3.2.1. Synchronized Water Level Gap in Different Aquifers
- (1)
Topsoil thickness.
The relationships curves of the topsoil thickness and additional force with different water level gap values are shown in
Figure 10. The additional force grows when the topsoil shows an increased trend under different water level gap conditions. For instance, this force ranges from 4.13 MPa to 5.28 MPa, with a water level gap of 50 m, when the topsoil thickness ranges from 100 m to 200 m, while this value increases to 18.87 MPa when the thickness reaches 300 m. This phenomenon indicates that the appearance of drainage has a large impact on the subject of the additional force. The maximum additional force reaches 25.19 MPa when the topsoil thickness is 300 m under a water level gap of 90 m. This phenomenon may be because the occurrence of drainage reduces the water pressure and enhances the effective stress of the overlying sediment, which results in the settlement and causes the additional force. The whole settlement amount increases and then induces a larger additional force as the topsoil thickness increases. To further illustrate the effects of the range in topsoil thickness and water level gap on this force, the proportional relationships of the maximum additional force with an increasing water level gap and topsoil thickness are calculated and shown in
Figure 11.
Based on the above figures, it can be observed that the increment of the maximum additional force of the shaft nearly remains at 2 MPa under different water level gaps in the aquifer, when the topsoil thickness is below 200 m, which shows that this force almost presents a linear increase when the water level gap grows. However, the increment of increase in the maximum additional force increases abruptly, with a water level gap value of 0~10 m when the topsoil thickness ranges from 200 m to 300 m. For example, when the water level gap ranges from the 0 condition to 10 m condition, the increment would be 1 MPa with a topsoil thickness of 100 m, but this value will increase to 11.47 MPa when the topsoil thickness reaches 300 m, as shown in
Figure 11a. One probable reason is that the influence of the drainage on this force is more obvious in the initial stage when the thickness of the topsoil exceeds a certain value; however, the sediment settlement becomes more serious with continuous drainage and the additional force value between the shaft and the surrounding stratum changes more significantly.
The increment of increase in the maximum additional force progressively rises, with the increasing thickness of the topsoil, when the water level gap is constant. The values are relatively similar when the thickness of the topsoil is 200 m, which indicates that the additional force values generated by different water level gaps in shallow topsoil are closer and less hazardous than those in deep sediment. The increment of increase in the maximum additional force increases abruptly when the thickness of the topsoil surrounding the shaft changes from 200 m to 300 m. For example, the increment value ranges from 0.06 MPa to 3.42 MPa when the increase in the thickness of the topsoil changes from 150–200 m to 200–250 m, with a water level gap of 10 m. This phenomenon shows that the increasing trend of the additional force shows an obvious increase in the transition from the shallow topsoil part to the deep sediment part, indicating that the vertical additional force should be reduced by adding shrinkable layers to avoid shaft wall fracture, especially in deep sediment.
- (2)
Shaft wall thickness.
The relationships between the maximum additional force and shaft wall thickness under different water level gap conditions are shown in
Figure 12. From
Figure 12, it can be observed that the maximum additional force decreases with increasing shaft wall thickness under different water level gap conditions, while the difference in growth amplitude is relatively smaller than that induced by the increase in topsoil thickness. This phenomenon shows that the increasing shaft wall thickness can reduce the additional force by enhancing the shaft wall’s resistance to deformation, and the increasing thickness enlarges the cross-sectional area, which reduces the additional force when the overall deformation of the topsoil is constant. The maximum additional force also increases with the increasing water level gap under different shaft wall thicknesses, while the magnitude of the increase is relatively constant.
The relationships between the maximum additional force, the water level gap and the shaft wall thickness are calculated and shown in
Figure 13, where it can also be seen that the increment of the increase in maximum additional force continuously grows when the water level gap shows an increasing trend, while the increment magnitude of this force decreases. This phenomenon can be proven by the fact that the increment amplitudes with water level gap values of 70~90 m and 10~30 m are 3.31 MPa and 2.48 MPa when the shaft wall thickness remains at 0.8 m, while these two values are 2.37 MPa and 1.78 MPa when this thickness ranges to 1.2 m. Increasing the thickness can reduce the additional force and enhance the bearing capacity of the shaft and effectively prevent shaft wall fractures. However, the reduction in the maximum additional force also decreases with increasing thickness of the shaft wall; for example, the reduction in the maximum additional force is approximately 0.66 MPa, for a water level gap of 90 m, when the thickness of the shaft increases from 1.1 m to 1.2 m. Hence, the shaft safety produced by increasing the wall thickness does not match its construction cost, so it is necessary to design the wall thickness reasonably by considering the actual shaft situation and economic benefits.
- (3)
Bottom aquifer thickness.
The additional force shows an increasing trend under different water level gap conditions as the bottom aquifer thickness shows an increase trend, as shown in
Figure 14. The additional force changes from 1.09 MPa to 1.13 Mpa, with a water level gap of 10 m, as the thickness changes from 15 m to 35 m, and this force increases from 9.98 MPa to 11.58 MPa with a water level gap of 90 m. This phenomenon shows that, when the drainage settlement tends to increase significantly when the water level gap decreases (the water level loss), the effect of this settlement on the frictional force will also strengthen and then enhance the additional force.
The increment of this force also grows constantly as the water level gap shows an increase trend, as shown in
Figure 15. For instance, the increment of the additional force increases from 1.09 MPa to 2.44 Mpa, with a bottom aquifer of 15 m, when the water level gap increases from 0 m to 90 m, while this value increases from 1.13 MPa to 3.1 MPa with a bottom aquifer of 35 m. Interestingly, the thickness of the bottom aquifer shows little effect on the increment of the additional force when the water level gap ranges from 0 m to 90 m. These results show that the drainage settlement of the bottom aquifer should be considered, while water level gaps show a greater effect on the increment of the additional force.
- (4)
Effect of the number of central aquifers.
Figure 16 demonstrates that this force shows a clear trend towards increasing, with a growing number of central aquifers, under different water level gap conditions, while the difference in growth amplitude is relatively higher than that induced by other parameters. For instance, this force changes from 1.5 MPa to 31 MPa, with a water level gap of 70 m, when the number of central aquifers increases from 0 to 4, while it increases from 2 MPa to 41 MPa when the water level gap is 90 m. The increment of the additional force reaches 9 MPa, and even 12 MPa, with an increasing number of central aquifers. The possible reason may be that the water level gap value generated by water loss in the central aquifer increases with an increasing number of central aquifers, and then, the vertical additional force value increases at a high rate. The change in the number of central aquifers exerts relatively large effects on the maximum additional force, which shows the important role of the central aquifers in the study of additional force.
According to the results in
Figure 17, the increment in this force is enhanced constantly as the water level gap increases when the number of central aquifers is held constant, while this value is greater when the number of central aquifers increases. With the water level gap value changing from 0 m to 90 m, this increment would range from 0.25 MPa to 0.46 MPa, with the central aquifer number of 0, and the increment in the additional force increases from 3.85 MPa to 9.85 MPa when the number of central aquifers is 4. The appearance of the central aquifer would significantly affect this force value, and it is important to pay attention to the drainage settlement of topsoil containing multiple aquifers. Moreover, the increment in the additional force shows a constant growth, with an increasing number of central aquifers, when the water level gap is constant.
- (5)
Central aquifer thickness.
Relationships between this force and the central aquifer thickness, under different water level gap conditions, are shown in
Figure 18. The maximum additional force increases with an increasing water level gap, as shown in
Figure 18. With the water level gap value changing from 0 m to 90 m, this force would range from 0 MPa to 2.02 Mpa, with a central aquifer thickness of 0 m, and the force would range from 0 to 10.57 MPa when the thickness changes to 10 m. In addition, the maximum additional force increases slightly, with further increases in the central aquifer thickness. The appearance of this central aquifer leads to the more obvious settlement of topsoil and then enhances the additional force value.
The increment in this force shows a relatively slower growth rate as the water level gap grows when the central aquifer thickness is constant, as shown in
Figure 19a. The maximum additional force shows an increment of less than 3 MPa when the water level gap changes 20 m. Moreover, the variance in the additional force would obviously be influenced by the appearance of the central aquifer instead of the increase in the central aquifer thickness. In
Figure 18, the maximum additional force ranges from 2.02 MPa to 10.99 Mpa, with a water level gap of 90 m, when the thickness changes from 0 m to a value of 10 m; however, the maximum additional force remains nearly 11 MPa when the central aquifer thickness continues to rise to 30 m. The increment in the additional force decreases to nearly 0 Mpa, with an increasing water level gap, when the thickness exceeds 30 m, as shown in
Figure 19b. These results are similar to those of the force of the bottom aquifer thickness.
- (6)
Location of the central aquifer.
According to
Figure 20, the additional force on the shaft also shows a relatively obvious increase when the height of the central aquifer grows under different water level gap conditions. This force changes from 2.04 MPa to 13.56 Mpa, with a water level gap of 90 m, as this location increases from 0.7 H to 0.3 H. Moreover, the maximum additional force of the shaft grows with an enlarging water level gap under different locations of central aquifer conditions. For instance, this force would change from 0 to 2.04 Mpa, with a central aquifer of 0.7 H, as the water level gap ranges from the 0 m condition to the 90 m condition, and the force would change to 10.78 MPa if the location was 0.5 H. In addition, the relationships between the increment in the additional force with an increasing water level gap and the location are calculated to further illustrate the influence law of these parameters on the additional force (as shown in
Figure 21).
This force also presents a constant increase trend with the increasing water level gap, as shown in
Figure 21a. The increment in the additional force decreases constantly, with the decreasing height of the central aquifer, when the water level gap is constant. For example, the increment in the additional force decreases from −1.39 MPa to −7.38 MPa, with a water level gap of 90 m, when the location decreases from 0.3 H to 0.7 H, as shown in
Figure 21b. Therefore, measuring and acquiring the location is important for predicting the range of this force. Furthermore, the increment in the additional force changes from 0.95 MPa to 2.49 MPa when the location is 0.6H, and when the water level gap changes from 0 m to 90 m. In contrast, the increment decreases abruptly when the location is 0.7 H, and only ranges from 0.26 MPa to 0.46 MPa due to the consistent water level gap increase, as shown in
Figure 21a. This phenomenon may be because the additional force is mutually neutralized when the central aquifer is located at a greater depth, which means that a threshold value exists for the depth of the central aquifer in terms of its effect on the additional force.