Resistivity and Modulus Based Geo-Material Characterization to Assess Subsidence

Ground water decline, resulting in increased effective stresses in effected geo-materials, is a typical cause of ground subsidence in alluvial basins. In general, subsidence magnitudes are greater in finer grained basin materials than coarser grained materials. Subsidence may be greatest in clay dominated materials, although the very low permeabilities in these materials, with resulting excess pore pressures, can result in significant to profound time delay effects on the subsidence.  Resistivity provides a means to at least semi-quantitatively assess clay content in basin materials, especially in fresh-water aquifers.  Resistivity measurements can include large surface arrays (such as 1000-ft maximum electrode spacing Wenner arrays) when conditions permit, and when available, borehole geophysical logs.  In fresh water aquifers, such measurement characterization can discern, at a useful scale, alluvial materials with little to no clays (high modulus), fine grained alluvial materials including some clays (lower modulus with relatively little time delay), and clay-dominated alluvial materials (low modulus with significant time delay).

Percolation Theory (PT) provides a straightforward quantitative means to relate estimated material density and modulus relationships.  In a general form, the PT porosity-modulus relationship is

E = k ( P_c – P)^f

where E is elastic (low-strain) modulus, P_c is a percolation threshold porosity, P is the porosity of the material, k is a proportionality constant, and f is an exponential parameter defined by the type of modulus behavior.  A general PT density-modulus relationship for basin alluvium materials (not clay-dominated), with adjustments for large strains, is presented.  Using this relationship, variables of initial and final depths to groundwater table, and thickness of subsidable material, subsidence at seven locations in is estimated and compared to measured historic subsidence.  At five locations, estimated and measured subsidence agree to within 26 percent.  The other locations include significant clay-dominated alluvial materials.