进行定量地分析。研究结果表明,剪切带形成于峰值剪切强度之前;对于密实丰浦砂试样,随着围压的增加,其剪切强度(最大有效主应力比)减小且峰值强度出现越晚,剪切带厚度减小而剪切带倾角变化不大;丰浦砂试样的相对密度越高,剪切强度越大且峰值强度出现越早,剪切带厚度越小而剪切带倾角越高。此外,基于峰值内摩擦角的Coulomb公式可以较好地预测平面应变试验条件下丰浦砂的最大剪切带倾角。 相似文献
19.
非线性Hoek-Brown强度折减技术 总被引：1，自引：1，他引：0
为精确执行非线性Hoek-Brown(HB)强度折减,首先在p-q空间分析了HB曲线任意点切线与Mohr-Coulomb(MC)准则的对应关系,推求了HB屈服函数材料折减系数和强度折减系数的关系,提出了潜入强度折减系数的HB弹塑性分析模型,介绍了在Flac3D平台上二次开发实现非线性HB强度折减的基本思路。对一边坡算例用本文方法和简化Bishop法进行了对比分析,计算结果表明,潜入强度折减系数的HB弹塑性模型计算获得的边坡潜在滑动面形态、位置和相应的安全系数,与简化Bishop法计算结果很接近。 相似文献
20.
Sukanya Chakraborti Heinz Konietzky Katrin Walter 《Geotechnical and Geological Engineering》2012,30(4):925-934
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. 相似文献