A Model of Anisotropic Property of Seepage and Stress for Jointed Rock Mass

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Material parameters</td><td align="center">Values</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Undamaged Young’s modulus <svg height="15.4" id="M126" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 17.200001 15.4" width="17.200001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M609 650l-19 -162l-30 -2q2 69 -14 94q-9 18 -28.5 26t-74.5 8h-88q-30 0 -37 -6.5t-12 -36.5l-41 -212h103q48 0 69 5.5t32 19t26 50.5h29l-40 -198h-30q2 58 -11.5 70.5t-85.5 12.5h-99l-30 -167q-17 -87 3 -101q18 -15 111 -15q59 0 89 7t54 27q8 7 15.5 16t16 21.5
l14 20.5t15 23.5t13.5 21.5l29 -10q-52 -129 -71 -163h-500l6 28q66 4 83 17.5t28 73.5l77 409q11 61 -0.5 75.5t-78.5 18.5l10 28h467z" id="x1D438"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.8,15.187)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> (GPa)</td><td align="center">65</td></tr><tr><td align="left">Undamaged Poisson’s ratio <svg height="11.925" id="M127" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 13.825 11.925" width="13.825" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.638)"><path d="M457 332q0 -81 -41 -161.5t-105.5 -131.5t-129.5 -51q-46 0 -79 30.5t-33 86.5q0 18 7 51q18 95 46 187q6 19 6 33q0 7 -7 7q-24 0 -78 -64l-20 23q32 48 73 77t78 29q33 0 33 -46q0 -38 -10 -70q-28 -92 -39 -152q-7 -38 -7 -57q0 -78 69 -78q68 0 118 75.5t50 194.5
q0 43 -12 57q-11 12 -11 24q0 19 15 35.5t34 16.5q18 0 30.5 -34.5t12.5 -81.5z" id="x1D463"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.425,11.725)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg></td><td align="center">0.23</td></tr><tr><td align="left">Density (kg/m<sup>−3</sup>)</td><td align="center">2700</td></tr><tr><td align="left">Principal direction angle of joint plane <svg height="12.4375" id="M128" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.5874996 12.4375" width="8.5874996" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M475 507q0 -83 -20 -172t-56 -167.5t-93.5 -129t-125.5 -50.5q-157 0 -157 227q0 78 21.5 164t59 161t96.5 123.5t126 48.5q79 0 114 -58t35 -147zM391 522q0 155 -81 155q-62 0 -111 -82.5t-73 -200.5h253q12 81 12 128zM373 346h-255q-12 -91 -12 -150q0 -72 20 -123
t63 -51q34 0 64 28.5t52.5 77t39 103t28.5 115.5z" id="x1D703"></path></g>
</svg> (°)</td><td align="center">15</td></tr><tr><td align="left">Coupling parameter <svg height="16.6625" id="M129" style="vertical-align:-3.56265pt" version="1.1" viewbox="0 0 10 16.6625" width="10" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M558 587q0 -32 -14 -61t-40 -53.5t-48.5 -41t-54.5 -36.5q144 -51 144 -174q0 -55 -43.5 -108t-104.5 -87q-77 -42 -131 -42q-31 0 -54 20t-31 47l11 18q48 -29 108 -29q79 0 119.5 43t40.5 109t-44.5 107.5t-119.5 50.5l22 47q34 1 65 21q96 61 96 157q0 42 -24 67.5
t-62 25.5q-24 0 -43.5 -9t-35 -29.5t-27 -44t-22.5 -63t-19.5 -75.5t-18.5 -91q-57 -294 -68 -380q-26 -190 -35 -200q-26 -31 -97 -37l-4 26q19 9 48 170l77 413q23 121 52.5 187.5t83.5 114.5q70 62 148 62q51 0 88.5 -34t37.5 -91z" id="x1D6FD"></path></g>
</svg> (Pa<sup>−1</sup>)</td><td align="center">0.5</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Parameters used in the model to validate the model in simulating the anisotropic properties of stress and seepage.

Journal of Applied Mathematics

tab3

Table 3

Table 3: A Model of Anisotropic Property of Seepage and Stress for Jointed Rock Mass 