SUMMARYA virtual multidimensional internal bond (VMIB) model developed to simulate the propagation of hydraulic fractures using the finite-element method is formulated within the framework of the virtual internal bond theory (VIB) that considers a solid as randomized material particles in the micro scale, and derives the macro constitutive relation from the cohesive law between the material particles with an implicit fracture criterion. Hydraulic pressure is applied using a new scheme that enables simulation of hydraulically driven cracks. When the model is applied to study hydraulic fracture propagation in the presence of a natural fracture, the results show the method to be very effective. It shows that although the in situ stress ratio is the dominant factor governing the propagation direction, a natural fault can also strongly influence the hydraulic fracture behavior. This influence is conditioned by the shear stiffness of the fault and the distance to the original hydraulic fracture. The model results show that when the fault is strong in shear, its impact on hydraulic fracture trajectory is weak and the hydraulic fracture will likely penetrate the fault. For a weak fault, however, the fracture tends to be arrested at the natural fault. The distance between the fault and the hydraulic fracture is also important; the fault influence increases with decreasing distance. The VMIB does not require selection of a fracture criterion and remeshing when the fracture propagates. Therefore, it is advantageous for modeling fracture initiation and propagation in naturally fractured rock.

SUMMARY Propagation of fractures, especially those emanating from wellbores and closed natural fractures, often involves Mode I and Mode II, and at times Mode III, posing significant challenges to its numerical simulation. When an embedded inclined fracture is subjected to compression, the fracture edge is constrained by the surrounding materials so that its true propagation pattern cannot be simulated by 2D models. In this article, a virtual multidimensional internal bond (VMIB) model is presented to simulate three‐dimensional (3D) fracture propagation. The VMIB model bridges the processes of macro fracture and micro bond rupture. The macro 3D constitutive relation in VMIB is derived from the 1D bond in the micro scale and is implemented in a 3D finite element method. To represent the contact and friction between fracture surfaces, a 3D element partition method is employed. The model is applied to simulate fracture propagation and coalescence in typical laboratory experiments and is used to analyze the propagation of an embedded fracture. Simulation results for single and multiple fractures illustrate 3D features of the tensile and compressive fracture propagation, especially the propagation of a Mode III fracture. The results match well with the experimental observation, suggesting that the presented method can capture the main features of 3D fracture propagation and coalescence. Moreover, by developing an algorithm for applying pressure on the fracture surfaces, propagation of a natural fracture is also simulated. The result illustrates an interesting and important phenomenon of Mode III fracture propagation, namely the fracture front segmentation. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, a posture analysis method for the Crass-Country Autonomous Land Vehicle (CCALV) is proposed.To simplify the discussion, assume that(1) the terrain is hard and with random height.(2) the local terrain map is known through sensory system and described by a set of height data (2, 1 of the discrete ground pints I (x, ,y, ) 1 which are divided equally along x and y axes.(3) the C%ALV is replaced with a regular rectangular plane ABCD.At a special moment during steering of the FCALV, assume that its center (xo,y,) and steering direction, i.e the yaw angle p are given, we shall determine the contact plane between the plane ABCD and the ground. This plane is defined as the posture plane of the ccL4V with respect to (xo,yol 9) and the corresponding posture angle pair ( 0 ,~) is defined as the posture of the CCALV with respect to (xo,yo,p), where the 8 , y are the pitching angle and the r o l l angle of the CCALV respectively.The basic idea of the nunerica1 algorithm for solving the posture of the CCALV can be expressed as follows. For given (x ,yo,@), consider the admissible range of 0 , y E ( -5 , :). Divide it into small parts so that ( 0 ,~) is fixed relatively in each one. For each specially fixed p i r ( e l , y I J ) , find the projection region of the plane ABCD on XOY plane Q l , and based on it solve the contact posture of the plane with the ground ( 0 , y ) . Verify weather the postrue of the plane is coincident with the given (el , y I ) . The whole procedure may On n be described by the following step-by-step search algorithm.Main Algorithm step 1 Translate the origin of the ground coordinate system to (xoryOrO) and rotate @ around the new 2 axis; step 2 Determine the search series (y,(i=l,---,k), 0 (i=l,----,k; j=l,--.-,ml ) ) according to the projection region of ABCD on XOY plane which can be calculated through the hmrogeneous transformation between the plane and the ground coordinate systems;1.i step 3 For each projection region Q I J determined by ( y , , 0 ) , find the covering plane which contains the three heightest points P, (xk , y,, zk), k=1,2,3 on Q I J while the center line of ABCD passes throuh AP1pzP3. It is the possible contact plane of CCALV with the ground and can be easily obtained accoding to the heiht data (2,) on Q step 4 Solve the corresponding (@,I) according to the above covering plane.