## 3 Numerical Examples
### Edge Discontinuities in Unsaturated Porous Media
The value of cohesive traction decreases from tensile strength for zero openings to zero for initial notches. To minimize the crack opening and inhibit crack propagation, as is shown in Figure 5c, the suction increases around the fracture. As the crack opening increases at a specific point, the exerted cohesive force on the crack body decreases. At that point, suction plays a more active role as a preventative force against the crack opening. Still, since the intensity of suction is much lower than the cohesive force, its influence on the reduction in the crack aperture at that point is less that the cohesive force influence. As depicted in Figure 5d, the degree of saturation is also significantly affected by the presence of the cracks and varies intensely along the crack up to the maximum value of one at the crack tip where the crack is closed and there is no leakage flux. To better understand the impact that the presence of two cracks has on the unsaturated porous plate behavior, a comparison is made with the case when a single crack propagates from the left edge of the same plate. The distributions of various variables for the case of single crack propagation are presented in Figure 6 at different times. Figure 4: (**a**) Plate Deformation, (**b**) Normal Stress, (**c**) Suction, (**d**) Normal suction gradient, and (**e**) Degree of saturation distributions at different times for the problem one—the square plate with initial existing crack stretched out with the constant displacement rate of \(2.37\times 10^{-7}\) m/s. Figure 5: (**a**) Cohesive traction distribution, (**b**) Crack opening, (**c**) Suction distribution, and (**d**) Degree of Saturation at different times for Problem 1 (a square plate with initial existing crack depicts in Figure 3). Figure 6: \(Cont.\)  
As expected, the distributions of cohesive traction imposed on the crack body have the same upper limit in the two cases of one and two cracks. However, since the crack mouth opening in the final steps of single crack case analysis is more than its double crack counterpart (see Figures 5b and 6b), and as cohesive force depends directly on the crack opening, cohesive force at the crack mouth of single crack case analysis becomes less than its double crack counterpart at the final steps (Figures 5a and 6a). To compensate for a less cohesive force in a single crack case, the crack mouth suction increases more in this case than its double crack equivalent to prevent further crack mouth opening. This behavior accentuates the preventative role of suction to inhibit crack propagation. In addition, this comparison depicts the ability of the proposed model in its successful demonstration of natural force for preventing crack to propagate. To compare the load carrying capacity of the plate in the presence of two cracks with the case of single crack, load-displacement curves for the two cases are depicted in Figure 7. Since in the case of double cracks, the load is transferred via the suction instead of the solid matrix in a longer width along with the plate, two graphs are different from the beginning. The higher load carrying capacity is observed in the case of a single crack, the more displacement is observed to reach the failure of the plate. Sensitivity analysis is further performed to investigate the effect of permeability and initial crack length on the propagation of two cracks in the unsaturated porous plate. A series of reference permeability values and initial crack lengths are adopted to examine their influences on the response of the model. When the reference permeability is high,  
Figure 6: (**a**) Cohesive traction, (**b**) Crack opening, (**c**) Suction, and (**d**) Degree of saturation distributions at different times in the case of one existing initial crack—the goal of this result is to make a comparison with the case of two existing initial crack. Figure 7: Comparison of load–displacement in the case of single (Figure 6) and double cracks (Figure 5).