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Tension Crack 1
Introduction
A tension crack may develop in a slope when the inclination angle of the slip surface is steep and when the sliding mass is sitting on a weak foundation material. Considering the tension crack will eliminate the negative normal generated at the base of a slice, as a result, it gives more reasonable solution, and may improve convergence in some cases. The purpose of this example is to illustrate the various options in modeling the presence of a tension crack. Features of this simulation include:
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Analysis method: GLE
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A dry slope
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Entry and exit slip surface option
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Presence of a tension crack
Configuration and setup
A simple homogeneous embankment is used. The slope is assumed to be dry, therefore no pore water pressure is considered. A Mohr Coulomb soil model is used. The unit weight of the material is chosen to be 20 kN /m3 , the cohesion and frictional angle are assumed to be 15 kPa and 30o respectively. Since all surfaces are assumed to exit at the toe of the embankment, the exit zone is modeled with a single point. The geometry and material properties are shown in Figure 1. 24 22
Elevation (m)
20 18 16 Name: Embankment Model: MohrCoulomb Weight: 20 kN/m³ Cohesion: 15 kPa Phi: 30 °
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Distance (m) Figure 1 Geometry and material properties
SLOPE/W Example File: Tension crack.doc (pdf) (gsz)
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Analysis 1 - No tension crack
Figure 2 shows the factor of safety and the critical slip surface when the embankment is analyzed with no tension crack. Using the View Slice Info feature in CONTOUR, you will see that normal force of slice # 1 is pointing away (negative) from the base of the slice (Figure 3). In other words, the base normal force is in tension. Although the force polygon is still close showing the slice is in force equilibrium, nevertheless, the negative normal is not realistic and should avoided by allowing a tension crack to develop near the crest of the slope.
Figure 2 Critical slip surface and factor of safety with no tension crack
Figure 3 Free body diagram and force polygon of Slice # 1
SLOPE/W Example File: Tension crack.doc (pdf) (gsz)
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SLOPE/W provides three options to model the presence of a tension crack. These options are:
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modeled with a tension crack angle
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modeled with a tension crack line
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modeled automatically based on the negative base normal
Analysis 2 – Tension crack angle
Figure 4 shows the factor of safety and the critical slip surface when the embankment is analyzed with a tension crack angle. The tension crack angle is assumed to be at 115o . Note that the angle is measured from the positive x-axis.
Figure 4 Critical slip surface and factor of safety with a tension crack angle
As depicted in Figure 4, a tension crack has developed near the crest. The slip surface extended up vertically when the base angle of the slip surface reaches 115o. Figure 5 shows the free body diagram and the force polygon. Note that the base normal force is not in tension anymore (pointing towards the slice base).
SLOPE/W Example File: Tension crack.doc (pdf) (gsz)
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Figure 5 Free body diagram and force polygon of Slice # 1
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Analysis 3 – Tension crack line
Figure 6 shows the factor of safety and the critical slip surface when the embankment is analyzed with a tension crack line. A tension crack zone of about 0.8 m deep is defined using a tension crack line. With this option, the slip surface extended up vertically when the slip surface intersect the tension crack line. Figure 7 shows the free body diagram and the force polygon. Note that the base normal force is in compression (pointing towards the slice base).
Figure 6 Critical slip surface and factor of safety with a tension crack angle
SLOPE/W Example File: Tension crack.doc (pdf) (gsz)
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Figure 7 Free body diagram and force polygon of Slice # 1
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Analysis 4 – Auto tension crack
Figure 8 shows the factor of safety and the critical slip surface when the embankment is analyzed with an auto tension crack option. With this option, you do not need to specify a tension crack angle or a tension crack line, the slip surface extended up vertically from the base of the slice whenever the base of the slice is giving a negative normal force. After the slip surface is modified, the analysis is repeated to ensure that there is no more negative base normal. Figure 9 shows the free body diagram and the force polygon. Note that the base normal force is not in tension (pointing towards the slice base).
Figure 8 Critical slip surface and factor of safety with a tension crack angle
SLOPE/W Example File: Tension crack.doc (pdf) (gsz)
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Figure 9 Free body diagram and force polygon of Slice # 1
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Closing
It is a good practice to always examine the free body diagram and force polygon of the slices near the crest of the slope. When the base normal force is in tension (pointing away from the slice base), unless you are modeling a rock in which some tension may be possible, you may want to control the negative normal with a tension crack. The Auto tension crack option is convenient, in the sense that you do not need to specify a tension crack angle or the position of a tension crack line, however, it is much more computationally intense due to the iterative procedure.
SLOPE/W Example File: Tension crack.doc (pdf) (gsz)
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