论文标题
部分可观测时空混沌系统的无模型预测
Fault friction under thermal pressurization during large coseismic-slip Part I: Numerical analyses
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
In this paper, we study the role of thermal pressurization in the frictional response of a fault under large coseismic slip. We investigate the role of the seismic slip velocity, mixture compressibility, characteristic grain size and viscosity parameter in the frictional response of the coupled thermo-hydro-mechanical problem, taking into account the fault's microstructure. Starting from the mass, energy and momentum balance for Cosserat continua we derive the equations of our model. We complete the mathematical description using perfect plasticity and Perzyna viscoplasticity in the material constitutive behavior. We investigate both the rate independent as well as the rate dependent frictional response and compare with existing models found in literature, namely the rate and state friction law (Dieterich (1992),Ruina(1983a)). We show that our model is capable of predicting strain rate hardening and velocity softening without the assumption of a state variable. We observe traveling instabilities inside the layer that lead to oscillations in the fault's frictional response, like in the case of Portevin Le Chatelier (PLC) effect. This behavior is not captured by existing numerical analyses presented in Rattez et al. (2018c,b,a) and go beyond the established models of uniform shear (Lachenbruch (1980)) and shear on a mathematical plane (Rice (2006a)), which predict a strictly monotonous behavior during shearing. Recent experimental analyses, which have managed to insulate thermal pressurization from other weakening mechanisms (Badt et al. (2020)), corroborate our numerical results.
