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

Displacive carbonate crystal growth is recognized in a wide variety of settings, including calcretes, within phyllosilicates in sandstones, and in and around carbonate concretions. Displacive cement requires a mechanical response, but little attention to this has been given. Its incorporation in a model assuming constant calcite supersaturation satisfies observations for alternating D- and ND-shells in an elongate concretion composed of calcite-cemented sand.

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, (dr_e/dt)_D=K[RTlnW+s_rr(r_e)V₀]; for an ND-shell, in which growth is by filling of porosity, (dr_e/dt)_ND=K’RTlnW. r_e 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, s_rr 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 s_rr(r_e) 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 s_rr(r_e), 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 = E_o(1-IGV*/100) (d_e/a)/[(1+n)RTlnW], k = K’/K and m; d_e 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)(d_e/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 3^rd – e.g., m; the range in S may be estimated from concretion and field data.