Three-dimensional finite element simulation of fracture propagation in rock specimens with pre-existing fissure(s) under compression and their strength analysis     

Ramin Pakzad  Shanyong Wang  Scott W. Sloan 《国际地质力学数值与分析法杂志》2020,44(10):1472-1494

A FORTRAN program, consistent with the commercially available finite element (FE) code ABAQUS, is developed based on a three-dimensional (3D) linear elastic brittle damage constitutive model with two damage criteria. To consider the heterogeneity of rock, the developed FORTRAN program is used to set the stiffness and strength properties of each element of the FE model following a Weibull distribution function. The reliability of the program is assessed against available experimental results for granite cylindrical specimens with a throughgoing, flat and inclined fissure. The calibration procedure of the material parameters is explained in detail, and it is shown that the compressive to tensile strength ratio can have a substantial influence on the failure response of the specimens. Numerical simulations are conducted for models with different levels of heterogeneity. The results show a smaller load bearing capacity for models with less homogeneity, representing gradual coalescence of fully damaged elements forming throughout the models during loading. The maximum load bearing capacity is studied for various combinations of inclination angles of two centrally aligned, throughgoing and flat fissures of equal length embedded in cylindrical models under uniaxial and multiaxial loading conditions. The key role of the compressive to tensile strength ratio is highlighted by repeating certain simulations with a lower compressive to tensile strength ratio. It is proven that the peak loads of the rock models with sufficiently small compressive to tensile strength ratios containing two throughgoing fissures of equal length are similar, provided that the minimum inclination angles of the models are the same. The results are presented and discussed with respect to the existing experimental findings in the literature, suggesting that the numerical model applied in this study can provide useful insight into the failure behaviour of rock-like materials.  相似文献   

Implementation of a coupled plastic damage distinct lattice spring model for dynamic crack propagation in geomaterials          下载免费PDF全文

Chao Jiang  Gao‐Feng Zhao 《国际地质力学数值与分析法杂志》2018,42(4):674-693

This paper studies dynamic crack propagation by employing the distinct lattice spring model (DLSM) and 3‐dimensional (3D) printing technique. A damage‐plasticity model was developed and implemented in a 2D DLSM. Applicability of the damage‐plasticity DLSM was verified against analytical elastic solutions and experimental results for crack propagation. As a physical analogy, dynamic fracturing tests were conducted on 3D printed specimens using the split Hopkinson pressure bar. The dynamic stress intensity factors were recorded, and crack paths were captured by a high‐speed camera. A parametric study was conducted to find the influences of the parameters on cracking behaviors, including initial and peak fracture toughness, crack speed, and crack patterns. Finally, selection of parameters for the damage‐plasticity model was determined through the comparison of numerical predictions and the experimentally observed cracking features.  相似文献   

Analytical study of ground motion caused by seismic wave propagation across faulted rock masses          下载免费PDF全文

J.C. Li  N.N. Li  S.B. Chai  H.B. Li 《国际地质力学数值与分析法杂志》2018,42(1):95-109

Studying seismic wave propagation across rock masses and the induced ground motion is an important topic, which receives considerable attention in design and construction of underground cavern/tunnel constructions and mining activities. The current study investigates wave propagation across a rock mass with one fault and the induced ground motion using a recursive approach. The rocks beside the fault are assumed as viscoelastic media with seismic quality factors, Q_p and Q_s. Two kinds of interactions between stress waves and a discontinuity and between stress waves and a free surface are analyzed, respectively. As the result of the wave superposition, the mathematical expressions for induced ground vibration are deduced. The proposed approach is then compared with the existing analysis for special cases. Finally, parametric studies are carried out, which includes the influences of fault stiffness, incident angle, and frequency of incident waves on the peak particle velocities of the ground motions.  相似文献   

On a global expansion of the disturbing function in the planar elliptic restricted three-body problem     

C. Beaugé 《Celestial Mechanics and Dynamical Astronomy》1996,64(4):313-350

Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities.Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.  相似文献   

On the stability of particular solutions of the singly averaged Hill problem     

M. A. Vashkov’yak  N. M. Teslenko 《Astronomy Letters》2005,31(12):844-852

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.  相似文献   

济宁市嘉祥县石灰岩矿山地质环境评价与治理   总被引：1，自引：0，他引：1       下载免费PDF全文

贾德旺  吕宝平  贺汉庭  王学森  范纯信 《山东国土资源》2006,22(5):54-57

在对嘉祥县石灰岩矿进行地质灾害危险性评估、矿山环境地质问题评价的基础上,建立了一套评价体系,其中地质灾害危险性评估分为2个评价指标,矿山环境地质问题评价分为2种要素3个指标,同时将矿山恢复治理难易程度也作为一个评价因子。评价过程中对各指标危害性大、中、小程度均单独赋值,然后将各指标的分值进行叠加,确定出矿山环境地质问题的等级,将概划出的13个评价单元分为极差、差、一般3个区。提出了强化矿山管理、植树造林、科学避让、修建拦水坝等保护与治理措施及建议。  相似文献   

P‐wave transmission across fractures with nonlinear deformational behaviour     

X. B. Zhao  J. Zhao  J. G. Cai 《国际地质力学数值与分析法杂志》2006,30(11):1097-1112

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

有关边界层问题中一类奇异积分方程新的存在性结果     

石丽莉  张高勋 《成都信息工程学院学报》2006,21(6):891-896

对边界层理论新结果中出现的一类奇异积分方程w（t）=∫1 t（1-s）（λ＋λs＋s）/w（s）ds＋（1-t）∫t 0s/w（s）ds,t∈（0,1）进行讨论，并得出了上述方程在λ∈（-1/2,0）上正解存在性的新结果。  相似文献   

Plane of elastic non-resisting tension material under foundation structures     

A. Baratta  I. Corbi 《国际地质力学数值与分析法杂志》2004,28(6):531-542

In the frame of 2D-static problems one approaches the problem of elastic-NRT (not-resisting tension) semi-plane loaded on its limit line. This problem is intended to model the stress situation induced in the soil by a foundation structure. The solution, in terms of activated stress field, is searched for in the class of stress fields satisfying equilibrium and admissibility conditions, by applying an energy approach. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

The response of an elastic half‐space under a momentary shear line impulse     

Moche Ziv 《国际地质力学数值与分析法杂志》2003,27(3):207-232

The response of an ideal elastic half‐space to a line‐concentrated impulsive vector shear force applied momentarily is obtained by an analytical–numerical computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. The shear force is concentrated along an infinite line, drawn on the surface of the half‐space, while being normal to that line as well as to the axis of symmetry of the half‐space. An exact loading model is introduced and built into the computational method for this shear force. With this model, a compatibility exists among the prescribed applied force, the geometric decay of the shear stress component at the precursor shear wave, and the boundary conditions of the half‐space; in this sense, the source configuration is exact. For the transient boundary‐value problem described above, a wave characteristics formulation is presented, where its differential equations are extended to allow for strong discontinuities which occur in the material motion of the half‐space. A numerical integration of these extended differential equations is then carried out in a three‐dimensional spatiotemporal wavegrid formed by the Cartesian bicharacteristic curves of the wave characteristics formulation. This work is devoted to the construction of the computational method and to the concepts involved therein, whereas the interpretation of the resultant transient deformation of the half‐space is presented in a subsequent paper. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献