石英岩峰后加卸载非线性断裂扩展及动态长度定量测定

Nonlinear mode-I fracture propagation characteristics and crack length quantitative measurement of quartzite under post-peak multi-cyclic loading

岩体工程灾害是围岩内部原生裂隙/节理起裂、发育到失稳破坏的演化结果,而灾害严重程度与峰后岩体断裂动态扩展特征密切相关.为了实现峰后阶段岩石非线性断裂扩展精准表征及裂纹长度动态定量测定,本文以含预制缺口的石英岩为对象,通过夹式引伸计控制实现了石英岩三点弯曲I型断裂峰后阶段的准静态扩展,借助声发射(AE)和数字图像匹配(DIC)动态追踪了石英岩峰后循环加卸载断裂扩展全过程,提出了能耗展布-位移梯度-力学柔度相结合的非线性裂纹长度定量测定方法,并将动态测定结果与断裂力学理论模型进行了对比验证.结果表明:随着循环次数增加,裂纹张开位移-载荷(COD-P)和载荷点位移-载荷(LPD-P)曲线卸载斜率逐渐变缓柔度增加,裂纹逐渐向前扩展,试样承载能力逐渐下降;每次循环中,声发射在时间上集中出现在峰前损伤应力到峰后卸载点间,在空间分布集聚于裂纹的中上部区域,其定位坐标前端与DIC水平位移等值线交点相重合;在整个加卸载过程中,由AE能耗展布和DIC位移梯度法确定的裂纹长度相接近,其与基于COD-P和LPD-P曲线卸载柔度法反算的裂纹长度差值稳定在5.1 mm,该差值为石英岩断裂过程区(FPZ)长度;通过Dugdale-Barenblatt模型理论计算的石英岩FPZ长度为7.6 mm,其与声-图-力实测结果进行尺寸效应延伸获得无穷大尺寸FPZ渐进临界值吻合较好,验证了本文方法定量测定岩石非线性断裂扩展长度的可靠性,也表明了通过尺寸效应准则延伸来获取工程尺度岩体力学参数的重要性.

Rock engineering disasters result from the evolution result of crack initiation,propa-gation and fracture catastrophes in the surrounding rock.The severity of these disasters prima-rily depends on the dynamic propagation characteristics of fractures in the rock mass during the post-peak stage.To achieve precise characterization of the nonlinear fracture propagation in rocks and to quantitatively determine of dynamic lengths of cracks in the post-peak stage,this study focuses on quartzite beams with a prefabricated notch subjected to a three-point bending configuration.By utilizing a clip extensometer,the quasi-static propagation of mode-I fractures during the post-peak stage is achieved.The detailed crack propagation process in quartzite beam,under post-peak multi-cyclic loading,is visually tracked using acoustic emission(AE)and digital image correlation(DIC)techniques.Subsequently,a quantitative determination method for the nonlinear crack propagation length is proposed based on energy distribution of AE,displacement gradient from DIC,and mechanical compliance.The measured results are then compared with the theoretical model of fracture mechanics for validation.The results show that:with the increase of the post-peak cyclic number,the unloading slope of COD-P(i.e.,crack opening displacement-load)and LPD-P(i.e.,load point displacement-load)curves gradually becomes less steep,which indicates the crack gradually moves forward,and the bearing capacity of the quantize beam gradually decreases.During each cyclic process,the AE events become active starting from the pre-peak damage stress and continue until the post-peak unloading point,while the spatial distributions of these AE events tend to concentrate in the middle and upper regions of the crack.Additionally,the tips of AE events coincide with the in-tersection points of DIC horizontal displacement contour.During the post-peak cyclic loading of quartzite beam,the equivalent crack lengths determined using the AE energy distribution method closely align with the results obtained from the DIC displacement gradient method.Furthermore,the deviations from the traction-free crack length calculated using the unloading compliance method from the COD-P and LPD-P curves remain relatively stable at 5.1 mm.This specified value of 5.1 mm corresponds to the fracture process zone(FPZ)length of the quartzite.According to the Dugdale-Barenblatt model,the calculated FPZ length of quartzite is about 7.6 mm,which shows excellent agreement with the asymptotic critical value for an infi-nite size FPZ as derived from the extension of abovementioned results considering size effects.This agreement demonstrates the reliability of the proposed measurement approach for determi-ning the nonlinear crack propagation length,as well as emphasizes the significance of obtaining me-chanical parameters of rock at an engineering scale by extending the size effect criterion.