تعاريف. Hasan Ghasemzadeh. : Trend Dip direction. : Plunge Dip. Strike=dip direction-90 (+180 or -180) Azimuth. Dip direction. Maximum Dip.

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1 تصوير ناپيوستگيها تعاريف تصوير قطبها تصوير استريوگرافي كاربرد استريوگرافي در پايداري شيروانيها كاربرد استريوگرافي در پايداري حفاريهاي زيرزميني Hasan Ghasemzadeh مشخصات يك بردار در فضا مشخصات صفحه ترك Dip direction Maximum Dip Azimuth Dip : Trend Dip direction : Plunge Dip strike 90 (180) Strike=dip direction-90 (+180 or -180) آزيموت و شيب عمود بر صفحه ترك n n The intersection of the plane and the surface of the sphere is a great circle, A line perpendicular to the plane and passing through the centre of the sphere intersects the sphere at two diametrically opposite points called the poles of the plane. In rock mechanics, the lower-hemisphere projection is almost always used. The upper-hemisphere projection is often used in structural geology

2 If the poles of planes rather than great circles are plotted, the data for large numbers of discontinuities can be rapidly plotted on one diagram and contoured to give the preferred or mean orientations of the dominant discontinuity sets and a measure of the dispersion of orientations about the mean polar net dip dip directions given in bold در پولار نت نياز بيه چرخاندن صفحه و شرقي غربي كردن آن نداريم the numbers of poles lying within successive areas which each constitute 1% of the area of the hemisphere are counted. The maximum percentage pole concentrations are then determined and contours of decreasing percentage of pole concentrations around the major concentrations are established. The central orientations (mean) of the two major joint sets are 347/22 and 352/83 bedding planes is 232/81 contours 352/83 232/81 347/22 The higher the value of K, the less is the dispersion of values about the mean. For a random distribution of poles, K = 0.

3 تصوير N تصوير Stereonet lower hemispheres both upper and lower hemispheres

4 EXAMPLE dip direction, = 135 dip angle, = 50 denoted as 135/50 Dip Direction = 135 N Plot also 000/90 and 090/00 Rock Mechanics 19 Rock Mechanics 20 N Tracing paper with central drawing pin Step 1 Rotate the paper until the line marking the dip direction corresponds with the equatorial position (90 ) Rock Mechanics 21 Rock Mechanics 22 Steps 2 and 3 Measure 50 ( = the dip angle, ) from the outer circle RHS and trace the great circle for the plane as shown Measure (90 - ) or 40 from the outer circle, but this time from the LHS to locate the POLE of the great circle or plane Rock Mechanics 23 Rock Mechanics 24

5 Rotate back to the North position N POLE GREAT CIRCLE Rock Mechanics 25 Rock Mechanics 26 Intersections Two planes A and B have orientations A:060/30 and B:340/75 These planes intersect on the stereonet at the point A:B - this point represents the line of intersection of the discontinuities represented by the planes Plane B, 340/75 Plane A, 060/30 Rock Mechanics 27 Rock Mechanics 28 Plunge of intersection line Rotate tracing until intersection point lies on the E-W line intersection line The intersecting planes Read off the number of degrees from the perimeter to the intersection point = the plunge of the intersection line plane 1 plane 2 line of intersection Rock Mechanics 29 Rock Mechanics 30

6 Plunge of intersection line Rotate tracing until intersection point lies on the E-W line 35 Read off the number of degrees from the perimeter to the intersection point = the plunge of the intersection line Rock Mechanics 31 Rock Mechanics 32 Dip direction of intersection line Rotate tracing back to the datum Mark off dip direction as indicated The intersection point can be designated as 060/ Rock Mechanics 33 Rock Mechanics 34 Rock Mechanics 35

7 BH : the direction of the borehole vector, D maximum dip of the plane, N for the normal to the plane. 1-Rotate : borehole on the E-W line 2- move BH to the centre of the net-in 90-65= Move the normal N through the same angle, but along the small circle. In effect, the net has been inclined to be perpendicular to the borehole. Stereonet information can be used to indicate the likely instability Plots of the poles of discontinuity planes Contours to indicate high concentrations in areas of the net prevailing discontinuities Position of discontinuities with respect to the Great Circle for the Slope? Rock Mechanics 39 Rock Mechanics 40 Typical Slope Instability (a) no particular concentration of poles - circular failure (e.g. waste rock/ fractured slate) - similar to soil (use Bishop s method) Slope Instability (b) single concentration of poles above cut slope - plane failure slope Rock Mechanics 41 Discontinuity strike parallel to that for the slope Rock Mechanics 42

8 Conditions for planar failure The plunge of the slope > dip of the discontinuity Discontinuity daylights on the slope face Discontinuity has a dip angle > for the joint mechanically possible Dip direction of the discontinuity and slope lie within 20 The last condition 20 < 20 Strike of discontinuit y Rock Mechanics 43 Rock Mechanics 44 Slope Instability (c) double concentration of poles = intersecting joints - wedge failure most common slope Conditions for wedge failure The plunge of the slope > dip of the Intersection line Intersection line daylights on the slope face Intersection line has a dip angle > for the joints mechanically possible discontinuiti es Rock Mechanics 45 Rock Mechanics 46 Dip of intersection > friction angle intersection line plane 2 plane 1 intersection line, I 12 Slope Great Circle friction circle UNSAFE slope! Rock Mechanics 47 The Friction Circle The meridional plot is overlaid by the friction circle (same diameter) The slope is safe if the intersection point, I 12 is outside the friction circle ( ) for the joint - mechanically impossible to fail - assumes c = 0 kpa for the joint Rock Mechanics 48

9 Wedges intersecting slopes Great circle of slope surface Slope Instability (d) single concentration of poles below slope - toppling failure in hard rock slope intersection lines of planar discontinuities with the slope Rock Mechanics 49 discontinuity Rock Mechanics 50 - the block is stable - the block falls from the roof - the block slides (either along the line of maximum dip of a discontinuity, or along the line of intersection of two discontinuities)

10 block is stable Block falls from the roof Vertical direction the block slides Inclination face the line of maximum dip is not included within the block. Inclination face 1- the normal to the excavation surface (N f ) 2- the normals to the various discontinuity surfaces (N l, N 2 ) 3- the normal to the horizontal plane (N h ) 4- rotate such that N f lies on the E-W line. 5- The inclination is then applied any line which appears on the N hl -side of the inclined horizontal plane is directed downwards Block falls from the roof great circle, H, representing the horizontal plane and the associated pole, N hi,

11 the block slides the block slides Overhanging surfaces N hi is directed downwards Non overhanging surfaces for nonoverhanging surfaces, N hi is directed upwards. friction circle represents a cone of semi-angle (90 - ) around N hi for overhanging surfaces friction circle represents a cone of semi-angle (90 -+ ) around N hi for non-overhanging surfaces block is stable block is stable