A CYLINDRICAL CALCITE-CEMENTED CONCRETION IN SAND WITH ALTERNATING DISPLACIVE (D) AND NON-DISPLACIVE (ND) CORE AND CYLINDRICAL SHELLS:GROWTH MODEL AND FIT TO OBSERVATIONS
The set of radii at which D-shells and ND-shells initiated and their intergranular cement volumes (IGV) were measured for a single concretion. All D-shells have IGV ~ 70, and are treated as veins in which sand is incorporated; the IGV of ND-shells decreases outward from 56 to 20.
Observed sharp transitions between shells are modeled by conditions on the kinetics of radial growth in D- and ND-shells. For a D-shell, in which the host sand is deformed, (dre/dt)D=K[RTlnW+srr(re)V0]; for an ND-shell, in which growth is by filling of porosity, (dre/dt)ND=K’RTlnW. re is the external surface of the concretion where growth takes place, K and K’<K are kinetics constants, R is the gas constant, T is temperature, W is saturation state, srr is radial compressive normal stress, and V0 is calcite specific volume. The D-ND transition takes place when the displacive growth rate drops to the non-displacive rate. The ND-D transition occurs when the D-rate that would be operative at the current srr(re) equals 1+m times the ND rate. The assumption is that nucleation of a D-shell requires overstep, while the transition to an ND shell does not. To compute srr(re), the sand is treated as elastic. The Young’s Modulus (E) of sand is 10-70 MPa << 1–70 GPa of the cemented concretion, so the concretion is treated as rigid.
Model dimensionless parameters are: S = Eo(1-IGV*/100) (de/a)/[(1+n)RTlnW], k = K’/K and m; de is an effective vein thickness, in which all displacive calcite is put into a single external vein with inner surface r = a, and IGV* is for the prior ND-shell, The model requires that (1-IGV*/100)(de/a) for all D-shells be equal, and ratios of all pairs of successive radii at which D-shells are initiated be equal; both are satisfied by the data. Two parameters can be fixed for an arbitrary value of the 3rd – e.g., m; the range in S may be estimated from concretion and field data.