准脆性材料声发射的损伤模型及统计分析

岩石、混凝土等材料的声发射是与材料内部损伤密切相关的伴生现象，对其信息的研究有助于揭示材料破裂机制，在地震、岩爆、岩体稳定、应力量测等工程领域有广泛的应用。利用累积声发射数与损伤变量一致的观点，建立准脆性材料声发射的损伤模型，得到声发射率和Kaiser效应的一般表达式，并给出恒位移速率和恒荷载速率加载方式下声发射率与时间的解析关系。在一般情况下，声发射的位移或应变变化率与加载方式和加载体的刚度无关，由材料本身决定；当采用恒位移速率加载并调节加载体的刚度或采用恒荷载速率加载，声发射都会出现前震-主震模式。通过假定损伤演化函数分别为Weibull和对数正态分布概率密度函数，证实材料的声发射活动普遍存在初始平静、接近强度极限时剧烈、后期逐渐沉寂等过程；当材料均匀程度由高到低变化，声发射存在主震、前震-主震-后震和群震3种声发射模式，再现Kaiser效应，并且每次重新加载并超过前次荷载水平后，声发射活动变得更加剧烈。

A DAMAGE MODEL AND STATISTICAL ANALYSIS OF ACOUSTIC EMISSION FOR QUASI-BRITTLE MATERIALS

The damage process is accompanied by the acoustic emission(AE)for quasi-brittle materials such as rocks,concretes,ceramics and so on.The facts and data of the AE and the Kaiser effect can reveal some useful information about the damage and crack mechanisms.The AE techniques have wide applications in many aspects including earthquake,rock burst,stability,stress estimation,etc..A damage model for the AE of quasi-brittle materials is established based on that the numbers of cumulative AE hits are proportional to the damage variable.The AE hit rates versus strain,deformation and time,and the Kaiser effect are formulated with this model.The analytical relationships of the hit rate versus time in uniaxial compressions with constant deformation increase and constant stress increase are obtained.It is found that the hit rate versus deformation or strain is determined only by the material itself and is independent of the loading pattern and the stiffness of loading system.When compressed at constant stress rate,all kinds of materials have only one AE type,i.e.foreshock-main shock type.Some comparative statistical analyses are conducted by further consumption that the damage evolution functions are the Weibull probabilistic density function and the lognormal probabilistic density function.For all kinds of materials,the AE activity develops from the beginning calmness to the high frequency in the vicinity of the material strength and vanishes gradually in the end.As the homogeneity varies from low to high,the AE of materials loaded at constant deformation rate has three fundamental types,i.e.distributional shock type,foreshock-main shock-aftershock type and main shock type.The damage model expressed by both distributions also demonstrates the Kaiser effect.It can be observed obviously that the AE activity becomes active as the reloading level exceeds the historic maximum load.