The limitations of a standard phase-field model in reproducing jointing in sedimentary rock layers

Geological applications of phase-field methods for fracture are notably scarce. This work conducts a numerical examination of the applicability of standard phase-field models in reproducing jointing within sedimentary layers. We explore how the volumetric-deviatoric split alongside the AT1 and AT2 phase-field formulations have several advantages in simulating jointing, but also have intrinsic limitations that prevent a reliable quantitative analysis of rock fracture. The formulations qualitatively reproduce the process of joint saturation, along with the negative correlation between joint spacing and the height of the sedimentary layer. However, in quantitative comparison to alternative numerical methods and outcrop observations, the phase-field method overestimates joint spacings by a factor of 2 and induces unrealistic compressive fractures in the AT1 model, alongside premature shearing at layer interfaces for the AT2 model. The causes are identified to be intrinsic to the phase-field lengthscale and the unsuitable strength envelope arising from the Volumetric-Deviatoric split. Finally, our analysis elucidates on the phase-field lengthscale's distortion of the stress field around dilating fractures, causing the sedimentary layer to reach joint saturation prematurely, thereby stopping the nucleation of new fractures and leading to larger joint spacings than in natural examples. Decreasing the lengthscale results in gradual improvement but becomes prohibitively computationally expensive for very small lengthscales such that the limit of ``natural'' behavior was not reached in this study. Overall, our results motivate the development of constitutive phase-field models that are more suitable for geological applications and their benchmarking against geological observations.