Abstract
The development of prediction techniques for the evolution of karstic caves is essential for geohazard prevention because limestone collapse commonly accompanies their complex dissolution process. Previous studies to understand the dissolution mechanisms focus on field-based and/or small-scale experimental approaches. Although several large-scale numerical simulations have been conducted due to improved computing capabilities, mathematical modelling and numerical simulation for the three-dimensional dissolution of limestone remains unavailable. In this study, we examine the three-dimensional dissolution phenomenon of calcium carbonate in limestone and propose mathematical and numerical models based on an advection, reaction, and diffusion system involving Darcy’s law. Additionally, we implement the models using a finite difference method involving the constrained interpolation profile with conservative semi-Lagrangian scheme, and dissolution patterns of the calcium carbonates obtained by the proposed model are presented. The simulation demonstrates that the dissolution of calcium carbonate is strongly related to the groundwater flow, with increasing pores and cavities toward the groundwater flow direction, and the dissolution rate depends on the contact area between the groundwater and limestone.
Highlights
Rock weathering is associated with geohazards such as landslides, rock falls, and sinkhole
The simulation demonstrates that the dissolution of calcium carbonate is strongly related to the groundwater flow, with increasing pores and cavities toward the groundwater flow direction, and the dissolution rate depends on the contact area between the groundwater and limestone
The results suggest the following: (1) The 3D spatial patterns of calcium carbonate dissolution from limestone were obtained from a system involving advection, reaction, and diffusion
Summary
Rock weathering is associated with geohazards such as landslides, rock falls, and sinkhole. Matsubara and Yamada [11] presented a mathematical and numerical approach based on the advection, reaction, and diffusion systems, allowing calculations for the calcium carbonate dissolution process. Through this approach, complex calcium carbonate dissolution patterns such as the dissolution of limestones with openings are achievable. Developing accurate 3D calcium carbonate dissolution simulation techniques is important for understanding the morphology, response to weathering and stability of karstic caves. In this study, we investigate the temporal and spatial morphological patterns of calcium carbonate dissolution and present 3D mathematical and numerical models based on the approach by Matsubara and Yamada [11]. The results of this study help in mitigating geohazards associated with limestone by chemical weathering
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