Tutorial_02_Scaling_Wedge_Size

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<p>Scaling Wedges Tutorial 2-1</p><p>Scaling Wedges Tutorial</p><p>Unwedge always initially calculates the maximum sized wedges which</p><p>can form around an excavation.</p><p>This tutorial demonstrates how to scale down the size of the wedges, to</p><p>represent the actual size of wedges observed in the field. This is done</p><p>with the Scale Wedges option, which allows you to scale the size of</p><p>wedges according to field measurements such as joint trace lengths, joint</p><p>persistence, wedge face area etc.</p><p>Wedge scaling is important because the assumed wedge size can have a</p><p>significant effect on support requirements (e.g. pattern spacing,</p><p>positioning or orientation of bolts, and the thickness or strength of</p><p>shotcrete).</p><p>The model represents a section of an underground spiral access ramp.</p><p>Topics Covered</p><p>• Scaling Wedge Size</p><p>• Scaling All Wedges</p><p>• Scaling Individual Wedges</p><p>• Safety factor and Scaling</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-2</p><p>Model</p><p>For this tutorial we will start by reading in the file Tutorial 02 Scaling</p><p>Wedges.weg which you should find in the Examples > Tutorials folder in</p><p>your Unwedge installation folder.</p><p>Select: File → Open</p><p>Navigate to the Examples > Tutorials folder in your Unwedge installation</p><p>folder and open the Tutorial 02 Scaling Wedges.weg file.</p><p>The model should appear as follows.</p><p>Figure 1: Maximum sized perimeter wedges for tutorial 2 example.</p><p>As you can see, all of the Perimeter Wedges (roof, sides and floor wedges)</p><p>are the maximum possible size for the excavation cross-section.</p><p>NOTE: the Plunge of the Tunnel Axis Orientation is 15 degrees, because</p><p>the model represents a section of an inclined ramp, rather than a</p><p>horizontal tunnel.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-3</p><p>Scaling Wedges</p><p>To scale down the size of wedges, select the Scale Wedges option from</p><p>the Analysis menu.</p><p>Select: Analysis → Scale Wedges</p><p>You will see the Scale Wedges dialog.</p><p>Wedge size can be scaled according to joint trace length, joint persistence</p><p>or wedge data (e.g. volume, face area etc). Although we can enter</p><p>multiple scaling parameters at the same time, let’s enter parameters one</p><p>at a time, to see the results at each step.</p><p>Select the Joint 1 (Trace Length) checkbox, and enter a Scaling Value of 4</p><p>meters. Select OK.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-4</p><p>Your screen should look as follows.</p><p>Figure 2: Wedge size scaled by Joint 1 trace length = 4 meters.</p><p>Notice that all of the wedges have been scaled down in size. To indicate</p><p>that scaling has been applied to a wedge, the letter “s” is displayed beside</p><p>the wedge number (e.g. the roof wedge is numbered “8s”). NOTE: if you</p><p>do not see the wedge numbers, go to Display Options, select the Wedge</p><p>View tab, and make sure the Wedge Numbers checkbox is selected.</p><p>Before we proceed further, select the Filter List button in the Sidebar.</p><p>1. In the Wedge Information Filter dialog, select the Defaults</p><p>button (so that only the Wedge Name, Factor of Safety and</p><p>Wedge Weight checkboxes are selected).</p><p>2. Now select the Scaled By checkbox and the Joint Trace</p><p>Lengths checkbox, as shown in the following figure. Select OK.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-5</p><p>Now look at the Wedge Information panel in the Sidebar. NOTE:</p><p>• For all wedges, Scaled By = Joint 1 Trace Length</p><p>• For all wedges, Joint 1 Trace Length = 4 meters.</p><p>This is consistent with the single scaling value which we entered in the</p><p>Scale Wedges dialog (Joint 1 Trace Length = 4 meters).</p><p>At this point, we should note the following:</p><p>• When we use the All Wedges scaling option (in the Scale Wedges</p><p>dialog), this does not necessarily mean that all wedges will be</p><p>scaled (i.e. reduced in size). It means that all wedges will be</p><p>CONSIDERED for scaling. Wedges will only be scaled if their</p><p>current dimensions are larger than one of the scaling parameters.</p><p>If the parameters of a wedge are already smaller than the scaling</p><p>parameters, then the wedge will not be affected by the scaling.</p><p>In the current example, all of the wedges were reduced in size, but in</p><p>general this will not necessarily be the case.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-6</p><p>Figure 3: Wedge information after scaling by Joint 1 trace length.</p><p>Now let’s enter one more scaling parameter.</p><p>Select: Analysis → Scale Wedges</p><p>In the Scale Wedges dialog, select the Joint 2 (Trace Length) checkbox,</p><p>and enter a Scaling Value of 4 meters. Select OK.</p><p>Look at the Wedge Information panel in the Sidebar. The results are now</p><p>as follows:</p><p>• For the Floor Wedge and the Roof Wedge, Scaled By = Joint 2</p><p>Trace Length, and Joint 2 Trace Length = 4 meters.</p><p>• For the Lower Left and Lower Right wedges, Scaled By = Joint</p><p>1 Trace Length, and Joint 1 Trace Length = 4 meters.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-7</p><p>For the Floor and Roof wedges, the Joint 2 trace length (scaling value) is</p><p>now the governing parameter (the Joint 1 trace length is less than 4</p><p>meters).</p><p>For the Lower Left and Lower Right wedges, the Joint 1 trace length</p><p>(scaling value) is still the governing parameter, since the Joint 2 trace</p><p>lengths are already less than 4 meters, therefore the Joint 2 trace length</p><p>scaling value does not affect these wedges.</p><p>This illustrates the following important points:</p><p>• When you enter more than one Scaling Value, a given wedge is</p><p>ultimately scaled by only one parameter – the parameter which</p><p>gives the smallest wedge size.</p><p>• Furthermore, if Wedges to Scale = All Wedges (in the Scale</p><p>Wedges dialog), and you have entered multiple scaling values, the</p><p>governing scaling parameter can be different for different wedges.</p><p>Let’s enter a third scaling parameter.</p><p>Select: Analysis → Scale Wedges</p><p>In the Scale Wedges dialog, select the Joint 3 (Trace Length) checkbox,</p><p>and enter a Scaling Value of 4 meters. Select OK.</p><p>Look at the Wedge Information panel in the Sidebar:</p><p>• For all wedges, Scaled By = Joint 3 Trace Length</p><p>• For all wedges, Joint 3 Trace Length = 4 meters.</p><p>The Joint 3 Trace Length scaling value (4 meters) is now the governing</p><p>scaling parameter for all wedges. Notice that the actual Joint 1 and Joint</p><p>2 trace lengths for all wedges are now less than 4 meters.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-8</p><p>Figure 4: Wedge size scaled by Joint 3 trace length = 4 meters.</p><p>NOTE: if you go back to the Scale Wedges dialog, and turn OFF the</p><p>checkboxes for Joint 1 Trace Length and Joint 2 Trace Length, and select</p><p>OK, the results will not change, since the Joint 3 Trace Length scaling</p><p>value gives the smallest wedge size for all perimeter wedges.</p><p>Position of Scaled Wedges</p><p>For perimeter wedges which span multiple segments of the Opening</p><p>Section (e.g. the Roof wedge in this example), Unwedge uses an algorithm</p><p>which searches for the wedge with the maximum volume for the given</p><p>Scaling Value(s). An iterative process is required to find this wedge. This</p><p>determines the position of the scaled wedge on the perimeter.</p><p>In this example, if you compare Figure 2 and Figure 4, notice that the</p><p>Roof Wedge is off to one side in Figure 2 and is approximately centered in</p><p>Figure 4. The different positions of the Roof Wedge are due to the</p><p>Unwedge searching algorithm and the different scaling values used for</p><p>each case.</p><p>For wedges which are formed on a single flat surface of the excavation</p><p>boundary, the searching algorithm is not applicable, and the scaled</p><p>wedge position will be approximately centered on the surface.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-9</p><p>Scaling Individual Wedges</p><p>So far in this tutorial, we have considered all wedges for scaling, using</p><p>the same set of scaling values (i.e. in the Scale Wedges dialog, the Wedge</p><p>to Scale option was set to All Wedges).</p><p>It is also possible to consider individual wedges for scaling. This allows</p><p>you to enter</p><p>independent scaling values for any desired wedge(s). To</p><p>select individual wedges for scaling:</p><p>• You can select the desired wedge from the Wedge to Scale drop-</p><p>list in the Scale Wedges dialog.</p><p>• You can also right-click directly on a wedge, and select Scale</p><p>Wedge for that particular wedge from the popup menu, as shown</p><p>in the following figure. This will display the Scale Wedges dialog</p><p>with the wedge already selected in the dialog.</p><p>For example:</p><p>1. Right-click on the Roof Wedge, and select Scale Wedge: 8 Roof</p><p>from the popup menu, as shown in the above figure.</p><p>2. In the Scale Wedges dialog, select the Joint 2 Trace Length</p><p>checkbox and enter a scaling value of 3 meters. Select OK.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-10</p><p>3. Now look at the Wedge Information panel. The Roof wedge is now</p><p>scaled by the Joint 2 Trace Length = 3 meters. All other wedges</p><p>are still scaled according to the Joint 3 Trace Length scaling</p><p>value entered with the All Wedges scaling option.</p><p>Figure 5: Roof wedge scaled independently using Joint 2 Trace Length = 3.</p><p>You can scale any or all wedges individually, in this manner. When you</p><p>select individual wedges to scale, the Scaling Value parameters are</p><p>entered independently for each wedge, and the dialog will “remember”</p><p>the Scaling Values you have entered for each wedge.</p><p>NOTE: if you specify Scaling Values for All Wedges, AND for individual</p><p>wedges, at the same time in the Scale Wedges dialog, the program will</p><p>use the Scaling Value which gives the smallest wedge, for any given</p><p>wedge.</p><p>Resetting the Maximum Wedge Size</p><p>To reset all wedges to the maximum size, select the Maximize button in</p><p>the Scale Wedges dialog. This will clear all of the Scaling Values, for All</p><p>Wedges and also for any individual wedge Scaling Values you have</p><p>entered.</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Scaling Wedges Tutorial 2-11</p><p>Unwedge v.3.0 Tutorial Manual</p><p>Safety Factor and Scaling</p><p>We will now briefly discuss the effect of scaling the wedge size on the</p><p>wedge safety factor and support requirements.</p><p>Effect of Joint Strength</p><p>• Frictional Strength Only – if the shear strength of the joint</p><p>planes is purely frictional (cohesion = 0), then changing the size</p><p>of an unsupported wedge will NOT change the safety factor. You</p><p>can verify this for the current example (the Joint Shear Strength</p><p>of all joints is given by Phi = 30 degrees, cohesion = 0).</p><p>• Friction and Cohesion – if the shear strength of the joint</p><p>planes includes a non-zero cohesion, then the safety factor of a</p><p>wedge will, in general, depend on the size of the wedge.</p><p>• Other parameters – water pressure, field stress and other</p><p>parameters can also influence the dependence of wedge size and</p><p>safety factor.</p><p>Support</p><p>If support has been applied to a wedge (e.g. bolts or shotcrete), then in</p><p>general, changing the size of a wedge will affect the safety factor. This</p><p>can be due to several factors:</p><p>• The wedge size may affect the number of bolts which intersect a</p><p>wedge (pattern bolting).</p><p>• The wedge size will affect the relative embedded lengths of a bolt.</p><p>For a bonded bolt, the length which passes through the wedge,</p><p>and the length embedded in the rock mass will determine the</p><p>support force applied to the wedge.</p><p>• If shotcrete has been applied, then the wedge size will have a</p><p>direct effect on the exposed perimeter length of the wedge face.</p><p>This has a direct effect on the support force which is applied by</p><p>the shotcrete.</p><p>In conclusion, wedge scaling is of particular importance during support</p><p>design, since the assumed wedge size can have a significant effect on the</p><p>pattern spacing, positioning or orientation of bolts, and the thickness or</p><p>strength of shotcrete.</p><p>Wedge support is discussed in the next tutorial. That concludes this</p><p>tutorial on scaling wedge size in Unwedge.</p><p>Scaling Wedges Tutorial</p><p>Model</p><p>Scaling Wedges</p><p>Position of Scaled Wedges</p><p>Scaling Individual Wedges</p><p>Resetting the Maximum Wedge Size</p><p>Safety Factor and Scaling</p><p>Effect of Joint Strength</p><p>Support</p>