Under compression, cracks extend, branch and coalesce. These fracturing processes have received much attention recently. In this paper, an attempt is made to find the analytical solution of stress intensity factors for the special case of cracks situated along a straight line, and to set up a fracture criterion. Under compression, cracks close and the crack surface friction can resist crack surface sliding. Considering crack surface friction, a set of complex stress functions is proposed for the special case of cracks situated along a straight line. The analytical solution is formulated, and for the case of only two collinear cracks inside an infinite plate, the exact analytical solution of stress intensity factor is presented. Finally, an alternative form of crack propagation criterion for two collinear cracks under compression is developed, which is expressed in terms of principal stresses. For the case of materials without pre-existing macrocracks, this new propagation criterion becomes the well known Coulomb–Mohr criterion.

In order to investigate rock fracture and fragmentation mechanisms under dynamic loading, a cylindrical rock model with a centralized borehole is developed through the use of AUTODYN code. According to the material properties and loading conditions, four kinds of equation of state (EOS), linear, shock, compaction and ideal gas, are applied to the four kinds of materials employed in this numerical model. A modified principal stress failure criterion is applied to determining material status, and a well-behaved explosive, PETN, and a relatively homogeneous igneous rock, diorite, are used in this rock model. A single centrally located line source of explosive is fired numerically to produce the dynamic loadings operating on the surrounding rocks. This numerical model is applied to actual blasting conditions. The rock failure mechanism under dynamic loading is first analyzed, and then the influences of the following factors on rock fracturing are discussed: (a) coupling medium, (b) confinement, (c) boundary condition, (d) initiation location in an explosive column, and (e) air ducking. The results show that all these factors have significant effects on rock fracturing under dynamic loading. r 2007 Elsevier Ltd. All rights reserved.

To investigate the dynamic fracture mechanism related to blast-induced borehole breakdown and crack propagation, circular rock models containing a single centrally located source of explosive were numerically blasted using the AUTODYN 2D code. According to the material properties and loading conditions, four kinds of equations of state, linear, shock, compaction and ideal gas, are used. A modified principal stress failure criterion is applied to determining material status. The dynamic stresses at the selected target points in a rock sample are computed as a function of time following application of explosive load. It is shown that shear stress (resulting from intense compressive stress) causes a crushed zone near the borehole, the major tensile principal stress causes radial cracks, and the reflected stress wave from free boundary causes circumferential cracks some distance away from the free boundary. The influences of the factors of boundary condition, coupling medium, borehole diameter, decoupling and joint on rock dynamic fracture are discussed.

For a cracked specimen under compression, a set of complex stress functions is proposed and by using the boundary collocation method, the unknown coefficients of these complex stress functions are determined. Based on the calculation results of the boundary collocation method, the formulas of the stress intensity factor for a cracked specimen under compression are obtained, and by using these formulas, the influence of confining stress on stress intensity factor is analyzed. 2005 Elsevier Ltd. All rights reserved.

The mixed boundary problems for a mixed mode crack in a finite plate are studied. Based on the stress conditions of uniform loading on crack surfaces, a set of stress functions is proposed, which is also suitable for the case of crack surface without loading. The stress intensity factors (SIFs)are calculated by using the boundary collocation method. For mixed mode crack under resultant force boundary conditions, the present results agree very well with the existing solutions. For mixed mode crack under mixed boundary conditions, the SIFs have been obtained for different crack angles.

An improved method of boundary collocation for the problem in which the crack surface is subjected to uniform load is developed. A new stress function which is based on the stress boundary condition of crack surface is proposed. The conditions on the external boundaries are satisfied approximately by the collocation method. This improved method is applied to calculating the stress intensity factc,r (SIF) values of different angle cracks of square and circular internally cracked plates in which the crack surface is subjected to uniform normal compressive stress q, or uniform shear stress q, The new stre: s function and the calculation procedure are more convenient and simpler than other collocation techniques investigated [1, 2].

针对裂纹表面承受载荷时的应力条件，提出了新的应力函数，该应力函数对于各种裂纹模型、各种边界条件、各种边界形状、裂纹表面自由或承受均布载荷等均适用。并利用边界配位法，计算了在压缩载荷下，岩石内部裂纹的应力强度因子（SIF），给出了关于岩石断裂破坏的一些新结论。