Elastic properties of rocks (elastic modulus and Poisson's ratio) are essential parameters required for the design of projects involving rocks. These parameters can be found using static or dynamic tests, either in the field or in the lab. Limestone is a sedimentary rock encountered in many engineering projects worldwide. The objective of this paper is to present a comparison between elastic moduli as well as Poisson ratios determined in the laboratory using static and dynamic methods, for limestone rock specimens obtained from an outcrop in Saudi Arabia. To better characterize this rock, other material and mechanical properties of this rock are also presented.
The elastic constants (elastic modulus and Poisson's ratio) are considered to be the main fundamental mechanical properties of rocks. These constants are extensively used in various formulations and modeling techniques, in order to understand the stress-strain response of rocks subjected to various loading conditions. There are two ways of finding these constant: static and dynamic. In the static method. the elastic constants are computed from the stress-strain response of a representative specimen of the material subjected to a uniaxial loading. The dynamic method is based on nondestructive geophysical (seismic/acoustic) testing. It involves the measurement of compression and shear wave velocities of a known frequency traveling through the sample. The elastic constants, based on the dynamic method (ultrasonic or logging), are widely used for hydraulic fracture design and wellbore/perforation stability evaluations in the petroleum industry. However. the discrepancy in the values of constants between static and dynamic methods as reported in the literature requires good Judgment and further investigation of the relationship between the constants determined from the two methods. The static modulus and Poisson's ratio were determined for cylindrical specimens, 50.8mm long and 23.5mm in diameter.The load was applied using a strain-controlled loading frame equipped with a load cell to measure the load, an LVDT to measure displacement. and strain gauges to measure vertical and horizontal strains. The dynamic modulus and Poisson's ratio were determined for cylindrical specimens. 25.3mm long and 38mm in diameter. Measurements were made using an ultrasonic system equipped with pairs of transmittingand receiving transducers, one P-wave and two polarized S-waves. The data of static tests was analyzed to determine the effect of stress/strain level on the secant and tangent moduli as well as on Poisson's ratio. The static and dynamic results obtained for the investigated rock were analyzed and compared. The findings are also compared with similar results available in the literature for limestone rocks, in order to obtain a correlation between the static and dynamic parameters of limestone rocks.
The relationships between static and dynamic elastic properties have been studied since the early 1930's when techniques involving the propagation of acoustic waves were used in the characterization of rocks in mining, petroleum, and geotechnical engineering. Dynamic measurement are often used because they are easy to obtain, and are nondestructive. Also, there are rarely enough cores available for the static method.