The Law of Effective Stress for Rocks in Light of Results of Laboratory Experiments / Prawo Naprężeń Efektywnych Dla Skał W Świetle Wyników Badań Laboratoryjnych

Abstract

This paper presents the results of laboratory tests carried out in order to formulate effective stress law. The law was sought for two different cases: first -when rock was treated as a porous Biot medium (Biot, 1941;Nur & Byerlee, 1971) and second -when the law was formulated according to definition of Robin (1973) developed by Gustkiewicz (1990) and Nowakowski (2007). In the first case coefficents (4) and (5) of the Biot equation (3) were were determined on the basis of compressibility test, in the second one effective pressure equation (9) and effective pressure value (11) were found on the basis of results of so called individual triaxial compression test (see Kovari et al., 1983) according to the methodology given by Nowakowski (2007).On the basis of Biot coefficients set of values was found that volumetric strain of the pore space described by a coefficient (5) was not dependent on the type of pore fluid and the pore pressure of only, while in case of volumetric strain of total rock described by coefficient (4) both the structure and texture of rock were important.The individual triaxial compression test results showed that for tested rock an effective pressure equation was a linear function of pore pressure as (15). The so called Rebinder effect (Rehbinder & Lichtman, 1957) might cause, that the α coefficient in equation (15) could assume values greater than one. This happened particularly in the case when the porous fluid was non-inert carbon dioxide.In case of inert pore fluid like kerosene the test results suggested that the a coefficient in equation (15) decreased while the differential strength limit was increasing. This might be caused by, so called, dillatancy strengthening (see Zoback & Byerlee, 1975).Another considered important parameter of the equation (15) was the value of the effective press p'. The results showed that the value of this parameter was practically independend on the pore fluid type. This conclusion was contrary to previous research (see, for example, Gustkiewicz et al., 2003 andGustkiewicz, 1990) so these results should be treated with caution. There are no doubts, however, over p' increasing simultaneously with increase in R σ 1 -σ 3 . Basically, the differential strength limit of the specimen is greater the greater is confining pressure applied to it. Thus, higher R σ 1 -σ 3 values are accompanied by higher p'.