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1.
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   

2.
In this paper, distinct element method numerical modeling is applied to evaluate bearing capacity of strip footing rested on anisotropic discontinuous rock mass. As yet, a little work has been carried out to investigate the effect of joint set orientation on the bearing capacity of rock mass. Generally, the overall behavior of rock mass under loading is very complicated and such analysis should include deformation determination, sliding along discontinuities and failure of rock material. Failure mechanism of rock mass depended on both geometrical parameters of joint sets and strength parameters of rock mass. In this research, it is assumed that rock mass contains one joint set, and therefore the anisotropy in bearing capacity and rock behavior is only due to the existence and orientation of the joint set. In this study, by assuming constant strength parameters and using Mohr–Coulomb failure criterion for the single joint set and nonlinear Hoek–Brown failure criterion for rock material, variation of the bearing capacity values and the type of failure mechanism of rock mass with different joint set dips is investigated. The obtained results indicate that the ultimate bearing capacity of rock mass containing one joint set varies between 27 and 86 % of intact rock.  相似文献   

3.
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4.
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   

5.
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   

6.
An Empirical Failure Criterion for Intact Rocks   总被引：1，自引：1，他引：0  
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   

7.
《Engineering Geology》2002,63(1-2):69-82
The empirical method proposed by Hoek and Brown is combined with rock mass classifications to predict the deformation behaviour of İstanbul Metro. The rock mass was assessed using both Bieniawski's RMR89 and its strength was estimated from the formula of Hoek and Brown for the RMR89 system. The applicability and validity of the proposed procedure has been checked by comparing the predictions with actual observations. It is found that the predictions agree well with observations in the intact rock. Although there are some differences between predictions and observations in the faulted rock, these probably reflect the inevitable inaccuracies in empirical approaches, and differences in behaviour of the actual support system that is assumed in modelling. In addition, anisotropy features like faults which are not accounted properly in the Hoek et al. equation that assumes isotropic behaviour.  相似文献   

8.
A new three-dimensional (3D) Hoek–Brown (HB) failure criterion based on an elliptical Lode dependence is proposed to describe failure of rocks and concrete under multiaxial stress states. This criterion not only inherits all benefits of the classical HB criterion that is developed for the triaxial compression (TXC) of rocks but also accounts for the effect of the intermediate principal stress. It is capable of representing the strength difference between the triaxial extension (TXE) and TXC with the introduction of an additional coefficient k (0.5 ≤ k ≤ 1.0), which can be derived from TXE tests or taken as 0.53 for rocks in cases where the TXE test data is unavailable. Other two material constants (mi and σci) involved in this criterion can be obtained from TXC tests. Additionally, the failure surface of this criterion is smooth and convex on the deviatoric stress plane when 0.5 < k ≤ 1.0. The new criterion achieves very good fit to the test data of TXC/TXE, biaxial compression, and polyaxial compression (PXC) on a wide variety of rock materials and concrete, reported in the literature. Comparison of the new criterion with an existing 3D HB criterion based on the same Lode dependence has demonstrated that the new criterion performs better than the latter for test data of rock and concrete under multiaxial stress states except for PXC test data of one rock type. Finally, the influence of values of k on the accuracy of the new criterion is discussed.  相似文献   

9.
By using the upper bound finite‐elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive‐frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, ηc and ηγ, to be multiplied with Nc and Nγ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ? in case of fully granular and cohesive‐frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ?, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

10.
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   

11.
The stress characteristics method (SCM) has been used to compute the bearing capacity of smooth and rough ring foundations. Two different failure mechanisms for a smooth footing, and four different mechanisms for a rough footing have been considered. For a rough base, a curvilinear non-plastic wedge has been employed below the footing. The analysis incorporates the stress singularities at the inner as well as outer edges of the ring footing. Bearing capacity factors, Nc, Nq and Nγ are presented as a function of soil internal friction angle (ϕ) and the ratio (ri/ro) of inner to outer radii of the footing.  相似文献   

12.
This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.  相似文献   

13.
By using the lower bound limit analysis in conjunction with finite elements and linear programming, the bearing capacity factors due to cohesion, surcharge and unit weight, respectively, have been computed for a circular footing with different values of ?. The recent axisymmetric formulation proposed by the authors under ?=0 condition, which is based on the concept that the magnitude of the hoop stress (σθ) remains closer to the least compressive normal stress (σ3), is extended for a general c–? soil. The computational results are found to compare quite well with the available numerical results from literature. It is expected that the study will be useful for solving various axisymmetric geotechnical stability problems. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

14.
By using the method of characteristics, the effect of footing–soil interface friction angle (δ) on the bearing capacity factor Nγ was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance Bt from the footing edge. For a given footing width (B), the value of Bt increases continuously with a decrease in δ. For δ=0, no trapped wedge exists below the footing base, that is, Bt/B=0.5. On the contrary, with δ=?, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in ?. The magnitude of Nγ increases substantially with an increase in δ/?. The maximum depth of the plastic zone becomes higher for greater values of δ/?. The results from the present analysis were found to compare well with those reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

15.
The strength parameter mi in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between mi and the physical characteristics of intact rock, this paper presents a systematic study of mi by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on mi. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on mi. The strength parameter mi increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter mi, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

16.
By applying the lower bound finite element limit analysis in conjunction with non-linear optimisation, the bearing capacity factors, Nc, Nq and Nγ, 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 Nc, Nq and Nγ 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 Nγ, the factors Nc and Nq 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.  相似文献   

17.
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 (quE) is expressed in terms of single coefficient NγE. 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 (df/B0), seismic acceleration (kh, kv) are studied on the variation of seismic bearing capacity co-efficients.  相似文献   

18.
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19.
The effect of a smooth rigid stratum, located beneath a dense sand layer, on the bearing capacity and settlement of surface and shallow strip footings is investigated using an advanced experimental model. A theoretical analysis is presented for the bearing capacity of surface footings. The results indicate that the bearing capacity reaches a minimum value at a specific sand-layer thickness. Any increase in the layer thickness above this value causes an increase in the bearing capacity up to that corresponding to a continuous media.Notation H= thickness of the sand layer - B= foundation width - N q and N = bearing capacity factors for a semi-infinite layer - N qs and N s= bearing capacity factors for a finite layer - H o /B= limiting depth - D r= relative density - = angle of soil internal friction - M= model width - D= depth of surcharge - q= bearing stress, pressure applied on the footing - q u= bearing capacity - = unit weight of sand  相似文献   

20.
A finite element approach based on an advanced multi‐surface kinematic constitutive model is used to evaluate the bearing capacity of footings resting on granular soils. Unlike simple elastic‐perfectly plastic models, often applied to granular foundation problems, the present model realistically accounts for stress dependency of the friction angle, strain softening–hardening and non‐associativity. After the model and its implementation into a finite element code are briefly discussed, the numerical difficulty due to the singularity at the footing edge is addressed. The bearing capacity factor Nγ is then calculated for different granular materials. The effect of footing size, shape, relative density and roughness on the ultimate bearing capacity are studied and the computed results compare very favourably with the general experimental trends. In addition, it is shown that the finite element solution can clearly represent counteracting mechanisms of progressive failure which have an important effect on the bearing capacity of granular foundations. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

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