【作者】 吴子科；

【导师】 刘传孝；

【作者基本信息】 山东科技大学 ， 工程力学， 2007， 硕士

【摘要】 本文通过断裂力学理论得出了岩石裂纹尖端附近的应力场和位移场的二维解析解，并推导出了裂纹尖端应力强度因子的表达式，该强度因子就是裂纹扩展趋势和裂纹扩展推动力的度量。探讨了含有裂隙的岩石在压缩状态下的破坏机制。如果工程岩体内深埋裂纹的长轴明显大于短轴，那么椭圆形深埋裂纹可以简化为椭圆形贯穿裂纹来进行处理。推导出了有效裂纹长度理论表达式，提出了裂纹扩展率这一概念。并用试验的手段得到了理论分析和数值模拟所需要的岩石试件的物理力学参数。计算出了在不同压应力作用下六种模型的有效裂纹长度与裂纹扩展率的理论值。通过FLAC^3D有限元软件模拟分析了岩石裂纹尖端在压应力作用下的扩展规律及应力集中情况，得出了裂纹开裂方向，并从裂纹尖端演化状态的评价参数中提取出了应力等指标的时间序列。裂纹的塑性区状态表明了裂纹区域的张拉破坏形式，并且塑性区的范围随着压应力的增大而增加。比较裂纹扩展率的理论值和数值实验值，发现在不同压应力作用下两者基本吻合。垂直应力等值线表明裂纹集中区域最大主应力与裂纹尖端水平方向相差一个具体的角度θ，θ随着压应力的增大而变大。通过相空间的重构，求得水平应力和垂直应力等指标的时间序列嵌入饱和维下的最大Lyapunov指数。由于最大Lyapunov指数均为正值，表明裂纹尖端扩展状态是混沌的。通过Kolmogorov熵定量地评价了裂纹尖端扩展的混沌程度，得出：岩石裂纹尖端扩展状态在低应力作用下混沌程度较低，15MPa以后的相对高应力作用下混沌程度较高。更多还原

【Abstract】 Through the fracture mechanics theory, two-dimensional analytic solution of stress field and displacement field on the tip of crack had been obtained. And expression of crack’s stress intensity factor, which is a measure of the crack expansion tendency and the crack expansion propelling force, was inferred. Destruction mechanism of rock included crack under compressive stress condition had been discussed. If elliptical shape immerged crack’s long axis is obviously greater than minor axis in project rock mass, then it will be allowed to simplify to be a breakthrough ellipse crack on processing. The expression of effective crack length was deduced. And concept of crack expansion rate was proposed. And rock’s test physical mechanical parameters which are useful for theoretical analysis and numerical experiment were got by experimental method. The theoretical values of effective crack length and crack expansion rate under the different compressive stress were calculated.Through finite element software FLAC3D numerical experiment, the crack’s expansion rule and stress concentration situation under different compressive stress are analyzed. And then the crack dehiscence direction had been obtained. Further more, time series were extracted from the crack’s the stress field. The crack plastic condition had indicated crack’s destruction form, and the plastic area scope increases along with the compressed stress increases. The experiment value of crack expansion rate, contrasting with theoretical value, is basically concordance under different compressive stress. The impressive stress isoclines indicates between the biggest principal stresses in crack concentrates region and the crack’s horizontal direction presents a angle, and it increases along with compressed stress under the model increases.Through reconfiguration of time series’ phase space, the biggest Lyapunov exponent was extracted from the horizontal stress and the vertical stress’s time series. All of exponents are positive, which indicates this system is chaotic. Then the stress condition of tip of crack is in chaos. Finally the level of chaos about stress of crack is evaluated by Kolmogorov entropy. The extended state of rock crack is much more chaotic under higher stress while is less under lower stress.更多还原