自由面压力作用下横观各向同性地基多裂纹分析
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摘要
针对自由面均布压力作用下横观各向同性地基中的水平矩形裂纹问题,发展了基于横观各向同性双材料基本解的一种数值方法,该方法不需要离散自由面边界。采用基于横观各向同性双材料基本解的弹性场数值方法获得表面外部圆形荷载作用下地基内的附加应力场,应用断裂力学应力场叠加原理,得到裂纹面上的面力,进而采用横观各向同性双材料对偶边界元方法得到相应的裂纹面间断位移和裂尖应力强度因子。计算结果表明:自由面均布压力作用下横观各向同性地基中的水平矩形裂纹为Ⅱ型和Ⅲ型的混合裂纹。对于处在不同大小附加应力场位置的两条水平矩形裂纹,其裂纹间的相互作用除与两裂纹间距离有关外,还与裂纹位置处附加应力场大小有关,其相互作用对处在附加应力较大位置裂纹的裂尖应力强度因子的影响更大。
A novel numerical method based on the fundamental solutions for two joined transversely isotropic solids is developed. The method is employed to analyze horizontal rectangular cracks in a semi-infinite transversely isotropic medium subjected to uniform circular compressive loading on the free surface. And this method can avoid the discretization of the free surface boundary of the semiinfinite transversely isotropic medium. A numerical method established in the past is utilized to calculate the stress fields of the semi-infinite transversely isotropic medium without a crack. The tractions acted on the crack surface are determined based on the stress fields and the superstition principle of stress field in fracture mechanics. The discontinuity displacements between two cracksurfaces are calculated by the dual boundary element method based on the same fundamental solutions. The stress intensity factors( SIF) at the crack tip are obtained according to the discontinuity displacements. The results show that a single horizontal rectangular crack in a semiinfinite transversely isotropic medium subjected to uniform compressive stress on the free surface leads to a coupled fracture mode including II and III types. For two horizontal rectangular cracks located at different additional stress fields,the interaction between the two horizontal rectangular cracks is related to both the magnitude of the additional stress field at the crack surface and the distance between the two cracks. The interaction between the two cracks has more influence on the SIF of cracks located at a high additional stress field.
A novel numerical method based on the fundamental solutions for two joined transversely isotropic solids is developed. The method is employed to analyze horizontal rectangular cracks in a semi-infinite transversely isotropic medium subjected to uniform circular compressive loading on the free surface. And this method can avoid the discretization of the free surface boundary of the semiinfinite transversely isotropic medium. A numerical method established in the past is utilized to calculate the stress fields of the semi-infinite transversely isotropic medium without a crack. The tractions acted on the crack surface are determined based on the stress fields and the superstition principle of stress field in fracture mechanics. The discontinuity displacements between two cracksurfaces are calculated by the dual boundary element method based on the same fundamental solutions. The stress intensity factors( SIF) at the crack tip are obtained according to the discontinuity displacements. The results show that a single horizontal rectangular crack in a semiinfinite transversely isotropic medium subjected to uniform compressive stress on the free surface leads to a coupled fracture mode including II and III types. For two horizontal rectangular cracks located at different additional stress fields,the interaction between the two horizontal rectangular cracks is related to both the magnitude of the additional stress field at the crack surface and the distance between the two cracks. The interaction between the two cracks has more influence on the SIF of cracks located at a high additional stress field.
引文
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[13]徐栋栋,郑宏,杨永涛,等.多裂纹扩展的数值流形法[J].力学学报,2015,47(3):471-481.
[14]王炳军,肖洪天,党彦,等.横观各向同性地基各向异性对应力场影响研究[J].四川大学学报(工程科学版),2015,47(6):40-48.
[2]PAN E,YUAN F G.Boundary element analysis of three dimensional crack in anisotropic solids[J].International Journal for Numerical Methods in Engineering,2000,48:211-237.
[3]SAEZ A,ARIZA M P,DOMINGUEZ J.Three-dimensional fracture analysis in transversely isotropic solids[J].Engineering Analysis with Boundary Elements,1997,20(4):287-298.
[4]ARIZA M P,DOMINGUEZ J.Boundary element formulation for 3D transversely isotropic cracked bodies[J].International Journal for Numerical Methods in Engineering,2004,60(4):719-753.
[5]陈梦成.横观各向同性材料三维裂纹问题的数值分析[J].计算力学学报,2009,26(1):109-119.
[6]YUE Z Q.Elastic fields in two joined transverselyisotropic solids due to concentrated forces[J].International Journal of Engineering Science,1995,33(3):351-369.
[7]YUE Z Q,XIAO H T,PAN E.Stress intensity factors of square crack inclined to interface of transversely isotropic bi-material[J].Engineering Analysis with Boundary Elements,2007,31:50-56.
[8]王炳军,肖洪天,孙凌志,等.无限域横观各向同性岩体介质中折线裂纹边界元方法[J].岩土力学,2015,36(3):885-890.
[9]王炳军,肖洪天,岳中琦.半无限横观各向同性介质中共面双裂纹边界元分析[J].计算力学学报,2012,29(4):494-499.
[10]WINIARSKI B,GUZ I A.The effect of cracks’interaction for transversely isotropic layeredmaterial under compressive loading[J].Finite Elements in Analysis and Design,2008,44:197-213.
[11]孙可明,张树翠,李天舒.横观各向同性油气藏水力压裂裂纹扩展规律研究[J].计算力学学报,2016,33(5):767-772.
[12]王洪建,刘大安,黎立云,等.扩展有限元法在岩石断裂力学中的应用[J].工程地质学报,2015,23(3):477-484.
[13]徐栋栋,郑宏,杨永涛,等.多裂纹扩展的数值流形法[J].力学学报,2015,47(3):471-481.
[14]王炳军,肖洪天,党彦,等.横观各向同性地基各向异性对应力场影响研究[J].四川大学学报(工程科学版),2015,47(6):40-48.