| Summary: | A longstanding mine backfill design challenge is determining the strength required if the (partially) cured backfill is subsequently undercut. Mitchell (1991) called the undercut backfill a sill mat and proposed an analytical solution that is still often used, at least for preliminary design, and has motivated subsequent empirical design methods. However, fully employing the Mitchell sill mat solution requires knowledge of the backfill material’s Unconfined Compressive Strength (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mi>C</mi><mi>S</mi></mrow></semantics></math></inline-formula>), tangent Young’s modulus (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>E</mi><mi>t</mi></msub></mrow></semantics></math></inline-formula>), tensile strength (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>σ</mi><mi>t</mi></msub></mrow></semantics></math></inline-formula>), as well as estimates of stope wall closure. Conducting a high-quality <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mi>C</mi><mi>S</mi></mrow></semantics></math></inline-formula> test poses challenges but relating the test result to the remaining material parameters is more difficult. Some new material testing data is presented and compared to available published results. Using the parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mi>i</mi></msub><mo>=</mo><mi>U</mi><mi>C</mi><mi>S</mi><mo>/</mo><msub><mi>σ</mi><mi>t</mi></msub></mrow></semantics></math></inline-formula> the range of available testing data is found to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mi>i</mi></msub><mo>=</mo></mrow></semantics></math></inline-formula> 3 to 22, however, the most compelling data is obtained when the Mohr’s failure circle in tension is tangential to the corresponding Mohr–Coulomb failure envelope determined from other strength tests. In these cases, the value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mi>i</mi></msub><mo>=</mo></mrow></semantics></math></inline-formula> 4 is found for the materials tested, which is much lower than the value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>m</mi><mi>i</mi></msub><mo>=</mo></mrow></semantics></math></inline-formula> 10 commonly assumed and implies a limiting <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mi>C</mi><mi>S</mi></mrow></semantics></math></inline-formula> 60% lower compared to the conventional assumption. It is also found that the relationship between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>E</mi><mi>t</mi></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mi>C</mi><mi>S</mi></mrow></semantics></math></inline-formula> is described by a power function that is close to linear, but the values for the constant and exponent in the power function depend on the material tested. However, for given tailings the power function is found to be independent of void ratio, binder type or concentration, curing time, and water salinity, within the ranges these parameters were investigated. Therefore, when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>E</mi><mi>t</mi></msub></mrow></semantics></math></inline-formula> is used in the Mitchell sill mat solution it should be correlated with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>U</mi><mi>C</mi><mi>S</mi></mrow></semantics></math></inline-formula> using the appropriate power function. These correlations are then used with the Mitchell sill mat solution and published measurements of backfill closure strains to estimate the Mitchell solution’s range of applicability based on its underlying assumptions, and a similar analysis is extended to an “empirical design method” motivated by the Mitchell sill mat solution. It is demonstrated that these existing approaches have limited applicability, and more generally a full analysis in support of rational design will require numerical modeling that incorporates the effect of confining stress on the material’s stiffness and mobilized strength.
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