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Similar simulation study on the deformation and failure of surrounding rock of a large section chamber group under dynamic loading

2021-07-10XueshengLiuShilinSongYunlingTnDeyunFnJinguoNingXuebinLiYnchunYin

矿业科学技术学报 2021年3期

Xuesheng Liu ,Shilin Song *,Yunling Tn, *,Deyun Fn ,Jinguo Ning ,Xuebin Li ,Ynchun Yin

a College of Energy and Mining Engineering,Shandong University of Science and Technology,Qingdao 266590,China

b State Key Laboratory of Mining Disaster Prevention and Control,Shandong University of Science and Technology,Qingdao 266590,China

Keywords:Dynamic disturbance Large section chamber group Deformation and failure Similar simulation test

ABSTRACT Large and super-large section chamber groups in coal mines are frequently affected by dynamic loads resulting from production activities such as roadway driving and blasting.The stability of the surrounding rock is poor,and it is difficult to control.In this paper,a similar simulation test was used to study the deformation and evolution laws of the surrounding rock of a triangle-shaped chamber group under different dynamic loads.The results showed that under dynamic loading,the vertical stress of the surrounding rock of the chamber group increased in an oscillatory form.The maximum stress concentration coefficient reached 4.09.The damage degree of the roof was greater than that of the two sides.The deformation of the roof was approximately 1.2 times that of the two sides.For the chamber closer to the power source,the stress oscillation amplitude of the surrounding rock was larger,and the failure was more serious.The force of the anchorage structure showed a phased increasing characteristic;additionally,the force of the anchorage structure on the adjacent side of the chambers was greater than that on the other side.This study reveals the deformation and failure evolution laws of the surrounding rock of large section chamber groups under dynamic loading.

1.Introduction

In recent years,the depth and intensity of coal mining in China has gradually increased and steadily progressed towards largescale and intelligent mining.Increasing numbers of high-power,large-volume coal mining machines have been used in underground coal mining,resulting in many large section chambers[1-13].It is difficult to excavate and maintain the surrounding rock of these kinds of large section chamber groups,especially in the complex environment of the ‘‘three high disturbance”in deep regions.The mine pressure in chamber groups is intense.Furthermore,the deformation and damage of the chamber groups is severe.When disturbed by dynamic loads,the chamber group often requires multiple repairs and reinforcements to ensure the stability of the surrounding rock.It is one of the main threats to the safety of underground mining activities [14-28].

Mastering the laws of stress,deformation,and fracture evolution of the surrounding rock of large and super-large section chambers and chamber groups is the premise and guarantees for effective control.Domestic and foreign experts have carried out a considerable amount of meaningful research on this topic.For a single chamber,the section size is an important factor affecting the instability and failure of large and super-large section chambers.With an increase in the section size of the chamber,the plastic zone and stress of the surrounding rock increase quadratically,and the floor heave increases linearly.For example,the plastic zone radius of a super-large section chamber with section width and height of 10 m is 2.2 times that of an ordinary section chamber with section width and height of 6 m [29-31].Additionally,the lithology of the surrounding rock is an important factor that affects the instability and failure of large and super-large section chambers.When the surrounding rock of large and super-large section chambers is soft rock or coal seam,the chamber is prone to unstable failure.The failure forms mainly abscission layer flexure failure and shear failure.Abscission layer flexure failure can be divided into two types:gradual instability and mutation induced failure[32-37].Currently,underground production systems of coal mines often contain many large and super-large section chambers.These chambers cooperate with each other to form large and super-large section chamber groups.Therefore,stability control of the surrounding rock of the chamber groups becomes very important[2-10].For the chamber group,there are many reasons leading to large deformation and severe failure of the surrounding rocks,such as high ground stress,complex geological structures,weak surrounding rock,arrangement forms,and construction sequences.Additionally,it was found that constructing a small section chamber first and the large section chamber later would have the lower impact on the stability of the surrounding rocks of the chamber[36,37].The above mentioned studies provided strong support for the control of surrounding rocks of large and super-large section chambers and chamber groups in deep regions.

However,owing to the complexity of the deep stress environment,especially the dynamic disturbance caused by the fault movement and blasting of the overburden,there are still some deficiencies in the understanding of the instability mechanism of the surrounding rock of deep large section chamber groups.For example,the fracture increment and instability criterion of large sections of surrounding rock under different dynamic disturbances and the interaction of the deformation and fracture evolution of the surrounding rock between multiple chambers are still unknown.

On the basis of the geological conditions of a typical deep coal mine underground coal gangue separation system,this paper used a similar material test to study the stress,deformation,and fracture evolution of the surrounding rock of the chamber group composed of three large section chambers.This method could provide a basis for the stability control of the surrounding rock in similar conditions.

2.General engineering background

The Xinjulong coal mine,located in the town of Longgu in Heze city,Shandong province,is one of the main production mines of the Xinwen Mining Group,China.Its design production capacity is 6 million tons in a year.In response to the national concept of green mining,to save costs,and to achieve that gangue does not rise wells,multiple chambers or roadways were excavated at -810 m underground.A coal gangue separation system(Fig.1) was arranged.This system includes mainly a screening crushing chamber,screening product transfer chamber,shallow channel gangue discharge chamber,slime water adding medium chamber,and gangue discharge roadway.The cross-sectional areas of the three chambers,which are the screening product transfer chamber,shallow channel gangue discharge chamber,and slime water adding medium chamber,are all greater than 50 m2.Their spacing is small with a minimum spacing of 60 m.Therefore,it is a typical close-distance chamber group.

In this paper,the above mentioned three chambers are the research focus.The chamber group is located within a triangular area enclosed by a belt transportation roadway in the north,first mining wind uphill,and the 1301 mining area.The chamber group is located above the coal seam,and the surrounding rock is mainly siltstone and fine sandstone,which has good stability.The rock stratum histogram is shown in Fig.2.The section shapes of the three chambers are all three center arches with straight walls.The sizes of screening product transfer chamber,shallow channel gangue discharge chamber,and slime water adding medium chamber are 8.0 m × 8.0 m,7.5 m × 8.0 m,and 7.0 m × 7.5 m,respectively.All three chambers are supported by bolts,mesh,cables,and shotcrete.A Φ22 × 2500 mm resin anchor bolt is used.When the roof is complete,the row spacing between the anchor bolts is 1000 mm × 1000 mm.When the roof is broken or passes through the fault,the row spacing between the anchor bolts reduces to be 800 mm × 800 mm.The size of the anchor cable is Φ22 × 6300 mm.When the roof is complete,the row spacing between the anchor cables is 3000 mm×3000 mm.When the roof is broken or passes through the fault,the row spacing between the anchor cables reduces to be 3000 m × 1600 mm.

The chambers would be affected by the dynamic load disturbance produced by various production activities after the excavation.The KJ 551 microseismic monitoring system was used to monitor the microseismic activities of the chamber group.It was found that the dynamic load disturbance energy was approximately 106J,which generated a vertical stress of 37.5 MPa.The dynamic load can be simplified to be a sinusoidal stress wave,and the stress vibration frequency was approximately 15 Hz.Considering that the strength similarity ratio is 1:75,the dynamic load cylinder applied a dynamic load disturbance with a magnitude of 0.5 MPa and frequency of 0.2 Hz to a similar simulation model.

3.Similar simulation test

3.1.Model laying

A two-dimensional similar simulation test bed was used for the test.The test bed is 3.0 m long and 0.4 m wide,and the maximum laying height is 2.1 m.When the similarity theory and geological conditions in the field are combined,the geometric similarity ratio is 1:50,and the bulk density similarity ratio is 1:1.5.Furthermore,the elastic modulus similarity ratio is 1:75,the strength similarity ratio is 1:75,the Poisson’s ratio similarity coefficient is 1,and the laying height of the similar materials is 1.8 m.

Owing to limitations in the two-dimensional similar test conditions,the position relationship of the downhole chambers could not be completely restored in the room.Therefore,the three chambers in this study were arranged in a triangular shape in parallel;these chambers(i.e.the screening product transfer chamber,slime water adding medium chamber,and shallow channel gangue discharge chamber) are denoted as 1#,2#,and 3# chamber,respectively.The floor of the 1# chamber is 3 m above the coal seam.The floor of the 2# chamber is 4.5 m above the coal seam.The 1# and 2# chambers are 25 m apart.The floor of the 3# chamber is 24 m above the coal seam,20 m from the left side of the 1#chamber,and 22 m from the right side of the 2# chamber.Their relative position is shown in Fig.3.To ensure that the distance between the roof of 1# and 2# chambers and the power source was identical,the roof of 1#and 2#chambers was set at the same level.The cross-sections of the three chambers are rectangular.Specifically,their cross-sectional dimensions are 19 cm × 20 cm,15 cm×15 cm,and 18 cm×18 cm,which correspond to the actual cross-sectional areas of 95,56.25,and 81 m2,respectively.

Fig.1.Schematic diagram of the roadway layout for the coal gangue separation system.

Fig.2.Rock stratum histogram.

The materials used in similar simulation experiments are mainly divided into two parts:aggregates and cement.In this test,river sand with a particle size of ≤0.5 mm was used as the aggregate,gypsum was used as the main cement,and calcium carbonate was used as the auxiliary cement.The layers were separated by mica powder.On the basis of the physical and mechanical properties of each rock stratum measured in the laboratory,the material ratio of each rock stratum was confirmed in this test.The actual physical and mechanical properties of each rock stratum are shown in Table 1,and the material ratio and dosage of each rock stratum are shown in Table 2(for convenience of laying,the thickness of each stratum was processed according to the rounding rule).The surrounding rock of the chamber is supported by an anchor bolt/anchor cable.A screw rod of Φ3 mm × 50 mm was used to simulate the anchor bolt,and the preload was applied by the nut.A thin copper wire with a length of 100 mm was used to simulate the anchor cable,and the spoke cap was used to simulate the lock,which could exert the pretightening force on the anchor cable.The plate was simulated by a thin steel plate of 10 mm × 10 mm,and the thickness of the steel plate was 0.2 mm.The row spacing between the anchor bolts of 1#,2#,and 3# chambers was 20 mm × 20 mm,and the row spacing between the anchor cables was 40 mm × 40 mm.During the test,the anchor bolt/anchor cable was supported by pre-burial and locked after excavation.

Table 1 Actual physical and mechanical properties of each stratum.

Table 2 Proportion of model materials and laying level.

3.2.Test scheme

After the model was constructed,the following scheme was used for testing.

Step one:After the model was laid and dried,the baffles on both sides were removed;1 or 2 baffles were kept on the upper part to prevent the model from collapsing to the side.

Fig.3.Schematic of the similar simulation test model and dynamic load position.

Step two:The vertical stress was applied through the static loading cylinder at the top.The vertical stress was the rock stress of the upper non-simulated rock layer.According to Eqs.(1) and(2),the vertical stress (σp) was approximately 17.55 MPa,and the applied vertical stress (σm) was 0.234 MPa.

where σpiis the rock stress of the non-simulated strata in the prototype,MPa;ΔHithe thickness of the non-simulated strata in the prototype,732 m;γpithe bulk density of each stratum of the nonsimulated strata in the prototype,24 kN/m3;Clthe geometric similarity ratio,1:50;and Cγ the bulk density similarity ratio,1:1.5.

Step three:The 1#,2#,and 3# chambers were excavated sequentially.The nuts of the anchor bolts and locks of the anchor cables were installed to complete the support.A waiting period of 1-2 days was used to ensure that the surrounding rock of the chambers developed stably.

Step four:The dynamic load disturbance was applied by the 1#dynamic load cylinder.The dynamic loading frequency was 0.2 Hz,and the loading stress was 0.5 MPa.The dynamic load disturbance lasted for 2 h.After each 0.5 h of dynamic loading,the test was stopped for 10 min to prevent the dynamic load cylinder from overheating.Four hours passed after the application of the dynamic load to ensure that the surrounding rock of the chambers was fully developed and stable.

Step five:The dynamic load disturbance was applied by the 2#dynamic load cylinder.The loading processes were the same with that in Step four.

Step six:The dynamic load disturbance was applied by the 3#dynamic load cylinder.The loading processes were the same with that in Step four.

3.3.Monitoring scheme

Fig.4.Layout of the measuring points.

Fig.5.Digital speckle monitoring device.

A variety of devices were used to monitor the stress,deformation,and failure of the surrounding rock and stress change of the anchor bolt during the process of chamber excavation stability to dynamic load application.The overall monitoring layout is shown in Fig.4.The deformation of the surrounding rock surface was monitored by the digital speckle method,and a white spot spray with a black background layer was sprayed on the front side of the model.The monitoring device included an HD camera,fill-in light,and computer,as shown in Fig.5.The pressure box was used to monitor the stress change of the surrounding rock,and 21 measuring points of the pressure box were arranged.To ensure the accuracy of the monitoring results,steel plates were placed on the upper and lower sides of the pressure box so that the stress was even.The stress of the anchor bolt was monitored by bonding the strain gauge on the anchor bolt body (the strain gauge was bonded on the anchor bolt body by universal glue),and 9 strain gauge measuring points were arranged.The monitoring data of the surrounding rock stress and anchor bolt stress were collected by a DH 3815 acquisition system and transmitted to a computer for processing.

4.Results and discussion

4.1.Stress change of the surrounding rock

The three chambers were excavated in sequence.After a period of time,the stability of the surrounding rock was good,and the stress of the surrounding rock was stable.After the three dynamic load cylinders were applied sequentially,the vertical stress of the roof of the chambers obviously changed,that is,it increased in an oscillatory motion.In this study,a total of 21 pressure cells were arranged around the chamber group to monitor the stress of the surrounding rock of the chamber group.Under the dynamic load disturbance,their changing rules were almost the same.Therefore,this study mainly analyzed the monitoring results of the 2#,5#,and 8# pressure boxes,the stress variations of these boxes during the three stages were shown in Fig.6.

In summary,the vertical stress curves of the roofs of the three chambers are similar to oscillating wave curves.Furthermore,because of the differences in the section size and burial depth,the peak stress values and stress curves are slightly different.The vertical stress of the roof of the 3# chamber had the largest variation range,which was 0.27 MPa.The vertical stress of 2#chamber had a maximum variation range of 0.2 MPa.And the vertical stress of 3#chamber was the smallest,with a maximum variation range of only 0.06 MPa.Because of the large cross-sectional area close to the power source,the 3# chamber was most affected by the dynamic load compared to the other chambers.The vertical stress of the roof was the most obvious,and the curve changed the most.The 1# and 2# chambers were at the same level,but because the section size of the 1# chamber was larger than that of the 2#chamber,it was greatly affected by the dynamic load.Additionally,the vertical stress change of the roof of the 1# chamber was more obvious than that of the 2# chamber,but the vertical stress curve of the roof changed more slightly than that of the 3# chamber.Owing to its small cross-sectional area,the 2# chamber was less affected by the dynamic load,and the stress change in the top plate was the least obvious compared to that of the other chambers.

Fig.6.Monitoring results of the surrounding rock stress under the dynamic load.

4.2.Deformation and failure characteristics

After the three chambers were excavated,the deformation of the surrounding rock was small,and there was no obvious damage in the roof,floor,or sides.The integrity of the surrounding rock was good,as shown in Fig.7.After the dynamic load was applied,the deformation of the surrounding rock increased obviously,and the rock was damaged to varying degrees,as shown in Figs.8-12.

Fig.7.Completed excavation of the 1#,2#,and 3# chambers.

Figs.8 and 9 illustrate the results obtained from the dynamic signal acquisition and analysis system.It can be seen from Fig.8 that the range and value of roof subsidence of the chamber group increased with the dynamic load disturbance.The roof of the 3#chamber had the largest sinking area followed by these of the 1#and 2#chambers.The floor heave of the three chambers appeared in different degrees,but the range of floor heave had minimal change.The floor heave scope of the 3# chamber was the largest,while that of the 2#chamber was the smallest.It can be seen from Fig.9 that the deformation of two side walls of the chamber group experienced varying degrees changes with the dynamic load disturbance.The two sides of the 1# and 2# chambers changed slightly while the two sides of the 3# chamber changed substantially.The displacements of the right side of the 1#,2#,and 3#chamber were all larger than that of the other parts of the chambers.The maximum displacement was approximately 12 mm.

Fig.8.Vertical displacement of the chamber group.

Fig.9.Horizontal displacement of the chamber group.

Fig.10.Test results after applying the dynamic load from the 1# dynamic load cylinder.

Fig.11.Test results after applying the dynamic load from the 2# dynamic load cylinder.

From Fig.10,it can be seen that after the dynamic load was applied to the left side of the model by the 1#dynamic load cylinder,the right corner of the 1# chamber was the first to be damaged.Under the dynamic load,the roof of the chamber was partially damaged,which may result in roof falling accidents.There was essentially no damage to the 2# chamber,and only a small amount of crushed stone fell from the roof.The roof of the 3#chamber was damaged first,and then the roof fell.After that,the right side was damaged,spalling occurred,and large rocks were peeled off from the right side.It can be seen from Fig.11 that after the dynamic load was applied on the middle of the model by the 2# dynamic load cylinder,the roof of the 1# chamber was damaged more seriously,and large rocks fell from the roof.A few transverse cracks appeared on the surface of the model (marked with red lines in Fig.11),and the roof of the 1# chamber showed signs of falling.The roof of the 2# chamber was slightly damaged,a small amount of rock fell,and the corner surface cracked.The damage degree of the roof and the right side of the 3#chamber was further intensified,and the scope of damage to the right side was obviously increased.Furthermore,a small area of rock spalling appeared on the surface of the right side of the 3# chamber.It can be seen from Fig.12 that after the dynamic load was applied on the right side of the model by the 3# dynamic load cylinder,a large crack extending to the depth (marked with red lines in Fig.12)appeared at the side angle of the 1#chamber,and the roof obviously sank.The roof damage degree of the 2# chamber was further intensified,the extent and scope of the damage increased in varying degrees,and the scope of the corner cracks of the two sides further expanded.The destruction scope of the right side of the 3# chamber further expanded,part of the roof collapsed,and the surrounding rock of the chamber was unstable.

Fig.12.Test results after applying the dynamic load from the 3# dynamic load cylinder.

It can be seen from Figs.8-12 that all three chambers were damaged with different degrees.The damage degree to the 3#chamber was the most severe followed by that of the 1# chamber and that of 2#chamber.The roof displacement of the 3#chamber was 1.2 times larger than that of the two sides.When the failure modes of the three chambers at different stages were compared,it can be seen that the destruction scope and extent of the 1#and 2# chambers were small during the three loading stages.This is because that the 3#chamber had been severely damaged by the dynamic load.The dynamic loading waves were continuously consumed in the transmission process,and only a small number of dynamic loading waves were passed to the 1# and 2# chambers.Moreover,owing to the damage of the 3#chamber under dynamic loading,the concentrated stress generated by the excavation was released,and the stress continuously transferred to the deeper regions.The stress of the surrounding rock was redistributed,and the stresses around the 1# and 2# chambers were reduced.Therefore,the damage scope and degree of the 1# and 2# chambers were less than those of the 3# chamber.Furthermore,it can be found that the damage degree of the 1# chamber was slightly larger than that of the 2#chamber.This result was due to the larger section size of the 1#chamber and the earlier excavation time.After the excavation of the 3# chamber,the surrounding rock of the 1# chamber was severely damaged.Therefore,under dynamic loading,the damage degree of 1# chamber was significantly greater than that of the 2# chamber.

In summary,the surrounding rock of the 3#chamber was considerably deformed because it was close to the power source,and it was more severely damaged than that of the other chambers.For the 1# and 2# chambers at the same level,the deformation and damage of the surrounding rock of the 1# chamber was severe because of its larger section size,and the deformation and damage of the 2#chamber were the smallest.The dynamic load caused different damage degrees of the roof,and the damage of the right side obviously occurred prior to that of the left side.Under dynamic loading,the chamber roof first partially fell followed by a large area roof fell,which was further accompanied by slope accidents.Then,the whole surrounding rock of the chamber failed and became instability.

4.3.Force variation of the anchoring structure

After the dynamic load was applied,the anchor bolts/cables of the surrounding rocks were subjected to different degrees of impact force,and the supporting effects of the anchor bolt/cable support varied differently,as shown in Fig.13.The monitoring results of anchor forces were shown in Fig.14.

During the test,it was found that some plates of roof bolts in the 1# chamber fell off after the dynamic load was applied by the 1# dynamic load cylinder.The support condition of the 2#chamber was in good condition,some bolt plates in the corner of the 3# chamber fell off.After the dynamic load was applied by the 2# dynamic load cylinder,some of the anchor locks on the two sides of the 1# chamber became invalid,some bolt plates on the roof of the 2#chamber fell off,and all the bolt plates and cable nuts fell off.After the dynamic load was applied by the 3#dynamic load cylinder,most of the bolt plates of 2# chamber and the cable nuts of the two side corners fell off,and the anchor structure of the roof and the right side of the 3# chamber completely failed.

During the three dynamic loads,for the 1# chamber,the cable force of the right side was the largest,while that of the left side was the smallest;for the 2#chamber,the cable forces were larger than those of 1# chamber,the force of left side was the largest while that of the right side was the smallest;for the 3# chamber that maintaining stable,the bolt force of roof was the largest while that of the left side was the smallest.It can be seen that the bolt force of the pillar between the 1#and 2#chambers was much larger than those at other locations.The ratio of bolt force between the adjacent side and the nonadjacent side is approximately 1.18-1.34,which occurs because there were many cracks in the rock column between the 1#chamber and the 2#chamber.Therefore,it was necessary to provide a greater anchoring force to maintain the stability of the chamber and prevent failure of the side.

In summary,the bolt forces of the anchoring structure increased in a curved manner during the dynamic loading process.The 1#and 2#chambers were far from the power source,neither of them suffered major damage,and the anchoring structure did not fail,which could effectively support the chambers.The 1# and 2#chambers affected each other,and the bolt force of the adjacent part of the two chambers were greater than those of the other positions.

Because the 3#chamber was too close to the power source,the bolt force of the roof and the right side started to decline in the second stage and suddenly changed to 0 in the third stage.The anchoring structure failed in the third stage.

Fig.13.Support condition of the three chambers after dynamic loading.

Fig.14.Monitoring results of force on the anchor bolts.

4.4.Discussion

The surrounding rock of the underground chambers and roadways is not only affected by static loads but also by different dynamic loads [38-43].With the development of large-scale and intelligent mining equipment,there are more large and superlarge section chamber groups.The surrounding rock stability control of large section chamber groups under dynamic loading is becoming a hot topic [44-47].

It was found that the side of adjacent chamber near the disturbed area was destroyed first,while the further side was destroyed later [48-50].The results obtained by the similar simulation test in this paper were comparable with these results.A few researchers have found that the damaging effects of the dynamic sources were more sensitive to its location.With the distance to the source increasing,the deformation and failure degree of the surrounding rock under dynamic loading decreased [51-53].Disturbed by the dynamic loads on the top,the chamber group roof was destroyed before the side,which verified the above conclusions.Moreover,this study showed that the upper chamber in the triangle-shaped chamber group played a pressure relief role on the lower chamber,which could effectively reduce the damage degree of the lower chamber.Additionally,the chamber section size was another important factor affecting its deformation and failure.These research results have a significant guiding benchmark for the excavation,support and maintenance of underground chamber group.

However,the specific influence of factors such as the crosssectional size and spacing on the stability of the surrounding rock has not been realized.In the future,more indoor tests,numerical simulations and field detection need to be carried out to provide more reliable support for the support design of chamber groups in field engineering.

5.Conclusions

In this study,through a similar simulation test under dynamic loading,the stress,deformation,and failure of the surrounding rock of a chamber group and their change characteristics under dynamic loading were systematically analyzed.The following conclusions were obtained.

(1) The vertical stress of the roof of each chamber in the group increased in an oscillatory form.As the chamber became close to the power source,the peak value of the vertical stress of the roof became greater,while the characteristics of the vibration change became more obvious.An obvious stress concentration zone was formed in the roof of the chambers and the coal pillar between the lower chambers,and the maximum stress concentration coefficient reached 4.09.

(2) The deformation of the surrounding rock of the chamber group increased with the disturbance process.The increase in the roof deformation was obviously larger than that of the side deformation,especially for the upper chamber,which was closer to the dynamic load source.The roof deformation was approximately 1.2 times that of the two sides.For the chambers with a triangle shape arrangement,when the chambers was disturbed by the upper dynamic load,the upper chamber was destroyed first.And the failure characteristics showed the roof falling off first and the two sides breaking later.Therefore,a supporting scheme of strengthening the roof should be adopted.

(3) The force of the anchoring structures of the chamber group shows the gradual rising law.Because of the interaction between the chambers,the force of the anchorage structure on the adjacent side of the chambers was obviously greater than that on the nonadjacent side.The force ratio between the adjacent side and the nonadjacent side was approximately 1.18-1.34,and it was also affected by the location of the dynamic load source.The side closer to the dynamic load source had a greater increase in the force of the anchoring structure than that farther from the dynamic load source.

Acknowledgements

The authors gratefully acknowledge the financial support from the National Key R&D Program of China (No.2018YFC0604703),National Natural Science Foundation of China (Nos.51804181,51874190,and 52074168),and Key R&D Program of Shandong Province (No.2019GSF111020).


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