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An explicit formulation of the macroscopic strength criterion for porous media with pressure and Lode angle dependent matrix under axisymmetric loading

Jincheng Fan, Laurence Brassart, Wanqing Shen, Xiurun Ge

2021
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Journal of Rock Mechanics and Geotechnical Engineering
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This paper aims to propose an explicit formulation of the macroscopic strength criterion for porous media with spherical voids. The matrix is assumed rigid and perfectly plastic with yield surface described by the three-parameter strength criterion, which is Lode angle and pressure dependent and capable of accounting for distinct values of the uniaxial tensile strength, uniaxial compressive strength (UCS) and equal biaxial compressive strength (eBCS). An exact upper bound of the macroscopic
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... the macroscopic strength is derived for porous media subjected to purely hydrostatic loading. Besides, an estimate of the macroscopic strength profile of porous media under axisymmetric loading is obtained in parametric form. Moreover, a heuristic strength criterion in explicit form is further developed by examining limit cases of the parametric strength criterion. The developed strength criteria are assessed by finite-element based numerical solutions. Compared with the parametric strength criterion which involves cumbersome functions, the heuristic one is convenient for practical applications. For specific values of the matrix's strength surface, the proposed heuristic strength criterion can recover the well-known Gurson criterion. The present work also addresses the effect of the ratio of matrix's eBCS to UCS on the macroscopic strength of porous media. For matrix with distinct values of eBCS and UCS, neglecting the difference between eBCS and UCS would result in an underestimation of the macroscopic strength, especially when the pressure is large. (Wanqing Shen). 1 J o u r n a l P r e -p r o o f macroscopic strength of porous material with pressure-sensitive matrix obeying Drucker-Prager (DP) criterion was conducted by Jeong and Pan (1995) and later extended by Guo et al. (2008). Recently, Shen et al. (2020) reviewed the macroscopic strength criteria for porous materials with DP matrix and evaluated them through numerical solutions. Based on an improvement of the strength predictions for purely shear loading, Shen et al. (2020) proposed one heuristic strength criterion, which could give better predictions of the macroscopic strength. For materials with local yield function depending on the third invariant of stress, one can refer to recent investigations in the context of Tresca matrix (Cazacu et al., 2014), Mohr-Coulomb (MC) matrix (Anoukou et al., 2016) and matrix described by the strength criterion proposed by Bigoni and Piccolroaz (Brach et al., 2018) . As an alternative method, statical limit analysis has been adopted to formulate the macroscopic strength criterion for porous materials with von Mises matrix (Cheng et al., 2014; Shen et al., 2015) and Hill orthotropic matrix (El Ghezal et al., 2017) . Effect of the void shape on the macroscopic strength of porous media was discussed in Shen et al. (2017) for DP matrix and Monchiet et al. (2008) for Hill-type matrix. An accurate description of the macroscopic strength of a particular porous material is contingent on the accuracy of the local plasticity model Cazacu and Revil-Baudard, 2017) . Strength of geomaterials, such as rocks and concrete are pressure and Lode angle dependent (Chemenda and Mas, 2016). Neither the von Mises criterion nor the DP criterion can account for the effect of the third invariant of stress. In contrast, the Tresca model depends on the third invariant, however it is pressure-independent and hence does not apply to pressure-dependent materials. Although the MC criterion has been widely adopted in the mechanics community to describe the shear dominated failure mechanism (Jaeger et al., 2009; Labuz and Zang, 2012) , it neglects the effect of the middle principal stress and fails for materials with distinct values of uniaxial compressive strength (UCS) and equal biaxial compressive strength (eBCS). Besides, the established strength criterion for porous materials with MC matrix under axisymmetric loading in Anoukou et al. (2016) is in parametric form, and the parametric functions are cumbersome. In fact, in the present work we also developed an explicit formulation of the macroscopic strength criterion for porous MC materials under axisymmetric loading, which is more applicable for practical applications. Recent studies have revealed that the eBCS of geomaterials such as concrete and rocks is larger than their UCS (Kupfer et al., 1969; Brown, 1974; Amadei and Robison, 1986; Hussein and Marzouk, 2000) . Lee et al. (2004) experimentally investigated the failure of plain concrete and showed the eBCS was about 17% higher than the UCS. Sirijaroonchai et al. (2010) performed equal biaxial compression tests on high-performance fiber-reinforced cement material and concluded that the eBCS was about 1.5 and 1.6 times the UCS respectively for hooked and spectra fiber-reinforced cement material. Guo (2014) reviewed the main experimental results for the eBCS of concrete and pointed out the ratio of eBCS to UCS of concrete lay in 1.15-1.35. Experimental study of the eBCS and UCS of concrete at early ages has been conducted by Dong et al. (2016) , and experimental results revealed the ratio of eBCS to UCS approximately decreased from 3.5 to 1.2 within the first 7 d and remained at a value of 1.15 up to the age of 28 d. Yun et al. (2010) observed that the difference between the BCS and UCS of granite increased dramatically with the confining pressure up to some threshold value, beyond which the BCS dropped, but still remained higher than the UCS. In that study, the eBCS of granite was about 1.13 times the UCS on average. Although the MC criterion can account for the strength difference under uniaxial tensile and compressive loading, it cannot account for different eBCS and UCS values. In this respect, the established macroscopic yield functions in the literature are not expected to be accurate for such porous materials. Lately, the three-parameter strength criterion has been considered as an appropriate candidate to describe the yield surface of geomaterials (Yu, 2017 (Yu, , 2018 . Through appropriate choice of parameter values in the expression of the yield function, the three-parameter strength criterion can retrieve classical strength criteria, such as the MC and Tresca criteria. It can also linearly

doi:10.1016/j.jrmge.2021.03.013
fatcat:5vgci3eomnbcfgh6sazvj62vze