## 4 Failure Modes
### Failure Dominated by Joint 1: S-90-90  
Taking S-90-90 as an example, Figure 6 illustrates the crack propagation behavior and the variation trend of AE parameters of specimens under various stress levels. When the stress is loaded to 33.45 MPa, observe the principal strain field during stage I (Figure 6a). A red coplanar strain band initiates at the tip of joint 1, and the inner coplanar strain band extends upwards through the layer; meanwhile, the principal strain field at the tip of joint 2 undergoes significant changes, but no macroscopic cracks are observed. During stage I, the \(b\)-value first increases and then decreases (Figure 6b), experiencing a transition from small failures dominating during the initial compaction stage to large failures dominating during plastic deformation. Observing the AE counts and crack ratios during stage I, the AE counts surge to 12 \(\times\) 10\({}^{3}\) at the end of this stage (Figure 6b), and the cumulative tensile crack ratio climbs to 63.27%. Notably, the real-time tensile crack ratio remains around 99% during this stage (Figure 6c), which is attributed to the coplanar tensile cracks initiated at the tip of joint 1 dominating the failure. As the stress climbs to 34.21 MPa, approaching the peak strength, observe the variations in the principal strain field (Figure 6b). The coplanar strain band at the inner tip of joint 1 extends upwards to the left side of joint 2; a red strain band appears at the tip of joint 2, and a coplanar strain band initiates at the outer tip; simultaneously, an inclined strain band initiates at the right tip of the soft layer. Observing Figure 6b, the AE counts and \(b\)-value during stage II tend to stabilize, indicating that no crack coalescence leading to sample instability has occurred. The cumulative tensile crack ratio climbs from 63.27% to 74.47% during stage II (Figure 6c), attributed to the extension of tensile cracks in joint 1. Meanwhile, the real-time tensile crack ratio remains around 98%, suggesting that the inclined strain band at the right tip of joint 2 has little influence on the failure mode. As the stress decreases to 32.32 MPa, entering stage III, observe the principal strain field (Figure 6a). The coplanar tensile cracks in joint 1 continue to extend towards both tips, approaching the bottom; the red strain band at the tip of joint 2 expands, and the coplanar strain band at the outer tip extends upwards, with the appearance of out-of-plane tensile strain bands; simultaneously, the strain band at the right tip spreads to the outer tip of joint 2, overlapping and completing crack coalescence. Observing the AE parameters during stage III (Figure 6b), AE counts and \(b\)-value do not change significantly; the proportion of tensile microcracks increases to 82.53%, contributed by both tensile cracks penetrating the soft-hard interface and out-of-plane tensile strain bands. As the stress drops to 29.64 MPa (stage IV), observe the changes in the principal strain field (Figure 6a). The tensile cracks at the upper tip of joint 1 extend to near joint 2 and coalesce with the cracks at the inner tip of joint 2. Observing the AE parameters during stage IV (Figure 6b), the \(b\)-value rapidly increases and then decreases within a short period, indicating accelerated tensile failure. Meanwhile, the real-time tensile microcrack ratio decreases from 97% to around 93%, attributed to the shear slip caused by the coalescence of inclined shear cracks on the right side of the specimen. However, the crack coalescence mode during stage III remains dominated by tension. Figure 6: Principal strain field and AE parameter profiles of the S-90-90 specimen: (**a**) principal strain field; (**b**) stress–strain curves, \(b\)-value, and AE counts; (**c**) shear-tension cumulative crack proportion and real-time tensile crack proportion.