26 



Shiffman et al. (1985) review the available theories regarding 

 consolidation (compaction). The simplest is Terzaghi's "Conventional 

 Theory" governed by 



2 



, d u _ au , 3^o da /o i„\ 



'v 2 at at at ^-^-^a; 



k(l + e ) 

 cv = 2_ (3.1b) 



where u is the excess pore water pressure, Uq is the hydrostatic pressure, 

 a is the total stress applied to the system, k is the hydraulic 

 conductivity, Bq is the initial void ratio, p^ is the mass density of the 

 fluid (water) , and a^ is the compressibility of the soil skeleton. Solving 

 Eq. 3.1 for u and applying the continuity equation for conventional theory 



d_ /k_ au\ ^ an r"^ 9") 



dz >„ dz^ at ^ ^^ 



soil porosity n is determined. Knowing the porosity as a function of time 

 and the initial thickness of the soil layer, the time history of ground 

 level subsidence can be calculated. Except for very idealized cases, this 

 problem must be solved numerically. Shiffman et al. (1985) also describe a 

 nonlinear finite strain theory, which removes several assumptions of 

 conventional theory but requires difficult numerical solution. Fig. 3.1 

 displays comparison of the two theories to centrifuge experiments , with the 

 finite strain theory providing good results. 



3.2 MEASURING COMPACTION 



As noted in section 2, a simple yet effective device for measuring 

 compaction rates has been developed in Japan and has been widely used there 

 for at least the past 30 years, see Murayama (1970). This device, shown in 

 Fig. 3.2 (see also Fig. 2.7), consists of two concentric pipes that 

 penetrate to a desired non-compactable stratum. The outer pipe is 

 perforated to allow the groundwater table to move freely up and down in the 



