Is there any equation, law or previous research, for ground subsidence due to water interaction?

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Kaveh Zamani

See chapter 9 in the book "Hydrology of Disasters" By Vijay Singh.

Also see this book chapter:

Chapter Land Subsidence — A. A State-of-the-Art Review

Formulations is discussed in both.

Nasir Khattak

You can take help from previous reseach of Applied Mathematecian. You have to cantact Applied Math Deptt in US universaties

Bayan Hussien

https://www.slideshare.net/AcademiaDeIngenieriaMx/ground-deformation-effects-on-subsurface-pipelines-and-infrastructure