3.2.1. Effect of Rockfall Mass
In order to study the effect of rockfall mass on the dynamic response of the shed tunnel, the rockfall impact velocity and direction are fixed to be 20 m/s and perpendicular to the buffer layer. The rockfall radius is assumed to be 0.2 m (five impacts), 0.25 m (five impacts) and 0.3 m (four impacts, because the model is destroyed at the fifth impact, and the calculation cannot converge), and, accordingly, the rockfall mass is 70.3 kg, 137.31 kg and 237.26 kg, respectively. The interval between two neighboring impacts is 0.05 s.
- (1)
The impact force on the buffer layer
The following results can be obtained from the calculation results shown in
Figure 5 and
Table 4. First of all, after each impact, the pattern of the time–history curve of the impact force is basically the same. The impact force first increases to the maximum and then decreases to 0 with time going on. Second, when the rockfall mass is fixed, with an increasing impact number, the peak impact force increases rapidly after the second impact and then tends to be relatively stable. When the rockfall is 70.3 kg, the peak impact force increases from 221.32 kN of the first impact to 259.12 kN of the second impact, whose increase extent is 17.08%. And then the increase extent of subsequent impacts is not as high as that of the second impact. The peak impact force reaches the maximum 298.77 kN in the fifth impact, which increased by 15.3% compared with the second impact. When the rockfall mass is 137.31 kg, the peak impact force rapidly increases from 311.36 kN of the first impact to 445.18 kN of the second impact, whose increase extent is 42.98%. The peak impact force reaches the maximum 484.25 kN at the fifth impact, which increases by 8.78% compared with the second impact. When the rockfall mass is 237.26 kg, the peak impact force rapidly increases from 546.89 kN of the first impact to 622.54 kN of the second impact, whose increase extent is 13.83%. The peak impact force reaches the maximum 677.58 kN at the third impact, which increases by 8.84% compared with the second impact. This is mainly because the buffer layer is not compressed at the first impact, and its buffer performance is the best. With increasing the impact number, its buffer capacity gradually weakens, so the peak impact force will increase at the first several times. However, with the impact continuing, the buffer layer can hardly be compressed anymore, so its buffer performance tends to be stable, resulting in the peak impact force also tending to be stable. At the same time, it can also be seen that the greater the rockfall mass, the lower the impact number required to reach the maximum. Finally, the larger the rockfall mass, the greater the peak impact force. Here, we explain that the number of repeated impacts of rockfall is set to five, because for the case of
m = 237.26 kg, the shed tunnel is destroyed after five impacts, and, therefore, the number of repeated rockfall impacts is set to 5.
- (2)
The impact depth in the buffer layer
The calculation results of the time–history curve of the impact depth in the buffer layer with different rockfall masses are shown in
Figure 6, from which the following conclusions can be obtained. First of all, after each impact, the buffer layer will have a certain degree of rebound, because it is an elastic–plastic material, and the elastic deformation will recover after the impact force is unloaded. Second, when the rockfall mass is fixed, with an increasing impact number, the maximum impact depth gradually increases, but its increase extent is less than that of the first impact. When the rockfall mass is 70.3 kg, the impact depth of the first impact is 0.099 m, and that of the second impact is 0.035 m, which is only 35.35% of the first one. When the rockfall mass is 137.31 kg, the impact depth of the first impact is 0.115 m, and that of the second impact is 0.039 m, which is only 33.91% of the first one. When the rockfall mass is 237.26 kg, the impact depth of the first impact is 0.119 m, and that of the second impact is 0.185 m, which is only 55.46% of the first one. This is mainly because the soil is compacted after the first impact, resulting in the impact depth of the first impact being much greater than that of the subsequent impacts. Meanwhile, when the rockfall mass is small (70.3 kg), the rebound ratio of each impact is large. However, when the rockfall mass is large (237.26 kg), the rebound ratio is small. Finally, the greater the rockfall mass, the greater the impact depth of the buffer layer.
- (3)
The maximum plastic strain of the rebar
The calculation results of the time–history curve of the maximum plastic strain of the rebar with different rockfall masses are shown in
Figure 7, from which the following conclusions can be obtained. First of all, the maximum plastic strain of the rebar shows a monotonically increasing trend on the whole. Second, the plastic strain of the rebar increases rapidly first and then tends to be stable. This is because the deformation in the reinforced concrete plate will drive the rebar to produce plastic strain. When the reinforced concrete plate reaches balance, the rebar no longer generates more plastic strain and achieves stability. Third, the greater the rockfall mass is, the faster the maximum plastic strain of the rebar increases. The maximum plastic strain of the rebar is sensitive to the rockfall mass, and the plastic strain produced by five rockfall impacts of 70.3 kg is less than that produced by one rockfall impact of 237.26 kg. When the rockfall mass is small (70.3 kg), the plastic strain is not generated in the first few impacts, but when it is large (237.26 kg), the plastic strain is generated in the first impact. When the rockfall mass is 237.26 kg, the plastic strain produced by four impacts is 0.0673. When the rockfall mass is 70.3 kg, the plastic strain produced by five impacts is 0.00467, which is only 6.94% of the rockfall mass of 237.26 kg. When the rockfall mass is 137.31 kg, the plastic strain produced by five impacts is 0.0464, which is 68.95% of the rockfall mass of 237.26 kg.
- (4)
The vertical displacement of the shed roof
The calculation results of the vertical displacement of the shed roof with different rockfall masses is shown in
Figure 8, from which the following conclusions can be obtained. First of all, there is a rebound phenomenon in the vertical displacement of the shed roof, which is mainly speculated to be caused by the existence of the rebar. Because concrete is a typical brittle material, no rebound will occur in it in theory, so it is speculated that the existence of the rebar leads to the rebound of the shed roof. To verify this hypothesis, a comparative experiment is designed. The rockfall radius is set to 0.25 m, and, accordingly, its mass is 137.31 kg. The impact velocity is set to 20 m/s, and the impact direction is vertically downward. The time–history curve of the vertical displacement of the shed roof is compared in one model with rebar and the other model without rebar. It can be seen from the calculation result shown in
Figure 9 that when it has the rebar, the shed roof has obvious rebound, while when it has no rebar, the shed roof’s vertical displacement increases monotonically, and there is no rebound phenomenon. It shows that the rebar has a great influence on the strength and deformation of the reinforced concrete plate. If the shed roof has no rebar, it fails very easily. Second, when the rockfall mass is large (137.31 kg, 237.26 kg), the vertical displacement of the shed roof gradually increases with an increasing impact number. When the rockfall mass is small (70.3 kg), the rebound ratio of the vertical displacement of the shed roof after each impact is large, and the vertical displacement of the shed roof after stability shows very little change compared with the initial state. However, when the rockfall mass is large (237.26 kg), the rebound ratio is small. Finally, upon increasing the rockfall mass, the vertical displacement of the shed roof increases significantly.
- (5)
The maximum axial force of the rebar
The calculation results of the maximum axial force of the rebar with different rockfall masses are shown in
Figure 10, from which the following conclusions can be obtained. First of all, when the rockfall mass is fixed, in the first few impacts, the axial force of the rebar basically shows a trend of increasing from zero to the maximum and then decreasing to zero. However, after several subsequent impacts, the axial force of the rebar will not recover to zero, because the plastic deformation of the rebar cannot recover, so a certain axial force remains. Compared with the upper and lower rebars, the axial force of the lower rebars is obviously greater than that of the upper rebars. Because the lower rebars bear greater tensile stress, it is important to strengthen the reinforcement of the lower part of the reinforced concrete plate. What is more, comparing the calculation results with three kinds of rockfall mass, it can be seen that the greater the rockfall mass is, the greater the variation in the rebar axial force. This is because the rockfall impact force increases with the rockfall mass, and, accordingly, the axial force of the rebar also increases.
- (6)
The plastic strain of the shed tunnel
The calculation results of the plastic strain contour of the shed tunnel with different rockfall masses are shown in
Figure 11, from which the following conclusions can be obtained. After many impacts, large plastic deformation occurs in the shed tunnel, which mainly concentrates in and around the center of the shed tunnel. The greater the rockfall mass, the greater the plastic zone and the greater the damage caused by the rockfall to the shed tunnel. The plastic strain of the shed tunnel is sensitive to the rockfall mass, and the damage range of the shed tunnel produced by five impacts of the rockfall with 70.3 kg is far less than that produced by four impacts of rockfall at 237.26 kg. The damage of the shed tunnel begins from the bottom of the span, and cracks gradually propagate towards the upper and both sides of the reinforced concrete plate.
3.2.2. Effect of the Rockfall Impact Velocity
- (1)
The impact force on the buffer layer
The calculation results of the time–history curve of the impact force on the buffer layer with different rockfall impact velocities and its peak are shown in
Figure 12 and
Table 5, respectively. The following conclusions can be obtained. First of all, when the impact velocity is fixed, the peak impact force increases rapidly after the second impact and then tends to be stable with an increasing impact number. When the rockfall impact velocity is 15 m/s, the peak impact force increases from 266.52 kN of the first impact to 326.66 kN of the second impact, whose increase extent is 22.56%. And then the increase extent of subsequent impacts is not as high as that of the second impact. The peak impact force reaches the maximum 363.20 kN in the fifth impact, which increases by 11.19% compared with the second impact. When the rockfall impact velocity is 20 m/s, the peak impact force rapidly increases from 311.36 kN of the first impact to 445.18 kN of the second impact, whose increase extent is 42.98%. The peak impact force reaches the maximum 484.25 kN at the fifth impact, which increases by 8.78% compared with the second impact. When the rockfall impact velocity is 25 m/s, the peak impact force rapidly increases from 421.33 kN of the first impact to 516.98 kN of the second impact, whose increase extent is 22.70%. The peak impact force reaches the maximum 569.11 kN at the fourth impact, which increases by 10.08% compared with the second impact. It indicates that the greater the rockfall impact velocity, the lower the impact number required to reach the peak impact force. What is more, comparing the time–history curves of the impact force with these three velocities, it can be seen that the lager the rockfall mass is, the greater the peak impact force is.
- (2)
The impact depth in the buffer layer
The calculation results of the time–history curve of the impact depth in the buffer layer with different rockfall impact velocities are shown in
Figure 13, from which the following conclusions can be obtained. First of all, when the rockfall impact velocity is fixed, with an increasing impact number, the maximum impact depth gradually increases, but its increase extent is less than that of the first impact. When the rockfall impact velocity is 15 m/s, the impact depth of the first impact is 0.095 m, and that of the second impact is 0.027 m, which is only 28.42% of the first one. When the rockfall impact velocity is 20 m/s, the impact depth of the first impact is 0.115 m, and that of the second impact is 0.039 m, which is only 33.91% of the first one. When the rockfall impact velocity is 25 m/s, the impact depth of the first impact is 0.140 m, and that of the second impact is 0.056 m, which is only 40% of the first one. However, it can be seen that the increase extent increases much more after the fourth impact. This is mainly because the shed tunnel is seriously destroyed, which leads to significant displacement of the buffer layer. Meanwhile, when the rockfall impact velocity is small (15 m/s), the rebound ratio of each impact is large. However, when the rockfall impact velocity is large (25 m/s), the rebound ratio is small. Finally, the greater the rockfall impact velocity is, the greater the impact depth of the buffer layer is.
- (3)
The maximum plastic strain of the rebar
The calculation results of the time–history curve of the maximum plastic strain of the rebar with different rockfall impact velocities are shown in
Figure 14, from which the following conclusions can be obtained. First of all, the maximum plastic strain of the rebar shows a monotonically increasing trend on the whole. Second, the plastic strain of the rebar increases rapidly first and then tends to be stable. Second, with increasing the rockfall impact velocity, the maximum plastic strain of the rebar increases, which is sensitive to the rockfall impact velocity, and the plastic strain produced by five rockfall impacts of 15 m/s is less than that produced by one rockfall impact of 25 m/s. When the rockfall impact velocity is small (15 m/s), the plastic strain is not generated in the first few impacts, but when the rockfall impact velocity is large (25 m/s), the plastic strain is generated at the second impact. When the rockfall impact velocity is 25 m/s, the plastic strain produced by five impacts is 0.058. When the rockfall impact velocity is 15 m/s, the plastic strain produced by five impacts is 0.00556, which is only 9.59% of the rockfall impact velocity at 25 m/s. When the rockfall impact velocity is 20 m/s, the plastic strain produced by five impacts is 0.0464, which is 79.93% of the rockfall impact velocity at 25 m/s.
- (4)
The vertical displacement of the shed roof
The calculation results of the vertical displacement of the shed roof with different rockfall impact velocities are shown in
Figure 15, from which the following conclusions can be obtained. First of all, when the rockfall impact velocity is fixed, the vertical displacement of the shed roof gradually increases with an increasing impact number, and it has the rebound phenomenon. When the rockfall impact velocity is small, the displacement rebound is greater. When the rockfall impact velocity is large, the displacement rebound is reduced. Meanwhile, when increasing the rockfall impact velocity, the vertical displacement of the shed roof increases significantly.
- (5)
The maximum axial force of the rebar
The calculation results of the maximum axial force of the rebar with different rockfall impact velocities are shown in
Figure 16, from which the following conclusions can be obtained. First of all, when the rockfall impact velocity is fixed, in the first few impacts, the axial force of the rebar basically shows a trend of increasing from zero to the maximum and then decreasing to zero. However, after several subsequent impacts, the axial force of the rebar will not recover to zero, because of the plastic deformation of the rebar, so a certain axial force remains. Comparing with the upper and lower rebars, the axial force of the lower rebars is obviously greater than that of the upper rebars, which indicates that the lower rebars bear greater tensile stress. What is more, comparing the calculation results with three rockfall impact velocities, it can be seen that the greater the rockfall impact velocity is, the greater the variation in the rebar axial force is.
- (6)
The plastic strain of the shed tunnel
The calculation results of the plastic strain contour of the shed tunnel with different rockfall impact velocities are shown in
Figure 17, from which the following conclusions can be obtained. After many impacts, large plastic deformation occurs in the shed tunnel, which mainly concentrates in and around the center of the shed tunnel. The greater the rockfall impact velocity is, the greater the plastic zone is and the greater the damage caused by the rockfall to the shed tunnel is. The plastic strain of the shed tunnel is sensitive to the rockfall impact velocity, and the damage range of the shed tunnel produced by five impacts of the rockfall with 15 m/s is far less than that produced by five impacts of rockfall at 25 m/s. When the rockfall impact velocity is 25 m/s, the shed tunnel almost completely fails after five impacts.
3.2.3. Effect of the Rockfall Shape
Assume the rockfall mass is all 137.31 kg; accordingly, three kinds of rockfall shapes are spheres with a radius of 0.25 m, cuboid 1 with 0.403 m × 0.403 m × 0.403 m and cuboid 2 with 0.570 m × 0.570 m × 0.201 m, respectively. The contact faces of the latter two rockfalls are 0.403 m × 0.403 m and 0.570 m × 0.570 m, respectively. The other calculation parameters are shown in
Table 3.
- (1)
The impact force on the buffer layer
The following results can be obtained from the calculation results shown in
Figure 18 and
Table 6. First of all, for the spherical rockfall, with an increasing impact number, the peak impact force increases rapidly from 311.36 kN of the first impact to 445.18 kN of the second impact, with an increase of 42.98%. And the growth rate of the subsequent impacts is lower than that of the second one. The peak impact force reaches 484.25 kN at the fifth impact, which increases by 8.78% compared with the second impact. For the cuboid rockfall, the peak impact force of the first impact is the largest, but that of the subsequent impacts decreases rapidly. When the bottom surface is 0.403 m × 0.403 m, the impact force generated by the first impact is the largest, reaching 1,180.86 kN, and then it decreases with an increasing impact number. It reaches the minimum of 518.67 kN at the fifth impact, which is only 43.92% of the first one. When the bottom surface is 0.570 m × 0.570 m, the peak impact force produced by the first impact is 1,960.09 kN, which is much greater than the subsequent ones. The peak impact force produced after the second impact reaches the minimum of 1090.65 kN, which is only 55.64% of the first one. Meanwhile, it can also be found that the impact force generated by the cuboid rockfall is much greater than that of the spherical rockfall, and the greater the contact area of the cuboid is, the greater the impact force is.
- (2)
The impact depth in the buffer layer
The calculation results of the time–history curve of the impact depth in the buffer layer with different rockfall shapes are shown in
Figure 19, from which the following conclusions can be obtained. First of all, with an increasing impact number, the maximum impact depth gradually increases, but its increase extent is less than that of the first impact. When the rockfall shape is spherical, the impact depth of the first impact is 0.0115 m, and that of the second impact is 0.039 m, which is only 33.91% of the first one. For the cuboid rockfall, when its bottom surface is 0.403 m × 0.403 m, the impact depth generated by the first impact is 0.081 m, and that of the second impact is 0.033 m, which is only 40.74% of the first one. When its bottom surface is 0.570 m × 0.570 m, the impact depth generated by the first impact is 0.069 m, and that of the second impact is 0.026 m, which is only 37.68% of the first one. Meanwhile, the rebound displacement caused by the cuboid rockfall is much greater than that of the spherical one. Finally, the impact depth caused by the cuboid rockfall is less than that of the spherical one. For the cuboid rockfall, the greater the contact area, the lower the impact depth.
- (3)
The maximum plastic strain of the rebar
The calculation results of the time–history curve of the maximum plastic strain of the rebar with different rockfall shapes are shown in
Figure 20, from which the following conclusions can be obtained. First of all, the maximum plastic strain of the rebar shows a monotonically increasing trend on the whole. The plastic strain of the rebar increases rapidly first and then tends to be stable. Second, when the rockfall mass and impact velocity are fixed, the rockfall shape has a significant effect on the maximum plastic strain of the rebar. Particularly, for cuboid rockfall, the greater the contact force, the lower the maximum plastic strain of the rebar. When the rockfall is spherical, the plastic strain produced by five impacts is 0.0464. When the rockfall is cuboid with a bottom surface of 0.403 m × 0.403 m, the plastic strain produced by five impacts is 0.0481, which is 103.66% of the spherical rockfall. When the rockfall is cuboid with a bottom surface of 0.570 m × 0.570 m, the plastic strain produced by five impacts is 0.0294, which is 63.36% of the spherical rockfall.
- (4)
The vertical displacement of the shed roof
The calculation results of the vertical displacement of the shed roof with different rockfall shapes are shown in
Figure 21, from which the following conclusions can be obtained. First of all, it can be seen that with an increasing impact number, the vertical displacement of the shed roof gradually increases. When the rockfall is spherical, the rebound ratio of each impact is large. However, when the rockfall is cuboid, the proportion of rebound is relatively small. Moreover, it can also be seen that when the rockfall is cuboid, the vertical displacement of the shed roof increases faster than that of spherical rockfall. Meanwhile, the greater the contact area, the slower the vertical displacement of the shed roof increases.
- (5)
The maximum axial force of the rebar
The calculation results of the maximum axial force of the rebar with different rockfall shapes are shown in
Figure 22, from which the following conclusions can be obtained. First of all, when the rockfall shape is fixed, the upper and lower layers of the rebars fluctuate in two states of tension and compression. The lower rebar is mainly subjected to tension, while the upper rebar is mainly subjected to compression, which is because the lower rebar bears the tensile stress of the lower part of the shed-tunnel structure. Meanwhile, it can be seen that the rockfall shape has a small effect on the axial force of the rebar.
- (6)
The plastic strain of the shed tunnel
The calculation results of the plastic strain contour of the shed tunnel with different rockfall shapes are shown in
Figure 23, from which the following conclusions can be obtained. After many impacts, large plastic deformation occurs in the shed tunnel, which mainly concentrates in and around the center of the shed tunnel. The plastic strain of the shed tunnel is sensitive to the rockfall shape, and the plastic deformation of the shed tunnel produced by the cuboid rockfall is far less than that produced by the spherical rockfall. For the cuboid rockfall, the less contact area there is, the greater the plastic deformation and damage to the shed tunnel. When the impact number reaches five, the shed tunnel almost completely fails.
3.2.4. Effect of the Rockfall Impact Angle
- (1)
The impact force on the buffer layer
The following results can be obtained from the calculation results shown in
Figure 24 and
Table 7. First of all, with an increasing impact number, the peak impact force increases rapidly from the second impact and then tends to be stable. When the impact angle is 30°, the peak impact force increases from 153.25 kN of the first impact to 339.96 kN of the second one, an increase of 53.40%. It reaches 292.45 kN at the fifth impact, which increases by 24.40% compared with the second one. When the impact angle is 45°, the peak impact force increases from 215.55 kN of the first impact to 333.96 kN of the second one, an increase of 54.93%. It reaches 354.67 kN in the fifth impact, which increases by 6.20% compared with the second one. When the impact angle is 60°, the peak impact force increases by 45.47% from 268.76 kN of the first impact to 390.97 kN in the second impact. The peak impact force reaches 432.65 kN at the fourth impact, which increases by 10.66% compared with the second impact. When the impact angle is 75°, the peak impact force increases from 301.69 kN of the first impact to 409.63 kN of the second impact, an increase of 35.78%. The peak impact force reaches 457.75 kN at the fifth impact, an increase of 11.75% compared with the second one. When the impact angle is 90°, the peak impact force increases from 311.36 kN of the first impact to 445.18 kN of the second one, an increase of 42.98%. The peak impact force reaches 484.25 kN at the fifth impact, which increases by 8.78% compared with the second one. Moreover, it can be seen that the greater the impact angle is, the greater the peak impact force is.
- (2)
The impact depth in the buffer layer
The calculation results of the time–history curve of the impact depth in the buffer layer with different rockfall impact angles are shown in
Figure 25, from which the following conclusions can be obtained. First of all, with an increasing impact number, the maximum impact depth gradually increases, but its increase extent is less than that of the first impact. When the rockfall impact angle is 30°, the impact depth of the first impact is 0.056 m, and that of the second impact is 0.027 m, which is only 48.21% of the first one. When the rockfall impact angle is 45°, the impact depth of the first impact is 0.082 m, and that of the second impact is 0.027 m, which is only 32.93% of the first one. When the rockfall impact angle is 60°, the impact depth of the first impact is 0.084 m, and that of the second impact is 0.044 m, which is only 52.38% of the first one. When the rockfall impact angle is 75°, the impact depth of the first impact is 0.086 m, and that of the second impact is 0.045 m, which is only 52.33% of the first one. When the rockfall impact angle is 90°, the impact depth of the first impact is 0.115 m, and that of the second impact is 0.039 m, which is only 33.91% of the first one. Moreover, it can also be found that the greater the impact angle is, the greater the impact depth of the buffer layer is.
- (3)
The maximum plastic strain of the rebar
The calculation results of the time–history curve of the maximum plastic strain of the rebar with different rockfall impact angle are shown in
Figure 26, from which the following conclusions can be obtained. First of all, the maximum plastic strain of the rebar shows a monotonically increasing trend on the whole. The plastic strain of the rebar increases rapidly first and then tends to be stable. Second, it can also be found that the greater the rockfall impact angle is, the faster the maximum plastic strain of the rebar increases. The maximum plastic strain of the rebar is sensitive to the rockfall impact angle. When the impact angle is small (30°), the plastic strain is nearly not generated, but when it is large (90°), the plastic strain is generated in the first impact. When the rockfall impact angle is 90°, the plastic strain produced by five impacts is 0.06187. When the rockfall impact angle is 30°, the plastic strain produced by five impacts is 0.0001931, which is only 0.31% of the rockfall impact angle of 90°. When the rockfall impact angle is 45°, the plastic strain produced by five impacts is 0.01445, which is 23.36% of the rockfall impact angle of 90°. When the rockfall impact angle is 75°, the plastic strain produced by five impacts is 0.04636, which is 74.93% of the rockfall impact angle of 90°.
- (4)
The vertical displacement of the shed roof
The calculation results of the vertical displacement of the shed roof with different rockfall impact angles are shown in
Figure 27, from which the following conclusions can be obtained. First of all, it can be seen that with an increasing impact number, the vertical displacement of the shed roof gradually increases. When the rockfall impact angle is small, the rebound ratio of each impact is large. However, when the rockfall impact angle is large, the proportion of rebound is relatively small. Moreover, it can also be seen that the greater the impact angle is, the faster the vertical displacement of the shed roof increases.
- (5)
The maximum axial force of the rebar
The calculation results of the maximum axial force of the rebar with different rockfall impact angles are shown in
Figure 28, from which the following conclusions can be obtained. First of all, when the rockfall impact angle is fixed, the upper and lower layers of the rebars fluctuate in two states of tension and compression. The lower rebar is mainly subjected to tension, while the upper rebar is mainly subjected to compression, which is because the lower rebar bears the tensile stress of the lower part of the shed-tunnel structure. Meanwhile, it can be seen that the impact angle has a small effect on the axial force of the rebar.
- (6)
The plastic strain of the shed tunnel
The calculation results of the plastic strain contour of the shed tunnel with different rockfall impact angles are shown in
Figure 29, from which the following conclusions can be obtained. After many impacts, large plastic deformation occurs in the shed tunnel, which mainly concentrates in and around the center of the shed tunnel. The greater the rockfall impact angle is, the greater the plastic zone is and the greater the damage caused by the rockfall to the shed tunnel is. The maximum plastic strain of the shed tunnel is sensitive to the rockfall impact angle, and the plastic strain of the shed tunnel produced by five impacts of the rockfall impact angle 30° is far less than that produced by five impacts of the 90° angle rockfall impact.