3.1 Evolution process of landslide in physical simulation test
In the whole process of physical model test, the three evolution stages of landslide are simulated by increasing the slope angle: Slow creep, Creep-slip, Accelerated creep and Rapid deformation stage (Xu et al., 2004).
From the macroscopic deformation and failure signs in the physical model experiment, it can be seen that when the landslide angle is 0 to 10°, the soil begins to be compacted gradually, the slope is relatively stable, and there are fine cracks in the front edge of the slope, which belongs to the stage of slow creep; When the landslide angle is from 10° to 20°, the fine cracks on the slope surface gradually expand and extend in the horizontal and longitudinal directions. At this time, the landslide is in the stage of uniform creep; When the landslide angle is from 20° to the critical angle (38°), the slope surface of the landslide forms a tension zone, obvious tension cracks appear behind the slope, and shear cracks appear on both sides of the middle and front of the slope, but the fracture system around the landslide has not been trapped, that is, the tension cracks on the top of the slope have not penetrated the whole sliding surface in the water square direction and have not reached the critical sliding stage. Therefore, it can be seen that the landslide is in the accelerated creep stage. When the landslide angle reaches the critical angle, the tension crack at the pipeline passes through the sliding surface to form a complete shear failure surface. It can be seen that the pipeline has the effect of preventing sliding on the slope, and then the overall instability failure is manifested as push type landslide (Xu et al., 2008). The landslide is a stage of rapid deformation, and then the soil stress is released rapidly, the slope tends to be stable as a whole, and no new landslide surface appears. During the whole experiment, the angle is raised slowly, and when reaching a certain stage, it is placed continuously to observe the landslide phenomenon, which can simulate the landslide disaster under engineering disturbance. At the same time, about 38 ° can be used as the critical angle of overall instability and failure of physical model test slope under no rain condition as the experimental reference.
3.2 Discussion of the changes in strain
To study the strain variation of the pipeline, the variations at the same landslide dip angle and different measuring points and the variations at the same measuring point and different landslide dip angles are evaluated. The same dip angle and different measuring points are used to study the bending law of different positions on the pipeline: moreover, the purpose of the same measuring point and different landslide dip angles is to study the bending of the pipeline with the change of the landslide dip angle.
(1) Same dip angle, different measuring points
The strain change processes in the direction of 3 o’clock (measuring point 17), 9 o’clock (measuring point 19), and noon (measuring point 18) on the section circumference at the centre of the pipeline are illustrated in Fig. 6: among them, the measuring points in the direction of 3 o’clock are those facing the motion direction of the landslide. It is found that the measuring points in the direction of 3 o’clock produce compressive strain, and the strain decreases. The maximum strain is 248. Meanwhile, the measuring points in the direction of noon monitor the strain just above the pipeline cross-section. As can be seen, compressive strain continues to occur at this point, indicating that the point does not experience the pressure facing the direction of motion of the landslide, thus experiencing a lower strain value with a maximum value of 100. Its trend is similar to that of the strain variation at the measuring points in the direction of 3 o’clock; the measuring point in the 9-o’clock-direction is facing backwards relative to the impact of landslides. The strain generated at this point is tensile, the pipeline generates a maximum strain value of 750, which is much larger than that generated at the point producing a compressive strain. It can also be seen from the figure that the strain changes in the three directions of 3 o’clock (measuring points 14 and 20), 9 o’clock (measuring points 16 and 22), and noon (measuring points 15 and 21) at the bilateral sides of the pipeline are similar to those in the section at the centre of the pipeline. Tensile strain is shown to occur in the left section of the pipeline in the direction of 9 o’clock. Due to the different stress conditions at different locations in the pipeline during the landslide, the law of tensile strain in the direction of 9 o’clock on the left-hand section of the pipeline first increases, and then decreases. This kind of spring-back phenomenon is because the section on the left-hand side of the pipeline is at the boundary of the slide. The slide boundary has a definite restriction effect on the measuring points of the left-hand section of the pipeline, which leads to the decrease of the strain thereat.
(2) Different dip angles at the same measuring point
The overall changes in strain can be divided into three stages, namely, slow-bending stage, constant-speed bending stage, and accelerated-bending stage. When the pipeline is in the lifting stage, the pipeline just begins to bear the sliding force generated by the soil, and the strain produced by the pipeline changes visibly, and the rate of change of strain is fast. The absolute value of strain on the pipeline changes more than in other three stages. In the constant-speed bending stage, the pipeline will still undergo a change in strain due to the increase of the dip angle, and the change is greater than that in the slow-bending stage. When the deformation of the pipeline reaches a certain extent, the pipeline will enter the accelerated-bending stage. At this time, the strain of the pipeline begins to increase sharply, and the pipeline may even buckle. The changes of the three stages are shown in Fig. 6. The strain changes of different dip angles of the pipeline at the same measuring point are ascertained here. As shown in Fig. 6, the strain variation of the pipeline under different dip angles is analysed by taking the measuring point 19 (subject to the largest impact force of the landslide) as an example. In the process of a landslide, as the dip angle is increased from 0° to 10°, the strain in the pipeline changes abruptly, and the maximum change therein is 550. After the dip angle of the landslide reaches 10°. The strain of the pipeline increases slowly at a rate of 1.4 × 10− 4 microstrain per second, when the dip angle of the landslide rises to 20°. The strain increases rapidly to 568 microstrain again and then springs back to a certain extent. After the dip angle of the landslide reaches 20°, the strain in the pipeline still increases slowly at the rate of 3.6 × 10− 4 microstrain per second. This is about twice the rate of increase when the landslide angle is 10°. When the dip angle rises to 30, the pipeline strain increases rapidly to 581 microstrain. After the dip angle of the landslide reaches 30°, pipeline strain increases slowly at a rate of 38.8 × 10− 4 per second. Compared with the rate of increase when the dip angle is 20°, the rate of increase at 30° is increased to about 27 times that at a landslide angle of 10°. When the slope angle reaches 38°, a landslide occurs, and the pipeline strain reaches 692. Then, the strain of the pipeline increases slowly, and the rate of increase reaches 108 × 10− 4 microstrain per second. When the dip angle of the landslide is 38°, the rate of slow increase is the greatest in the four stages, which is about 77 times that at a slope of 10°.
To sum up, according to the analysis of the same measuring point and different dip angles of the pipeline, it is found that the overall change of the pipeline conforms to the proposed staged changes. When raising the slope, the pipeline strain will increase rapidly, but because of its innate characteristics, the pipeline may spring back. However, when the dip angle of the landslide reaches the required dip angle, the pipeline will undergo a slow and stable strain increase due to the downward motion of the soil. In general, with the increase of the dip angle, the rate of slow increase of pipeline strain will also increase.
3.3 Discussion of the changes in stress
Like strain, the stress variations on a pipeline in a landslide are analysed. Herein, the stress variation is investigated from the same landslide angle, different measuring points, and the same measuring point, but at different landslide angles.
(1) Same dip angle, different measuring points
The pipeline is analysed using data from different measuring points with the same dip angle; the pipeline stress measuring points are the left-hand cross-section (measuring points 2 and 3), the central cross-section (measuring points 4 and 5), and the right-hand cross-section (measuring points 6 and 7). Among them, measuring points 2, 4, and 6 are those facing the direction of motion of the landslide, and measuring points 3, 5, and 7 face the opposite way. It can be seen from the figure that the maximum stress variation of the measuring points on the left-hand cross-section increases to 0.4 kPa, that on the right is 0.35 kPa, and that on the cross-section at the centre cross-section reaches 0.43 kPa. The stress variation of the measuring points at the bilateral sides of the pipeline is less than that of the measuring points on the cross-section at the centre of the pipeline. During landslide impact hazards, the cross-section at the centre of the pipeline is subject to the greatest impact load.
According to the analysis of the measuring points at different positions of the pipeline in three different stages, when the pipeline is in the slow-bending stage, similar rules are presented by the stress changes around the cross-section position. The stress change of the measuring point at the left-hand cross-section position is greatest. The maximum stress increases to 0.2 kPa, followed by that at the right (0.14 kPa), and the stress change at the measuring point at the centre cross-section position is the smallest, the maximum stress increases to 0.13 kPa thereat. The reason for this may be that the measuring points at the sides of the pipeline cross-section are located at the sides of the sliding mass. More auxiliary forces are generated by the baffles at the bilateral sides of the slideway, resulting in an increase in the force on the measuring points at the sides of the cross-section; when the pipeline is in the constant-speeding bending stage, the pressure increment of all the measuring points increases rapidly, the stress of the left-hand and right-hand sides reaches 0.36 kPa and 0.28 kPa, respectively. The stress on the cross-section at the centre reaches 0.30 kPa. The pressure increment of the measuring point at the left-hand cross-section remains greater than that at the centre, however, the measuring points at the sides of the cross-section experience different degrees of rebound, in which the stress change at the measuring point at the left-hand cross-section is the greatest. The rebound phenomenon is the clearest and when the landslide occurs, the maximum stress on the cross-section at the centre of the pipeline reaches 0.43 kPa, and the maximum stress on the left-hand and right-hand sides of the pipeline is 0.4 kPa and 0.35 kPa, respectively. The stress change at the measuring points at the sides of the pipeline cross-section is less than that at the centre of the pipeline cross-section.
Due to the irregularity of the landslide impact hazard, the stress change at the measuring point on the left exhibits quite particular behaviour: stress spring-back occurs and a certain degree of positive growth is presented therein. At this time, the measuring point on the left side of the cross-section is subject to a large reverse force. The reason for this phenomenon may be that all the soil around the pipeline at the measuring point has slipped, and the force acting on the pipe has almost disappeared. Due to the bending deformation of the pipeline, the measuring point on the left-hand cross-section undergoes a reverse displacement. Therefore, the cross-sectional measuring point is subject to a reversal of force, resulting in large-scale stress spring-back.
In summary, for the same dip angle and different measuring points, when the landslide hazard occurs, the stress on the cross-section at the centre of the pipeline is the largest, and the stress at the sides is lower. Due to the irregularity of the landslide, there is a certain degree of stress spring-back at the measuring point of the pipeline at the boundary of the sliding mass. If the soil around the measuring point of the pipeline slides away, then the pipeline is not stressed by the soil.
(2) Same measuring point, different dip angles
Under different dip angles of landslides, a similar trend is shown in the stress at each measuring point, therefore, the stress at the same measuring point at different dip angles is analysed by taking measuring point 4 as the object. When the slope angle reaches 10°, the stress on the pipeline increases at a rate of 38.1 × 10− 6 kPa/s, and the stress reaches 0.12 kPa. Then the stress on the pipeline increases at about 2.5 × 10− 6 kPa/s. With the further increase of the slope angle, the stress change of the pipeline increases; when the dip angle of the landslide reaches 20°, the stress changes at 28.5× 10− 6 kPa/s. When the slope angle reaches 30°, the stress on the pipeline increases at 9.3× 10− 6 kPa/s. When the slope reaches the angle posing a landslide hazard, the maximum rate of change of stress is about 26.9× 10− 6 kPa/s. Although the rate of change of stress is not the most rapid, a state of rapid linear increase is presented by the stress change at the measuring point, and the maximum stress reaches 4.3 kPa.
In summary, for the same measuring point, stress increases with the increasing dip angle. When the pipeline is in the slow-bending stage, a slow increase in stress occurs; when the pipeline is in the constant-speed bending stage, the stress increases rapidly. When the pipeline is in the accelerated-bending stage, the rate of increase of stress is accelerated, and a linear rapid increase in stress occurs until the stress on the pipeline reaches its maximum.