湿度场与围压耦合作用下基于Weibull分布的岩石损伤本构模型研究

Study on Rock Damage Constitutive Model Based on Weibull Distribution under the Coupling of Humidity Field and Confining Pressure

摘要: 在地基开挖、地铁施工等地下工程中，岩石常常受到湿度场–围压耦合作用。耦合作用会加剧岩石内部损伤，对于损伤本构模型的研究可以进一步揭示岩石损伤机理。目前对于在湿度场–围压耦合作用下岩石的损伤本构模型研究尚不完善。本文基于Lemaitre应变等价性假设理论和SMP准则，引入双参数的Weibull分布，对岩石微元强度进行修正，建立了湿度场–围压耦合作用下的岩石损伤本构模型。然后，采用极值法得出所需的本构模型参数。对灰质泥岩的峰值应力和峰值应变进行理论与试验曲线对比研究，提出的理论模型表现出较好的吻合度，验证了该本构模型及参数的合理性以及适用性。本研究对软岩的损伤模型研究提供了参考，有一定的工程实用性和指导性。

Abstract: In underground projects such as foundation excavation and subway construction, rocks are often subjected to humidity field and confining pressure coupling. The coupling will aggravate the internal damage of rocks, and the study of the damage constitutive model can further reveal the damage mechanism of rocks. At present, the damaged constitutive model of rocks under the coupling effect of humidity field-confining pressure is still not well studied. In this paper, based on the Lemaitre strain equivalence assumption theory and the SMP criterion, a two-parameter Weibull distribution is introduced to correct the strength of rock microelements, and the damage constitutive model of rocks under the coupling of humidity field and confining pressure is established. Then, the extreme value method was used to derive the required parameters of the constitutive model. The theoretical and experimental curves of peak stress and peak strain of the gray mudstone are compared, and the proposed theoretical model shows good agreement, which verifies the reasonableness as well as the applicability of the constitutive model and parameters. This study provides a reference for the damage modeling study of soft rock, which has certain engineering practicality and guidance.