1 Introduction Reinforcement with Anchors The purpose of this example is to show how anchor reinforcement is accommodated in a stability analysis. The example file makes use of the following SLOPE/W functionality: Anchor reinforcement; Distribution of the pullout forces across many slices; Inclusion of a shear force. 2 Configuration and setup Figure 1 shows the model configuration, soil properties, and entry/exit ranges. All slip surfaces are forced to exit at the toe of the slope. The Draw Reinforcement command was used to incorporate the anchor reinforcements within the domain. The four cases include: 1. Stability analysis with no anchor reinforcement; 2. Stability analysis that includes anchor reinforcement; 3. Distribution of the anchor pullout forces across multiple slices; 4. Inclusion of a shear force. SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 1 of 10
Figure 1 Geometry and soil properties 3 Case 1 Stability without reinforcement The factor of safety for the unsupported face is 0.965 (Figure 1). SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 2 of 10
Figure 2 Critical factor of safety and slip surface without reinforcement 4 Case 2 Stability with reinforcement Figure 3 shows the reinforcement parameters for case 2. The specified pullout resistance PR is 300 kpa, resistance reduction factor (RRF) 1.5, bond diameter (D) 1/π meters, grouted (bond) length 3 m, and spacing (S) in the out-of plane direction 2 m. The tensile capacity (TC) was specified as 180 kn with a reduction factor (RF) of 2. The factored pullout resistance (FPR) per length of grouted section behind the slip surface is calculated from the specified pullout resistance (PR) as: FPR = PR(πD) RRF(S)FS = 300( π1 π) 1.5(2) = 100 ( kn m ) /m The maximum pullout force must not exceed the factored tensile capacity FTC: FTC = TC RF(S) = 2000 = 667 kn 1.5(2) which is not possible in this case since there is only 3 m of grouted length. SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 3 of 10
Figure 3 Reinforcement parameters Figure 4 shows the critical factor of safety and slip surface. The factor of safety is 1.337. The maximum pullout force was governed by the factored pullout resistance and is therefore calculated from the available length of 3.0 m (View Object Information) as: PF = FPR(l) = 100 kn m m(3.0 m) = 300 kn per meter in the out-of-plane dimension. Both red boxes are inside the end of the anchor indicating that the entire grouted sections are behind the slip surface. SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 4 of 10
Figure 4 Critical factor of safety and slip surface Figure 5 and Figure 6 show the free body diagram and force polygon for Slices 12 and 22 that are intersected by the upper and lower anchors, respectively. The free body diagrams show the pullout force of 300 kn concentrated at the base of the slices. SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 5 of 10
Figure 5 Free body diagram and force polygon of slice 12 Figure 6 Free body diagram and force polygon of slice 22 View Object information can be used to view the inputs and calculations for each individual anchor (Figure 7). The governing component for both anchors is indicated as the (factored) pullout resistance (versus the tensile capacity). SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 6 of 10
Figure 7 Details of the upper anchor obtained via View Object Information Figure 8 shows the shear resistance along the slip surface (Draw Graph). The shear resistance spikes at slices 12 and 22 where the pullout forces are concentrated. SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 7 of 10
Figure 8 Shear resistance along slip surface 5 Case 3 Distributed pullout force SLOPE/W gives the following options for positioning the pullout force of an anchor on the free body: 1. Concentrated at the base the slice intersected by the reinforcement; and, 2. Distributed (i.e. apportioned) to the slices intersected by the reinforcement. The distribution option generally has a negligible influence on the results; however, the results can differ if the pullout force is large and/or convergence is jeopardized. In the latter case, convergence can sometimes be improved by distributing the pullout force to multiple slices. Figure 7 shows the critical slip surface and factor of safety if the pullout force is distrusted. The factor of safety is now 1.262 and the shear resistance is distributed across the intersected slices (compare Figure 8 with Figure 9). The pullout force of the top anchor has been distributed over the 26 slices that are intersected between the base of the slice and the wall. As such, the pullout force on a single slice is equal to: 300 kn 21 slices = 14.29 kn slice and on the 10 slices that also intersect the lower anchor: 300 kn 21 slices 300 kn kn + = 44.29 10 slices slice SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 8 of 10
Figure 7 Critical factor of safety and slip surface with uniform distributed anchor load Figure 9 Shear resistance along slip surface SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 9 of 10
6 Case 4 Anchor shear force SLOPE/W allows the simulation of a shear force in the anchor bar. In this case, the bottom anchor is assumed to have a shear force of 50 kn and a shear reduction factor of 2. The applied shear force is 25 kn, which causes an increase in the factor of safety. The shear force can be seen on the free body diagram for the intersected slice (View Slice Information). SLOPE/W Example File: Reinforcement with anchors.doc (pdf) (gsz) Page 10 of 10