The paper is motivated by a strong interest in numerical analysis of flow in fractured porous media, e.g., rocks in geo-engineering applications. It follows the conception of porous media as a continuum with fractures which are represented as lower dimensional objects. In the paper, the finite element discretization of the flow in coupled continuum and fractures is used; fluid pressures serve as the basic unknowns. In many applications, the flow is connected with deformations of the porous matrix; therefore, the hydro-mechanical coupling is also considered. The fluid pressure is transferred to the mechanical load in both pores and fractures and the considered mechanical model involves elastic deformations of the porous matrix and opening/closing of the fractures with the non-penetration constraint. The mechanical model with this constraint is implemented via the technique of the Lagrange multipliers, duality formulation, and combination with a suitable domain decomposition method. There is usually lack of information about problem parameters and they undergo many uncertainties coming e.g. from the heterogeneity of rock formations and complicated realization of experiments for parameter identification. These experiments rarely provide some of the asked parameters directly but require solving inverse problems. The stochastic (Bayesian) inversion is natural due to the mentioned uncertainties. In this paper, the implementation of the Bayesian inversion is realized via Metropolis-Hastings Markov chain Monte Carlo approach. For the reduction of computational demands, the sampling procedure uses the delayed acceptance of samples based on a surrogate model which is constructed during a preliminary sampling process. The developed hydro-mechanical model and the implemented Bayesian inversion are tested on two types of model inverse problems.

这篇论文的灵感来自于对破裂的多孔介质（例如，岩土工程应用中的岩石）中的流动进行数值分析的浓厚兴趣。它遵循多孔介质作为具有裂缝的连续体的概念，这些裂缝被表示为低维物体。在本文中，使用了连续体和裂缝耦合中流动的有限元离散化。流体压力是基本的未知数。在许多应用中，流动与多孔基体的变形有关。因此，也考虑了液力耦合。流体压力被传递到孔隙和裂缝中的机械载荷，并且所考虑的力学模型涉及多孔基体的弹性变形和具有非渗透约束的裂缝的打开/闭合。具有此约束的机械模型是通过Lagrange乘数，对偶公式化以及与适当的域分解方法结合的技术来实现的。通常缺少有关问题参数的信息，并且它们会遇到许多不确定性，例如，由于岩层的异质性和用于参数识别的实验的复杂实现。这些实验很少直接提供某些要求的参数，但需要解决反问题。由于提到的不确定性，随机（贝叶斯）反演是自然的。本文通过Metropolis-Hastings马尔可夫链蒙特卡罗方法实现贝叶斯反演。为了减少计算需求，抽样程序使用基于在初步抽样过程中构建的替代模型的样本延迟验收。在两种类型的模型反问题上测试了已开发的流体力学模型和已实现的贝叶斯反演。