The bearing capacity of a rock foundation is a function of the rock mass properties as assessed in the field, and the strength and deformation characteristics of intact rock determined in the laboratory. The inherent variability of the rock at the mass and laboratory scales introduces significant uncertainty in the calculated foundation bearing capacity. In many instances, an engineer may select a mean or median value or estimated high and low values for each data set for their calculations. As the field and laboratory data set is not captured in its entirety with this approach, the range of the data and the distribution of the values between the high and low within data set are then lost in the calculations. The techniques presented in this paper can be used in any analysis where there is uncertainty in the input variables. Some examples include: simplified slope stability calculations, rock mass modulus, and anchor pull-out strength.
This paper presents an example calculation of rock bearing capacity using the methods proposed in the USACE, 1994 Rock Foundations Engineer Manual (EM 1110-1-2908) and by AASHTO, 2002. The use of mean and median values for the laboratory data is presented along with a comprehensive use of the data sets. The data sets used in the comprehensive analysis comprise probability density functions for each input variable (friction angle, unit weight, and uniaxial compressive strength) based on the entire lab data sets, with Monte Carlo sampling of these data sets to develop an output distribution of anticipated bearing capacity values. As shown in the following sections, assuming a mean/median value results in an output that doesn't capture the variability of the rock mass, resulting in overly conservative or unconservative results.
The data set used for these calculations is from field and laboratory data obtained during a drilling, sampling, and testing program for a proposed dam modification. The foundation rock comprises extrusive and intrusive igneous rock, near the edge of a large batholith. The rock is generally a series of coarse-grained intrusions within Cretaceous-aged biotite granite. The batholith has extensive faulting with the rock underlying the dam found to be extensively fractured and sheared.