# Half-thickness discretized format for simulating compressible delay interbed

## TL;DR

This paper introduces a new simulation method for ground subsidence that improves efficiency and accuracy by using a half-thickness discretization approach.

## Contribution

The novel half-thickness discretization format under geostress variation improves simulation efficiency while maintaining accuracy.

## Key findings

- The half-thickness method reduces computation time by up to 46.23% and memory usage by 13.64%.
- The maximum difference in interbed water release between the new method and the CSUB module is less than 0.4%.
- The proposed method is suitable for large-scale, high-precision land subsidence modeling.

## Abstract

The simulation of compressible delay interbed is an important component of ground subsidence modeling. Currently, the most widely used groundwater simulation software, MODFLOW, has two modules: SUB and CSUB. While both can simulate compressible delay interbed using the one-dimensional head diffusion equation, they differ in approach. The SUB module relies on the principle of head change, while the CSUB module is based on the principle of geostress variation, addressing the shortcomings of the SUB module when simulating ground subsidence in unconfined aquifers. When based on the principle of head change, the effective stress acting on the top and bottom of the interbed is the same, leading to symmetric vertical consolidation and using half-thickness discretization. In contrast, the CSUB module is based on geostress variation, the effective stress acting on the top and bottom of the interbed is not the same, which results in asymmetric consolidation and requires full-thickness discretization. With the same vertical discretization interval for the compressible delay interbed, the computational workload and memory requirements are approximately twice that of the SUB module. Based on the characteristic of linear distribution of geostress in the vertical direction of the compressible delay interbed, this paper proposes a half-thickness discretization format under the principle of geostress variation, which can significantly improve simulation efficiency and reduce memory requirements. To validate this approach, three cases were tested with different numbers of discretization units, different interbed thicknesses, different heads, and different vertical hydraulic conductivities. A comprehensive comparison was made between the half-thickness discretization format and the full-thickness discretization format of the CSUB module. The differences in computation time and memory usage between the two methods were then analyzed. The results show that the maximum difference in the interbed water release between the half-thickness method and the CSUB module is less than 0.4%, indicating good accuracy. Additionally, the half-thickness method reduced computation time by 46.2303% and memory usage by 13.6364% in the tested cases, demonstrating significant computational advantages. This study provides an efficient and feasible technical approach for large-scale, high-precision land subsidence modeling.