【作者】 刘斌；

【导师】 刘正和；

【作者基本信息】 太原理工大学 ， 资源与环境（专业学位）， 2024， 硕士

【摘要】 在岩石力学领域,损伤和断裂是两种至关重要的破坏形式。它们不仅影响着岩石的物理属性,更直接关系到工程实践中的安全性和稳定性。岩石的损伤和断裂,其内在机制相当复杂,与岩石的内部结构、所承受的应力状态、力学属性以及所处的环境条件等多种因素紧密相连。岩石损伤相场模型,就是近年来在岩石力学领域兴起的一种新型模型。但传统的相场模型是建立在拉压对称性假设基础上的,这种假设对于许多材料来说是合理的,对于岩石材料却并不适用。因为岩石材料的抗拉强度和抗压强度有着巨大的差异,这种特性使得岩石在受到拉应力和压应力时,其断裂行为会呈现出明显的不对称性。同时,在传统的相场本构模型中,相场长度尺度与物理长度尺度之间是紧密联系的。当分析的结构尺寸比较大(即远大于其物理长度尺度)时,所需的网格密度会变得非常高,这会导致计算成本急剧上升,使得其难以应用于大尺度的实际工程案例。为了克服这一局限性,需要对传统的相场模型进行改进,以使其能够更准确地描述大尺度岩石的断裂行为。为了解决相场法模拟的上述问题,本论文主要完成的工作及结论如下:(1)首先运用了基于Drucker-Prager断裂准则的能量分解方法,成功实现了岩石在拉伸和压缩过程中的不对称断裂行为。在此基础上进一步推导了适用于Drucker-Prager断裂面中的相关参数。由于Drucker-Prager破坏面理论在描述岩石等颗粒状材料的破坏行为方面具有显著优势,所以本文将其与相场断裂模型的结合,可以更准确地模拟岩石在复杂应力状态下的断裂过程。同时在相场本构方程中引入了一种新型的退化函数,这一函数将原本紧密关联的相场长度与物理长度尺度分离开来,有效地消除它们之间的相互作用,降低了模型计算对网格密度的要求,提高了模拟的效率和准确性,也使得用相场法模拟大型结构中的裂纹增长成为可能。(2)构建了基于Drucker-Prager岩石断裂相场模型。基于ABAQUS平台二次开发搭建了便于分析大型结构中的裂纹增长的岩石损伤断裂相场模型。该模型引入了Drucker-Prager断裂准则的能量分解方法和一种新型的退化函数,旨在于实现大尺度岩石的断裂的相场法数值模拟。(3)通过模拟实验验证了该算法的准确性和高效性,同时模拟了实际工程案例中大型岩体中的裂纹扩展并进行分析。以上的一系列实验证明了该岩石断裂相场模型在大尺度岩石数值模拟方面的优势和潜力。基于本文的相场模型,可以更加准确地预测岩体的损伤和断裂过程,从而制定出更加科学、合理的工程设计和施工方案。更多还原

【Abstract】 In the field of rock mechanics,damage and fracture are two crucial forms of failure.They not only affect the physical properties of rocks,but also directly relate to the safety and stability in engineering practice.The internal mechanism of rock damage and fracture is quite complex,closely related to various factors such as the internal structure of the rock,the stress state it bears,mechanical properties,and the environmental conditions it is in.The rock damage phase field model is a new type of model that has emerged in the field of rock mechanics in recent years.However,traditional phase field models are based on the assumption of tension compression symmetry,which is reasonable for many materials but not applicable to rock materials.Due to the significant difference in tensile and compressive strength of rock materials,this characteristic leads to significant asymmetry in their fracture behavior when subjected to tensile and compressive stresses.Meanwhile,in traditional phase field constitutive models,there is a close relationship between the phase field length scale and the physical length scale.When the size of the analyzed structure is relatively large(i.e.much larger than its physical length scale),the required grid density becomes very high,which leads to a sharp increase in computational costs and makes it difficult to apply to large-scale practical engineering cases.To overcome this limitation,it is necessary to improve the traditional phase field model to more accurately describe the fracture behavior of large-scale rocks.In order to solve the above problems in phase field simulation,the main work and conclusions completed in this paper are as follows:(1)Firstly,an energy decomposition method based on the Drucker Prager fracture criterion was applied to successfully achieve the asymmetric fracture behavior of rocks during tension and compression processes.On this basis,relevant parameters applicable to the Drucker Prager fracture surface were further derived.Due to the significant advantage of the Drucker Prager failure surface theory in describing the failure behavior of granular materials such as rocks,this paper combines it with the phase field fracture model to more accurately simulate the fracture process of rocks under complex stress states.At the same time,a new type of degradation function is introduced into the phase field constitutive equation,which separates the originally closely related phase field length from the physical length scale,effectively eliminating their interaction,reducing the requirement for grid density in model calculations,improving simulation efficiency and accuracy,and making it possible to simulate crack growth in large structures using the phase field method.(2)A Drucker Prager rock fracture phase field model was constructed.A rock damage fracture phase field model was developed based on the ABAQUS platform for analyzing crack growth in large structures.This model introduces the energy decomposition method of Drucker Prager fracture criterion and a new type of degradation function,aiming to achieve numerical simulation of large-scale rock fracture using the phase field method.(3)The accuracy and efficiency of the algorithm were verified through simulation experiments,and crack propagation in large rock masses was simulated and analyzed in actual engineering cases.The above series of experiments have demonstrated the advantages and potential of the rock fracture phase field model in large-scale rock numerical simulation.Based on the phase field model presented in this article,it is possible to more accurately predict the damage and fracture process of rock masses,thereby formulating more scientific and reasonable engineering design and construction plans.更多还原