Numerical solutions for strain-softening surrounding rock under three-dimensional principal stress condition.

The associated flow law can be presented as follows: HT <math display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mtext>d</mtext><msubsup><mi> </mi><mi>i</mi><mi>p</mi></msubsup><mo>=</mo><mi mathvariant="normal">d</mi><mi> </mi><mfrac><mi> </mi><mi>f</mi><mrow><mi> </mi><msub><mi> </mi><mi>i</mi></msub></mrow></mfrac></math> ht Graph (7)where d I i is the constant plasticity multiplier. Thus, Eq. (16) can be expressed by HT <math display="block" overflow="scroll" xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mtext>d</mtext><msubsup><mi> </mi><mi> </mi><mi>p</mi></msubsup></mrow><mtext>d</mtext><mi> </mi></mfrac><mo>+</mo><mfrac><mrow><msubsup><mi> </mi><mi> </mi><mi>p</mi></msubsup><mo>-</mo><msubsup><mi> </mi><mi>r</mi><mi>p</mi></msubsup></mrow><mi> </mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mtext>d</mtext><msubsup><mi> </mi><mi> </mi><mi>e</mi></msubsup></mrow><mtext>d</mtext><mi> </mi></mfrac><mo>-</mo><mfrac><mrow><msubsup><mi> </mi><mi> </mi><mi>e</mi></msubsup><mo>-</mo><msubsup><mi> </mi><mi>r</mi><mi>e</mi></msubsup></mrow><mi> </mi></mfrac></math> ht Graph (17) The strain increments can be derived by combining Eqs. [Extracted from the article]