The 3rd issue of the journal, Vol.2, N. 1, January-June 2013 ... - ISRM

Influence of Anisotropic Stress Conditions on Design of Development Workings in Bord and Pillar Mining19and all resistive forces are treated as passive forces. Theactive force vector is given by equation (1):...(1)Where, = resultant active force, = vectorrepresenting wedge weight, = vector representingthe weight of shotcrete on the wedge, = activepressure (Support) force vector , water force vector and= seismic force vector. The passive force vector isgiven by equation (2):...(2)Where, = resultant passive force vector, =shotcrete shear resistance force vector, = passivesupport pressure force vector and = resultant boltforce vector.Once the active forces are computed, this is utilized fordetermination of the direction of the sliding of wedge. Itis worth noting that the passive forces do not influencethe sliding direction. For any tetrahedron, there can be 7– possible directions of sliding .The vector represents the mode of falling or lifting of thewedge. The and vectors represent the modeof sliding on a single plane. The and vectorsrepresent the mode of sliding of the wedge along theline of intersection of two joint planes. The equations forthe sliding direction vectors are given by equations (3),(4) and (5)....(3)...(4)...(5)Where, = falling or lifting direction of wedge, â = unitdirection of active force, = resultant active force, =sliding direction on joint ‘i’, n i= normal to joint face ‘i’directed into wedge, n j= normal to joint face ‘j’ directedinto wedge and = sliding direction on joint ‘I’ and ‘j’(intersection of joints).After the evaluation of the sliding direction, the evaluationof normal force on each of the three joint planes ofthe tetrahedron is affected. The equations (6), (7) and(8) describe the normal forces on the planes of thetetrahedron.For falling or lifting wedge N i= 0, N j= 0, N k= 0 ...(6)For sliding on a single joint ‘i’ N i= –F A, n i, N j= 0, N k= 0 ...(7)For sliding along joint ‘i’ and ‘j’...(8)Now, for the computation of the resisting force on thewedge, the normal force acting on each joint plane isevaluated. The normal stress is computed based on theactive and passive normal force computed on the jointplane and is given by equation (9)....(9)Where, σ niis the i th joint plane, N iis the normal force onthe i th joint and a iis the area of the i th joint. The resistingstress due to the shear strength of the joint is representedby the Mohr-coulomb failure criteria given by...(10)Eventually the resisting force due to shear strength ofthe joint is given by...(11)Where, = the magnitude of the resisting force due toshear strength of the joint = the shear strength ofthe joint the area of the joint the cohesionof the joint plane the angle of internal friction of thejoint strength and the angle between the sliding directionand the joint.The resisting force due to the tensile strength of the jointis taken as zero for the analysis in this paper.Finally the factor of safety for the three cases viz., (i)the falling factor of safety - (ii) unsupported factor ofsafety - and (iii) the supported factor of safety - iscalculated. The maximum amongst the three is reportedas the factor of safety of the wedge.As per the development carried out at Tandsi mine,four directions of galleries (Table 2) will be sufficient torepresent the drivage of the mine. Table 3 lists the detailsof the joint sets present in the roof.Table 2 : Direction of galleries at Tandsi mine.Sl. No. Location Gallery Trend Plunge1Level 078 0026D /9L2 Dip /Rise 171 043Level 120 01.710D / 14L4 Dip / Rise 033 03.7Volume 2 No. 1 January 2013