For the cases you are describing, you will generally need to account for evolution of porosity and permeability. For example in the sponge case, by squeezing the sponge you are compacting the pores - the pressure is likely slaved to the compaction rate (i.e. you would "squeeze harder" as the sponge stiffens due to strain hardening and the permeability decreases due to smaller pore throats; technically your rate of squeezing would be accelerating, assuming an elastic loading response.) In the sand-dam case, the permeability and porosity increase as sand is removed. In this system mass is not conserved (i.e. sand is removed by the flow). While the sand-dam system is self-accelerating, I would say the sponge system is driven more by outside forces. (For a sort of combination of the two, check out "injectites".)

For a physics perspective, you might check out "Biot Consolidation" (some references here). For a geology perspective, you might check out soft-sediment deformation.

Edit: Note that classical Biot consolidation assumes a linear-elastic porous medium. This means 1) infinitesimal strains, 2) linear "Hooke Law" for stress vs. strain, and 3) all strains are elastic, i.e. reversible. For your sponge case, at the least you would need to consider finite strain (if you like differential geometry, this may interest you; only 3d so simpler than general relativity I guess?). However with finite strain the model "constant coefficients", such as permeability & elastic moduli, will also most likely change (e.g. permeability reduction, nonlinear elasticity). Finally, when the porosity reduction is irreversible, the term compaction is used (i.e. consolidation vs. compaction = elastic vs. plastic strain).

For the cases you are describing, you will generally need to account for evolution of porosity and permeability. For example in the sponge case, by squeezing the sponge you are compacting the pores - the pressure is likely slaved to the compaction rate (i.e. you would "squeeze harder" as the sponge stiffens due to strain hardening and the permeability decreases due to smaller pore throats; technically your rate of squeezing would be accelerating, assuming an elastic loading response.) In the sand-dam case, the permeability and porosity increase as sand is removed. In this system mass is not conserved (i.e. sand is removed by the flow). While the sand-dam system is self-accelerating, I would say the sponge system is driven more by outside forces. (For a sort of combination of the two, check out "injectites".)

For a physics perspective, you might check out "Biot Consolidation" (some references here; the original paper is also quite readable). For a geology perspective, you might check out soft-sediment deformation.

Edit: Note that classical Biot consolidation assumes a linear-elastic porous medium. This means 1) infinitesimal strains, 2) linear "Hooke Law" for stress vs. strain, and 3) all strains are elastic, i.e. reversible. For your sponge case, at the least you would need to consider finite strain (if you like differential geometry, this may interest you; only 3d so simpler than general relativity I guess?). However with finite strain the model "constant coefficients", such as permeability & elastic moduli, will also most likely change (e.g. permeability reduction, nonlinear elasticity). Finally, when the porosity reduction is irreversible, the term compaction is used (i.e. consolidation vs. compaction = elastic vs. plastic strain).

For the cases you are describing, you will generally need to account for evolution of porosity and permeability. For example in the sponge case, by squeezing the sponge you are compacting the pores - the pressure is likely slaved to the compaction rate (i.e. you would "squeeze harder" as the sponge stiffens due to strain hardening and the permeability decreases due to smaller pore throats; technically your rate of squeezing would be accelerating, assuming an elastic loading response.) In the sand-dam case, the permeability and porosity increase as sand is removed. In this system mass is not conserved (i.e. sand is removed by the flow). While the sand-dam system is self-accelerating, I would say the sponge system is driven more by outside forces. (For a sort of combination of the two, check out "injectites".)

For a physics perspective, you might check out "Biot Consolidation" (some references here). For a geology perspective, you might check out soft-sediment deformation.

For the cases you are describing, you will generally need to account for evolution of porosity and permeability. For example in the sponge case, by squeezing the sponge you are compacting the pores - the pressure is likely slaved to the compaction rate (i.e. you would "squeeze harder" as the sponge stiffens due to strain hardening and the permeability decreases due to smaller pore throats; technically your rate of squeezing would be accelerating, assuming an elastic loading response.) In the sand-dam case, the permeability and porosity increase as sand is removed. In this system mass is not conserved (i.e. sand is removed by the flow). While the sand-dam system is self-accelerating, I would say the sponge system is driven more by outside forces. (For a sort of combination of the two, check out "injectites".)

For a physics perspective, you might check out "Biot Consolidation" (some references here). For a geology perspective, you might check out soft-sediment deformation.

Edit: Note that classical Biot consolidation assumes a linear-elastic porous medium. This means 1) infinitesimal strains, 2) linear "Hooke Law" for stress vs. strain, and 3) all strains are elastic, i.e. reversible. For your sponge case, at the least you would need to consider finite strain (if you like differential geometry, this may interest you; only 3d so simpler than general relativity I guess?). However with finite strain the model "constant coefficients", such as permeability & elastic moduli, will also most likely change (e.g. permeability reduction, nonlinear elasticity). Finally, when the porosity reduction is irreversible, the term compaction is used (i.e. consolidation vs. compaction = elastic vs. plastic strain).