3.1 Slope failure morphology
Constant centrifugal force, about 80g, was applied on the slope model until failure occurred. The excavation process was simulated in three steps in the case of no downtime. Figure 7 shows the whole process from deformation to failure that the slope model experienced after excavation. In general, it could be categorized into five stages. In the first stage, when excavation operation was finished, stress redistribution occurred inside the slope due to the unloading effect induced by excavation (Figure 7a). This led to the second stage, in which tensile fracture was observed on slope surface with further development of soil deformation, and continuous plastic zone was coming inside (Figure 7b). As the plastic zone and tensile fracture developed to interpenetration, the first slip occurred at the depth of the model, indicating the third stage of deformation process. According to the mechanical characteristics, the sliding was a retrogressive failure. The back wall showed in an arm-chair shape and the sliding distance of the landslide was short. The sliding body accumulated at slope foot, and the sliding started quickly. During the fourth stage, due to the instability of deep-sliding body, the plastic zone and fracture had a secondary development in the shallow part (Figure 7d). As a result, the second slip occurred in the fifth stage, which exhibits as a shallow sliding. According to the mechanical characteristics, similar to the first one, it also belongs to the retrogressive sliding, which presented an arm-chair shape at back wall. However, shorter sliding distance was observed for the second landslide, as well as faster response.
For a better understanding, the shape and location of the sliding surfaces formed during the overall instability process are shown in Figure 8. As mentioned above, two sliding surfaces were formed in the slope body, where one was deeper and the other was shallower. The distance perpendicular to slope surface was measured as 9.6 cm for the deeper sliding surface, and 4.2 cm for the shallower one. In addition, the deeper sliding surface has a higher inclination angle. Thus, compared to the first collapse that is an overall deformation triggered by the unloading effect, the second one was observed to be more local, resulting in deformation with smaller scale.
There were two fissures with vertical extension direction at the top of slope (Figure 8b). Due to the limited influence range of excavation zone, the closer the fissure is to the slope crest, the longer extension it has. After the first sliding, the slope back wall appears a new lateral face, leading to a small crack close to the back wall by the action of lateral force, which generates a small collapse later.
3.2 Stress field behavior
The variation of soil pressure with time is illustrated in Figure 9, which has obvious multistage characteristics. The developing process of soil pressure can be divided into: the acceleration and consolidation stage (0-1105 s), the first-step excavation stage (1105-2080 s), the second-step excavation stage (2290-3250 s), the third-step excavation stage (3504-4290 s), and the failure stage (4290-5156 s). Prior to excavation operation, it took 12 minutes for acceleration to reach a gravitational acceleration of 80 g, and 5 minutes for consolidation in such a condition. The value of soil pressure monotonically increased, and tended to be stable after consolidation.
During the first-step excavation stage, the sensor readings from T1 and T2 had an obvious variation, mostly because of the excavation starting from slope foot. The soil pressures at T3 and T7 showed a slow decreasing trend with time, while the rest had no significant change. As observed, the soil pressure at T1 decreased rapidly during excavation due to the reduction of upper loads. The soil pressure at T2, meanwhile, increased firstly and then decreased as a result of stress concentration phenomenon induced by the increase of local slope grade.
During the second-step excavation stage, the responses of T1, T2, T3 and T7 sensors were great. As the excavated soils cumulated above the T1 sensor, the measured soil pressure accordingly showed a slow rising trend. The soil pressure at T2 showed a trend of slow decreasing followed by a sharp decrease. This is attributed to the triangular soil distribution with thin top and thick bottom. The excavation at slope foot has little effect on the pressure distribution until it proceeds to be right above the T2 sensor, which causes a sharp decrease in soil pressure. Moreover, the excavation also affects the horizontal soil pressure since the soil pressures at T3 and T7 both gradually decreased with the excavation operation going on. In the condition of excavation, the confining pressure at T3 and T7 was greatly affected by the unloading effect, while that at T4 and T8 was not. This difference suggests that the pressure redistribution has very limited effect on the position of two sensors.
During the third-step excavation stage, the soil pressures at T2, T3, and T7 were mostly affected. The soil pressure at T2 continued to lower values and the decrease was more significant. It is because the T2 sensor was below the excavation area in the last excavation step. However, the soil pressures at T3 and T7 also decreased, indicating that the effect of unloading spread to the plane at this depth. Considering that these two sensors were installed inside the slope body, the decrease in soil pressure represents an aggravation of global deformation in this period.
The whole process of excavation was finished at 4190 s, and then slope failure took place at 4290 s. The soil pressure at T3 sharply decreased by half. Combined with our laboratory experiment, the results from unloading stress path tests showed that, the soil sample under the same confining pressure failed when the pressure was unloaded to about 0.45-0.56 of the initial. It agrees with the variation of soil pressure at T3. In this case, the soil located around the T3 sensor has broken, which means that the formed sliding surface is across or near this position. At the same time, a steady increase in soil pressure at T2 was observed, because the internal shear zone of the soil forms penetration and the first collapse which leads to the accumulation of the sliding soil around the T2 sensor. The soil pressure at T3 and T7 also decreased during the process of soil breaking and sliding. The second sliding, generated from the first sliding mass, occurred around 4755 s. Therefore, the soil pressures at T1 and T2 further changed, while the rest only had a weak change.
The whole process, from the completion of excavation at 4190 s to the occurrence of overall failure at 5156 s, is a gradual failure process. Not only does the soil pressure at each position have different changes, but also the soil deformation experiences different stages. The evolution of deformation field will be analyzed in detail in the following section.
3.3 Displacement field analysis
3.3.1 Analysis of displacement vectors
As mentioned above, the PIV particle imaging observation system was used to extract the displacement image of the slope throughout the test. By comparing the displacement variation, the displacement vector diagram at each excavation stage was obtained (Figure 10). Before excavation, the deformation of slope body is mainly presented as vertical displacement. With the proceeding of slope excavation, it is observed that the variation in slope position vector gets larger and the affected range of displacement vector increases accordingly. For these three excavation stages, the position where the magnitude and direction of displacement vector has the most significant changes is slope foot, indicating that the unloading effect mainly induces the displacement increment of slope body in horizontal direction. Meanwhile, the influence of excavation unloading on the horizontal displacement vector component becomes less from the slope surface to the inner. The direction of displacement vectors in the slope is observed to be more vertical and the magnitude of them shows a decreasing trend from the top to the slope base. This leads to the fact that the distribution of displacement vector shows an obvious arc-shape.
3.3.2 Analysis of the slope deformation
Figure 11 illustrates the isoline map of displacement obtained at different time point after excavation. In this figure, H-disp and V-disp represent the horizontal and vertical displacement, respectively. The cumulative value corresponding to each excavation step is shown.
As observed, both H-disp and V-disp varied with the deepening of excavation. The distribution characteristics of the isoline map experienced three stages. In the first excavation stage, the isolines are roughly parallel after the completion of excavation (Figure 11a and b), indicating that the displacement is linearly distributed without obvious local deformation. Thus, the linear deformation stage can be regarded for this period. With the excavation step increasing, the deformation value of slope induced by unloading gradually increased. When developing to the second excavation, it can be observed that the displacement isolines is no longer nearly parallel but close to the slope surface (Figure 11c and d). In the third excavation stage, the slope is at the stage of strain localization. The density of the displacement isolines near the slope surface increases, and gradually decreases into the inner of slope body, presenting a local regional characteristic (Figure 11e and f). Moreover, there are two local isolines concentrated at the top of the slope, which is exactly the location of the cracks that occurred. Both in the horizontal and vertical displacement isoline maps, the local concentration characteristics of the cracks exist near the slope surface, indicating that their formation and propagation are the result of both tension and shear. While those far from slope surface is only shown in the horizontal isoline map, which indicates that the cracks are mainly caused by tension.
3.3.3 Analysis of the slope deformation zoning
To determine the final influenced area after the three steps of excavation, a series of typical timing was selected for analysis, including after the first excavation (2290 s), after the second excavation (3504 s), after the third excavation (4335 s), and after the sliding (5140 s). The results of displacement distribution at the height of 9.49 cm, 15.0 cm, 23.4 cm and 32.1 cm are plotted according to the time point, as shown in Figure 12.
It can be found in Figure 12 that there is always a turning point in the displacement curve. The closer to the slope surface, the greater the displacement is. With the increase of excavation depth and scale, the position of the turning point is constantly approaching the slope body inside due to the uneven deformation of slope body, which means that the influence of excavation unloading extends to the inner. Thus, a boundary where the influence of excavation may reach can be defined according to the connecting line of the turning points at each height, which divides the whole area into two parts: influence zone for the left (Ⅰ part) and uninfluenced zone for the right (Ⅱ part). The boundary line is generated by the deformation of excavation effect. The boundary caused by deformation at this point is superimposed on the slope position grid graph. The influenced zone (Ⅰ part) during the localization deformation stage, can be further split into three parts. The part i is made up of a flat part and it exists the maximum displacement, but has a relative low gradient. And the part iii consists of the area with a moderate gradient and close to the surface of influence boundary. So the final area concentrates on the area between part i and part ii, which presents a largest displacement gradient. Apart from part i, distributing on the sliding area, all displacement curves exhibit a similar characteristic on different levels. Due to the higher gradient in part ii, the localized deformation concentration is observed, referring to horizontal displacement. On the basis of each turning points, the influence boundaries are lined and presented in Figre10. The sliding zone experience two parts, which can be observed that the lower zone is in the part ii and the upper part is in the part i, which shows that the formation mechanisms of sliding surface are in different. And further analysis of the different was conducted in the failure process.
In view of the deformation and the stress field variation, further subdivision can be made, as shown in Figure 13(b). The sliding zone is in the leading edge of the influence zone, that is from the sliding surface to the slope body. Within this range, a global sliding failure occurs, which is mainly characterized by horizontal displacement, followed by vertical displacement. The influence zone covers from the sliding surface to the influence boundary, where large soil deformation is observed but no significant sliding failure in this range. However, some cracks are distributed on the slope surface due to the unloading effect and larger deformation. Under the action of unloading, the slope produces different degree of horizontal displacement increment. The soil structure remains in good condition in the influenced zone and hence there is no large deformation and cracks to be found.
3.3.4 Analysis of evolution process of slope body
Based on the morphological characteristics of centrifugal model after failure, each characteristic point is measured to analyze the development process. As shown in Figure 14, the dotted and solid arrows indicate tensile failure and shear failure respectively. Both of sliding surfaces are the result of the interaction of tensile failure and shear failure, specifically presented as the tensile failure concentrated on the upper part and the shear failure concentrated on the lower part. After excavation, the first failure (i.e., deeper sliding) results in stress concentration at the slope foot and shear failure of soil. Under the lateral plane condition, the shear action of the soil at slope foot leads to the tensile action of the soil in the upper layer of the sliding surface, resulting in the observed tensile failure. For the deeper sliding, it takes a total of 4.5 s from formation to penetration; by comparison, the upper sliding has been in the plastic failure state in the early stage, in which case its penetration is relatively fast (in 1.0 s). Besides, two fissures at the slope top are different in location, extension depth, opening degree and cause of formation. The left one is formed by a long time of period, with deep extension and wide opening because of the combined action of tension and shear; while the right generated by the tensile action has a short forming time, showing short extension depth and small opening.
To further analyze the evolution process of slope deformation and the formation of shear zone, 3 pairs of corresponding measuring points (i.e., located on both sides of the sliding surface) are chosen. The change of horizontal and vertical displacement between the two measuring points with time is shown in Figure 15. As observed, each curve experiences a critical point, after which the horizontal and vertical displacement between the two measuring points gradually increases. Considering the increase of relative displacement, the critical point can be regarded as the beginning of shear failure. By comparing the time corresponding to critical point, it is found that the critical point on the I and II curves appears the earliest, around 37s, followed by III and IV curves, and V and VI curves. This explains that the development of shear zone is from the bottom to the top.
The evolution process of slope deformation can be summarized as following. The stress field of slope changes after excavation, resulting in the shear failure at the slope foot and the tensile failure at the slope top due to the stress redistribution. The overall deformation rate is relatively uniform in this period (between 0 s to 31 s) as the horizontal and vertical displacement between the two measuring points keep a uniform growth trend. With the further development of slope deformation, new tensile cracks appear at the slope top because the shear zone extends here, meanwhile, the existing ones also develop to the interior of slope body. When the shear zone meets the tensile crack near the front of the excavation face, the slope deformation increases sharply. In this case, the landslide forms and the crack at the slope top expands rapidly under the influence of overall deformation.
3.3.5 Analysis of the cause of the cracks at slope top
The crack type is analyzed based on the point-point displacement on both sides of crack. For tensile crack, the points displacement changes greatly in perpendicular direction, resulting in obvious variation in horizon and few in vertical displacement, which is opposite to the shear crack. In Figure 16, two main cracks are distributed on the slope top and the displacement changes at different positions of the crack. The first crack close to the slope side is 1 cm between the two points, and the second crack is 0.8 cm.
With respect to the first crack, as the excavation proceeds, the variation of horizontal displacement is much larger than that of vertical displacement (Figure 16a, b and c). It indicates that the crack is generated by tensile action at the beginning. However, further excavation leads to the fact that the crack is located in the influence zone and in the plastic zone. Shear stress therefore acts on the soil around crack due to the movement of sliding body, and the vertical displacement increases as a result. At the same time, a higher shear zone was formed on the side slope's arm-chair back wall. When the shear band is interpenetration, another slide will be formed. It shows that the loess landslide is a kind of backward landslide development process. The formation and propagation of the first crack are caused by the joint action of tension and shear. With respect to the second crack, the horizontal displacement between the two measuring points is significantly higher than the vertical displacement (Figure 16d and e). It can be inferred that the formation of crack is ascribed from the tensile stress caused by the deformation of soil mass in the middle and upper part of slope. Thus, the second crack can be classified as tensile crack.
3.3.6 Failure morphology analysis of slope.
To analyze the displacement field distribution characteristic after failure, three cross sections with respect to different height were selected, as shown in Figure 17. It can be observed that all displacement curves have a very similar developing trend. The displacement curves tend to be straight when far away from the slope surface and the displacement values of all curves are close to 0 cm. The horizontal and vertical deformation in the lower section is generally greater than that in the upper section, because the large uneven deformation is mainly concentrated in the middle of the slope body. Several typical points can be found based on the variation of curve slope. The curve at the point Ⅰ left shows a small variation of the displacement, but the right shows a large variation, which means that the point is located on the sliding surface. In addition, the curve at the point Ⅳ right keeps a little change and the horizontal displacement is about 0.3 cm, but the left not. The curve at point Ⅱ has two turning points, indicating that the slope at both sides of the turning point has a large displacement change. In the actual test results, the soil slides back and forth twice. In the slope body, the large uneven horizontal deformation is most concentrated in the slope body middle part.