Documentation for the Skeletal Storage, Compaction, and Subsidence (CSUB) Package of MODFLOW 6

Techniques and Methods 6-A62
By: , and 



This report describes the skeletal storage, compaction and subsidence (CSUB) package of MODFLOW 6. The CSUB package simulates the vertical compaction of compressible sediments and land subsidence. The package simulates groundwater storage changes and elastic compaction in coarse-grained aquifer sediments. The CSUB package also simulates groundwater storage changes and elastic and inelastic compaction in fne-grained, compressible interbeds, or in extensive confning units. The package can account for effective stress-dependent changes in storage properties. The CSUB package can also explicitly account for the contribution of water compressibility to groundwater storage changes.

Compaction of compressible sediments is formulated using Terzaghi’s elastoplastic model and assumes the total compaction is a small fraction of the total initial thickness of compressible sediments. Compaction is controlled by head or pore-pressure changes and overburden stress changes associated with water-table changes, and thus by effective stress changes within coarse-and fne-grained compressible sediments. If the stress in a compressible unit is less than the preconsolidation stress, compaction is elastic (recoverable). If the stress in a compressible sediment is greater than the preconsolidation stress, compaction is inelastic (irrecoverable) and permanent land subsidence occurs.

The propagation of head changes within fne-grained, compressible interbeds is represented numerically using a transient, one-dimensional (vertical) groundwater fow equation. This equation accounts for delayed release of water from storage or uptake of water into storage in the interbeds. Vertical hydraulic conductivity, elastic and inelastic skeletal specifc storage, and interbed thickness control the timing of interbed storage changes. Interbeds that are thin, have a relatively large vertical hydraulic conductivity, or relatively small specifc-storage values equilibrate quickly with heads/pore pressures in surrounding coarse-grained sediments and can be represented as no-delay interbeds that use the simulated groundwater head in a cell to calculate interbed compaction and do not need to be solved numerically using a vertically discretized interbed and the vertical groundwater fow equation.

In addition to the applicability to confned groundwater fow systems, several features of the CSUB package make it applicable to shallow, unconfned groundwater fow systems. Geostatic stress can be treated as a function of water-table elevation, and compaction is a function of computed changes in effective stress. The porosity, void ratio, and thickness of shallow and deep coarse-grained aquifer sediments, fne-grained interbeds, and extensive confning units can vary in time based on calculated strain.

Suggested Citation

Hughes, J.D., Leake, S.A., Galloway, D.L., and White, J.T., 2022, Documentation for the Skeletal Storage, Compaction, and Subsidence (CSUB) Package of MODFLOW 6: U.S. Geological Survey Techniques and Methods, book 6, chap. A62, 57 p.,

ISSN: 2328-7055 (online)

Table of Contents

  • Abstract
  • Introduction
  • Theory
  • Computing Skeletal and Interbed Storage Changes and Compaction
  • Incorporation of skeletal storage and interbed compaction into the CVFD Groundwater Flow Equation
  • Solution of Delay Interbeds Systems
  • Applicability and Limitations of the CSUB Package
  • References Cited
  • Appendix 1. List of Mathematical Symbols
Publication type Report
Publication Subtype USGS Numbered Series
Title Documentation for the Skeletal Storage, Compaction, and Subsidence (CSUB) Package of MODFLOW 6
Series title Techniques and Methods
Series number 6-A62
DOI 10.3133/tm6A62
Year Published 2022
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) WMA - Integrated Modeling and Prediction Division
Description Report: vi, 57 p.; Software Release
Online Only (Y/N) Y
Additional Online Files (Y/N) N
Google Analytic Metrics Metrics page
Additional publication details