Fletcher, R.C., Buss, H.L., Brantley, S.L., 2006.Aspheroidal weathering

model coupling porewater chemistry to soil thicknesses during

steady-state denudation. Earth Planet. Sci. Lett. 244, 444–457.

Abstract:

Spheroidal weathering, a common mechanism that initiates the transformation of bedrock to saprolite, creates concentric
fractures demarcating relatively unaltered corestones and progressively more altered rindlets. In the spheroidally weathering Rio
Blanco quartz diorite (Puerto Rico), diffusion of oxygen into corestones initiates oxidation of ferrous minerals and precipitation of
ferric oxides. A positive ΔV of reaction results in the build-up of elastic strain energy in the rock. Formation of each fracture is
postulated to occur when the strain energy in a layer equals the fracture surface energy. The rate of spheroidal weathering is thus a
function of the concentration of reactants, the reaction rate, the rate of transport, and the mechanical properties of the rock.
Substitution of reasonable values for the parameters involved in the model produces results consistent with the observed thickness
of rindlets in the Rio Icacos bedrock (≈2–3cm) and a time interval between fractures (≈200–300 a) based on an assumption of
steady-state denudation at the measured rate of 0.01cm/a. Averaged over times longer than this interval, the rate of advance of the
bedrock–saprolite interface during spheroidal weathering (the weathering advance rate) is constant with time. Assuming that the
oxygen concentration at the bedrock–saprolite interface varies with the thickness of soil/saprolite yields predictive equations for
how weathering advance rate and steady-state saprolite/soil thickness depend upon atmospheric oxygen levels and upon
denudation rate. The denudation and weathering advance rates at steady state are therefore related through a condition on the
concentration of porewater oxygen at the base of the saprolite. In our model for spheroidal weathering of the Rio Blanco quartz
diorite, fractures occur every ∼250yr, ferric oxide is fully depleted over a four rindlet set in ∼1000yr, and saprolitization is
completed in ∼5000yr in the zone containing ∼20 rindlets. Spheroidal weathering thus allows weathering to keep up with the high
rate of denudation by enhancing access of bedrock to reactants by fracturing. Coupling of denudation and weathering advance rates
can also occur for the case that weathering occurs without spheroidal fractures, but for the same kinetics and transport parameters,
the maximum rate of saprolitization achieved would be far smaller than the rate of denudation for the Rio Blanco system. The
spheroidal weathering model provides a quantitative picture of how physical and chemical processes can be coupled explicitly
during bedrock alteration to soil to explain weathering advance rates that are constant in time.

Fletcher, R.C., Buss, H.L., Brantley, S.L., 2006.Aspheroidal weathering

model coupling porewater chemistry to soil thicknesses during

steady-state denudation. Earth Planet. Sci. Lett. 244, 444–457.

Abstract:

Fletcher RC, Brantley SL. 2010. Reduction of bedrock blocks as corestones in the weathering profile: observations

and model. Am. J. Sci. 310:131–64

Abstract:

the Espiritu Santo and Mameyes rivers within the Luquillo Experimental
Forest (Puerto Rico) are interpreted as corestones, reduced from initial joint-bounded
bedrock blocks by subsurface weathering. Maximum corestone size, expressed as the
geometric mean of the three dimensions, S 3 abc, shows a smooth envelope when
plotted against elevation. We postulate that, for each catchment, they represent in situ
corestones within a stratified weathering profile, many tens of meters in thickness, that
has been subsequently exhumed by younger erosion. We formulate a simplified
one-dimensional model for reduction in corestone size within a steady-state weathering
profile that incorporates: (i) vertical fluid transport of the reactant and the soluble
products of chemical weathering; (ii) linear kinetics of corestone reduction; and,
subsequently, (iii) erosion. The rate of advance of a steady-state weathering profile is a
statement of the mass balance between entering reactants and weathering components,
here idealized as H and albite. The mathematical relations, tie the laboratory-determined rate constant for dissolution of albite (k) to a generalized
kinetic constant for the rate of decrease (K) in corestone diameter to the advance rate
of the weathering profile (V ). The last parentheses contain an effective roughness at
the scale of the weathering profile, where S0 is the maximum size of initial bedrock
blocks, inferred to be set by initial bedrock fracture spacing, and 3L* is the profile
thickness. The laboratory scale roughness value, , is the ratio of the surface area
accessed by BET analysis to that of the corestone grain scale. In the model, erosion is
not coupled with weathering, although the presence of corestones of finite size, SE>0,
exiting at the erosional surface may be postulated to affect the erosional flux. The
thickness of the corestone weathering profile derived for the model for the distance
between bedrock and a corestone-free saprolite cap is approximately This expression is the product of the effective pH buffering-adjusted input reactant
flux per unit area times a stoichiometeric factor linking this to net albite dissolution,
divided by the rate of corestone size reduction at the input concentration of protons.
Further, the profile thickness scales with the input “particle” size, S0. The model fit,
which yields the ratio is consistent with a rate constant for albite dissolution that lies between laboratorymeasured
and field-estimated values. Sensitivity to the reaction order of albite dissolution
with respect to H, N, is small, except near the base of the profile. This model
yields insights into the relationship between fracture spacing and the evolution of
particle size and chemistry in weathering profiles.