Experimental investigation on the invert stability of operating railway tunnels with different drainage systems using 3D printing technology

Linyi Li,Junsheng Yng,Jinyng Fu,b,*,Shuying Wng,Cong Zhng,Molong Xing

a School of Civil Engineering,Central South University,Changsha,410075,Hunan,China

b National Engineering Research Center of High-speed Railway Construction Technology,Changsha,410075,China

c School of Civil Engineering,Central South University of Forestry and Technology,Changsha,410004,China

Keywords:Operating railway tunnels Invert stability Tunnel drainage system Three-dimensional(3D)printing technology Model test

A B S T R A C T In recent years,the invert anomalies of operating railway tunnels in water-rich areas occur frequently,which greatly affect the transportation capacity of the railway lines.Tunnel drainage system is a crucial factor to ensure the invert stability by regulating the external water pressure(EWP).By means of a threedimensional(3D)printing model,this paper experimentally investigates the deformation behavior of the invert for the tunnels with the traditional drainage system(TDS)widely used in China and its optimized drainage system(ODS)with bottom drainage function.Six test groups with a total of 110 test conditions were designed to consider the design factors and environmental factors in engineering practice,including layout of the drainage system,blockage of the drainage system and groundwater level fluctuation.It was found that there are significant differences in the water discharge,EWP and invert stability for the tunnels with the two drainage systems.Even with a dense arrangement of the external blind tubes,TDS was still difficult to eliminate the excessive EWP below the invert,which is the main cause for the invert instability.Blockage of drainage system further increased the invert uplift and aggravated the track irregularity,especially when the blockage degree is more than 50%.However,ODS can prevent these invert anomalies by reasonably controlling the EWP at tunnel bottom.Even when the groundwater level reached 60 m and the blind tubes were fully blocked,the invert stability can still be maintained and the railway track experienced a settlement of only 1.8 mm.Meanwhile,the on-site monitoring under several rainstorms further showed that the average EWP of the invert was controlled within 84 kPa,while the maximum settlement of the track slab was only 0.92 mm,which also was in good agreement with the results of model test.

1.Introduction

With the development of the transportation infrastructure in China,a great number of railway tunnels have been constructed in the past decades.More than 16,000 railway tunnels with a total length of 19,630 km have been in operation by the end of 2020,and 2746 railway tunnels with a total length of more than 6000 km are under construction.As an increasing number of tunnels are put into operation,new problems such as invert anomalies arise,and they have attracted special attention of engineers(Li,2012;Mothersille and Littlejohn,2012;Shin et al.,2014).An unstable invert structure with features such as invert heave,cracking and mud pumping not only affect the service life of a railway tunnel,but also are harmful to the safety of transportation(Lee and Wang,2016;Du et al.,2020).Especially for high-speed railway(HSR)tunnels,even a slight uplift of track slabs can cause substantial disasters(Qian et al.,2018;Cai et al.,2019).Many railway tunnels have suffered from invert instability as shown in Fig.1,and even the railway transportation of some tunnels had been affected for several years(Dai,2016;Ouyang,2018).Studies show that high EWP is one of the main factors leading to the instability of invert structures(Arjnoi et al.,2009;Li et al.,2018;He et al.,2020;Zhou et al.,2021).The excessive EWP in operating tunnels may result from the groundwater level rising under torrential rains(Gao et al.,2019;Lin et al.,2019),or the failure of tunnel drainage systems during operation,which are often not considered in design.Thus,it is crucial to control the effect of EWP on invert structure in operating railway tunnels to solve the above-mentioned engineering problems.

Fig.1.Typical appearance of invert instability:(a)Uplift of track slab,(b)Cracks on the invert,and(c)Separation of invert filling and track slab.

Waterproofing and drainage systems play a notable role in controlling the EWP of the tunnel lining(Arjnoi et al.,2009;Ying et al.,2018;Lv et al.,2020).There are two main types of tunnel waterproofing and drainage systems,i.e.full sealing and drainage system setting(Fang et al.,2016;He et al.,2020).In China,most railway tunnels are equipped with drainage system to reduce the groundwater risks,and a typical waterproofing and drainage system(i.e.traditional drainage system(TDS))is shown in Fig.2a.The system includes geotextiles,waterproof board,drainage blind tubes and drainage ditches.After passing through the geotextile,groundwater is introduced into the tunnel through the external drainage blind tube and transverse drainage blind tube and finally discharged by both the side ditches and the central ditch.Generally,tunnel waterproofing is realized by a self-waterproof lining and waterproof board.Although such a drainage system has a good waterproofing and drainage effect in theory,it does not take into account the issue of EWP at the tunnel bottom in actual applications.Once the groundwater level suddenly rises or the drainage system fails,a great deal of groundwater will gather at the tunnel bottom to form an excessive EWP(Li et al.,2018;Fan et al.,2018),which is likely to cause a series of invert anomalies.To this end,aiming at the tunnel in water-rich fractured rock or karst development area,an optimized drainage system(ODS)with a bottom drainage function is proposed,as shown in Fig.2b.In addition to having the full drainage path of the TDS,the ODS is set up with a buried drainage pipe below the invert.As a result,an additional and efficient drainage path is created,which allows the groundwater gathered at the tunnel bottom to drain directly from the outside of the tunnel,rather than flowing through a long seepage path and then draining from the inside of the tunnel.The drainage system is expected to be conducive to maintaining the invert stability of operating tunnels with high water pressure.However,very few studies have focused on the drainage effect of ODS,as well as the invert stability under the influence of drainage system,although it is of great significance in maintaining the normal operation of railway tunnels.

Construction of the Nanyang tunnel provides a good opportunity to study such a program.This tunnel is constructed by new Austrian tunneling method(NATM)with a length of 5.73 km,and it carries a double-track HSR line in Jiangxi Province,China.Fig.3 shows the geological cross-section condition of the Nanyang tunnel.The lithology of the surrounding rocks is mainly limestone.In the limestone sections,the surrounding rocks are mostly classified as Grades IV and V according to the China Code for Design of Railway Tunnel(TB10003-2016/J449-2016,2017),due to the relatively broken rock mass.In addition,the results of the geophysical exploration suggested that karst features are intensely developed in limestone strata.Some karst depressions and dolines are continuously distributed on the surface of the tunnel.Due to the good hydraulic connection,the groundwater level in limestone formations is susceptible to a significant rise during heavy rainstorms(Wittenberg et al.,2019),which is a potential risk that endangers the normal operation of the HSR line.Thus,the ODS was adopted in the whole Nanyang tunnel to control the water risk during operation.

As a conventional method,model tests are widely used in stability analysis,structural behavior prediction and disease simulation in tunnel engineering(Guo et al.,2019).However,limited by the accuracy of the model production,it is often difficult to consider some refined structural features in the model test,such as the working state of the drainage system and the slight displacement of the track,which are the features expected.Due to the ability to make complex models and the advantage of high precision,3D printing technology has been gradually applied in civil engineering model tests(Kosi′n et al.,2020).For example,Jiang et al.(2016)studied the mechanical properties of 3D printing products of gypsum and polylactic acid(PLA)materials,and explored the feasibility of 3D printing technology in rock mechanics testing.Zuo et al.(2019)proposed a method for evaluating the rationality of the models and optimizing the parameters of the full-size 3D printing,and verified that the average deviation between 3D printing products and the original model can be controlled within 0.1 mm.In this work,the invert stability and drainage condition of operating railway tunnels with different drainage systems were analyzed using a fine model test.The 3D printing technology was applied to generation of a scaled model of the drainage railway tunnel to improve the refinement and visualization of the model tests.A series of testing cases,including tests on the groundwater level fluctuation and gradual failure of drainage system that are commonly encountered in engineering practice,was conducted to understand the deformation characteristics of invert structures under different drainage systems.Moreover,the variation trend of water discharge and the distribution of EWP were also discussed.The results could provide references for the design and maintenance of railway tunnels in water-rich areas.

2.Model test preparation

2.1.Similarity of scaled model test

The relationship between a scaled model and the corresponding prototype should satisfy the similarity requirements for the geometry,physico-mechanical properties,stress-strain relationship,seepage mechanics and boundary conditions,and thus the results of model tests can represent the behavior of the corresponding prototype(Li et al.,2016a).Under the interaction of the drainage tunnel and groundwater,the key parameters are as follows:lengthL,unit weight γ,hydraulic conductivityk,hydraulic headH,water pressureP,dischargeQ,strain ε,stress σ,elastic modulusE,and displacement δ.

Fig.2.Schematic diagrams of waterproof and drainage system:(a)TDS,and(b)ODS.

Fig.3.Geological cross-section condition of Nanyang tunnel.

The solution for the above quantities can be denoted as

where the lengthL,unit weight γ and hydraulic conductivitykare assumed to be the fundamental parameters.Based on dimensional analysis by the Buckingham Pi theorem,Eq.(1)can be re-written in the following form:

where the dimensionless parameters π1=H/L,π2=P/(γL),π3=Q/(kL2),π4=ε,π5=σ/(γL),π6=E/(γL),and π7=δ/L.

Considering the feasibility of the model test,the similarity ratios of three fundamental parameters(length,unit weight and hydraulic conductivity)were determined asCL=40,Cγ=1 andCk=1.According to Eqs.(1)and(2),the similarity ratio of all the parameters are listed in Table 1.

2.2.Simulated material for surrounding rocks

The prototype rocks were broken limestone where the surrounding rocks were classified as Grade V.Based on the on-site geological survey data,the physico-mechanical parameters of the prototype rocks are listed in Table 2.Artificial mixed materials have been shown to be appropriate for simulating broken surrounding rocks in scale model test(Li et al.,2016b;Gao et al.,2019).Meanwhile,Moncarz and Krawinkler(1981)pointed out that if an adequate model correctly scales the primary features of the problem where the secondary influences are allowed to deviate,the similarity between the prototype and model is not significantly affected.The seepage field of the surrounding rocks,as the key feature of the problem,must satisfy the similarity relationship in this model test,while the similarity of the mechanical parameters should be guaranteed as much as possible.The proportions of simulated materials for the surrounding rocks were determined through a series of laboratory tests,as listed in Table 3.The physicomechanical parameters of the simulated materials are also tabulated in Table 2.

Table 1Geometric,physical and mechanical parameters of surrounding rocks(Grade V).

Table 2Physico-mechanical parameters of surrounding rocks(Grade V).

Table 3Proportions of simulated material(mass ratio to quartz sand).

2.3.Manufacture of scaled tunnel model using 3D printing

2.3.1.Design scheme of Nanyang tunnel

Fig.4a shows the cross-section of the tunnel support for Grade V surrounding rocks.The tunnel is supported by a composite lining,including primary support,secondary lining,invert filling,etc.The CRTS I double-block ballastless track is adopted in Nanyang tunnel,as depicted in Fig.4c.The whole Nanyang tunnel adopts the ODS,and the details of the buried drainage pipe for bottom drainage are shown in Fig.4b.A concrete pipe with a diameter of 80 cm and drain holes on the upper surface is buried approximately 30 cm below the inverted arch.The concrete base supports the drainage pipe,and the pervious concrete is filled in the void between the drainage pipe and the invert.The geotextile covers the upper surface with drain holes to prevent fine particles from blocking the drainage pipe.Moreover,inspection wells are set at a longitudinal interval of 30-50 m,which connects the central ditch and the buried drainage pipe and is used for the maintenance of the buried drainage ditch.

2.3.2.Scaled model for tunnel support and bottom structure

Due to the complex relationship between the position of composite lining and that of the external drainage blind tubes(annular blind tubes and longitudinal blind tubes),it is difficult to fully simulate the tunnel support in the model test.With reference to the research of Li et al.(2016b),a multilayer geotextile is used to simulate the primary support,and the functions of sand isolation,water permeability and permeability reduction are mainly considered in the test.Since track irregularity is one of the main features of invert anomalies for railway tunnel,the fine features of the internal structure of the operating railway tunnel(such as invert filling and railway track)must be simulated.Thus,3D printing technology was used in the production of tunnel model and the production process is shown in Fig.5.

Fig.4.Cross-section diagrams of Nanyang tunnel structure:(a)Tunnel support scheme(unit:cm),(b)Detailed drawing of part A,and(c)Detail drawing of part B(unit:mm).

Concrete is the main component of the tunnel structure.Although the strength grading of concrete at various parts is different,the elastic modulus is approximately the same(28-32.5 GPa).According to the similarity ratio of the elastic modulus(CE=1:40),nylon 11 with an elastic modulus of 1.08 GPa is the closest common material(Li and Wang,2016),thus it was selected as the printing material for concrete.It should be noted that there are differences in the density of the concrete and nylon material.Considering that the gravitational stress balance of the tunnel structure occurs mainly during the construction phase,while the invert anomalies appear during the operational phase when the structure displacement has been stabilized for a long time,the effect of material density differences in the model test is insignificant.Considering the limitations on print size,a 3D model of a scaled tunnel with a prototype size of 14.02 m×11.68 m×14 m(span×height×longitudinal length)was built by 3D modeling software.In this 3D model,the secondary lining,invert filling,track structure and drainage ditches were considered,and the space for transverse drainage blind tubes and transverse connecting blind tubes was hollowed out.The parameters of the scaled tunnel model are listed in Table 4.

2.3.3.Scaled model for tunnel drainage system

The main difference between the two drainage systems is whether a buried drainage pipe is employed.For the TDS,the internal drainage system is manufactured in the scaled model of the tunnel structure,thus only the external drainage blind tubes need to be manufactured.The inner diameter of the scaled drainage blind tube was calculated based on the similarity ratio of the geometric length.In addition,the thickness of the scaled drainage tube was set to 0.8 mm due to the printing limitations of thin-walled structures.Table 4 lists the scaled parameters of drainage system.A 3D model of the external drainage blind tubes was established,and the 3D model was split into five parts to facilitate installation and replacement.Different from the tunnel structure,the drainage system does not participate in structural load-bearing,hence the mechanical similarity is not a requirement for drainage system materials.In view of the advantages of high strength and low cost(Yang et al.,2018),ultraviolet(UV)resin was selected as the printing material of the drainage system.The physical model of the external drain blind tubes after printing and assembly is shown in Fig.5.

A similar process was adopted for the manufacturing of buried drainage pipe,as shown in Fig.5.According to the length similarity,the design parameters of prototype are transformed into the parameters of the scaled model,as listed in Table 4.A 3D model of a drainage pipe with an outer diameter of 20 mm and drain holes on the surface was built by 3D modeling software.Geotextiles were selected to realize the functions of sand isolation and water permeability of prototype geotextiles.Furthermore,two locating blocks were designed to ensure that the buried pipe was fixed 0.75 cm(the prototype depth is 30 cm)below the invert.

Fig.5.Printing and assembly process of operating railway tunnel model with different drainage systems.

Table 4Typical parameters of scaled tunnel model.

2.4.Simulation of drainage system blockage

Decrease in drainage capacity is a common engineering problem during the operation of drainage tunnels,which leads to an increase in EWP and triggers structural deformation and even cracking(Kim et al.,2020).According to current studies,the main causes of decrease in drainage capacity include hydraulic deterioration of the geotextile layer and blockage of the drainage pipes(Jung et al.,2013;Yoo,2016;Chen et al.,2019).These phenomena are usually associated with the deposition of fine particles and the generation of crystallization(Shin et al.,2014;Jang et al.,2015).In this model test,the decrease in drainage capacity was simulated by blocking the drainage pipe for the convenience of test conducting.In tunnels with TDS,three-way pipe that connects the annular blind tube,the longitudinal blind tube and the transverse drainage blind tube has a high risk of blockage,and it is difficult to discover the blockage in a timely manner.Fig.6 shows the typical pictures of drain blockage in the field.In tunnels with ODS,although the additional buried drainage pipe also has the possibility of blockage,it is difficult for the drainage pipe being quickly and completely blocked by the sediment,because of its relatively large crosssection.More importantly,regular dredging of buried drainage pipes can be easily realized through inspection wells.Thus,the reduction of drainage capacity was finally simulated by blocking the three-way pipes in this test.

Four types of plugs were designed based on the blockage area ratio of the transverse drainage blind tube,as shown in Fig.7,including 25% blockage,50% blockage,75% blockage and total blockage.These plugs were installed in the pipe orifice of transverse drainage blind tubes,which can simulate the different degrees of drain blockage from full drainage to total blockage.Considering that the plugs only need to play the role of water plugging,UV resin was also selected as the printing material of the drain plugs due to its low cost and high strength.

3.Model test program

3.1.Model test system

In this study,the tests were carried out on a model test system applicable to water-rich tunnels,as shown in Fig.8.The model test system consisted of a steel frame,test soil box,groundwater control system,water pressure and structure displacement testing device and real-time monitoring devices.The test box with dimensions of 2.45 m×1.9 m×0.35 m(height×width×longitudinal length)was filled with the test soils,which can provide a prototype burial depth of 65 m for tunnel model.The box was assembled by toughened glass to allow the deformation process of the test soil to be observed,and it was wrapped in the high-strength steel frame.The waterproof adhesive was applied to all the joints of the box to produce good waterproofness.The groundwater control system was composed of a water tank,a flow control valve and drainage pipes,which can provide the groundwater level that needs to be set for the test.Micro-osmometers and electronic micrometers were used to monitor the hydraulic pressure and the displacement of the tunnel model,respectively.Finally,computer collected the data in real time.

3.2.Test equipment

Fig.6.Blockage of drainage system in the field engineering:(a)Crystal blockage,and(b)Silt blockage.

Fig.7.Design and installation of plug:(a)3D model of plugs,(b)Plug position,and(c)Plug installation.

Fig.8.Model test system:(a)Design sketch of the test system,and(b)Photo of the test system.

The water discharge,EWP and structure displacement are the essential parameters that reflect the characteristics of the tunnel seepage field and structure stability.In this test,a monitoring crosssection was considered for EWP(JC-1)and structure displacement(JC-2).In cross-section JC-1,eight water pressure sensors were arranged on the external surface of the tunnel model,as presented in Fig.9b.In cross-section JC-2,four vertical displacement sensors were arranged at typical locations,including the vault,the tunnel bottom,inner track and outer track,as shown in Fig.9c.Furthermore,the tunnel discharge was counted by collecting the water flow from the four outlets(two side ditches,a central ditch and a buried drainage pipe).It should be noted that the testing range of micro-osmometer is 0-30 kPa and the testing accuracy is 5 Pa,while the testing range of electronic micrometer is 0-10 mm and the testing accuracy is 0.001 mm.The range and accuracy of the sensors can meet the requirements of the tests.

3.3.Test conditions

In the model test,four types of drainage system layouts were employed,as shown in Fig.10,including two drainage systems and two cases of blind tube spacing.It should be noted that the spacing of the annular blind tube is changed by installing or removing two plugs of total blockage in the middle section.In each case of drainage system layout,various groundwater levels from 0 m to 60 m(seven cases of groundwater level,as shown in Fig.8a)were considered to simulate the variation in groundwater level caused by environmental factors,such as rainfall.The groundwater loading process of the model test is shown in Fig.11.In addition,five conditions of drain blockage were included in the test to simulate the different blocking states of the drainage system in operating tunnels.As listed in Table 5,a total of 110 testing cases were carried out to investigate the effect of design factors and environmental factors on the operation of railway tunnels in water-rich areas.

Table 5Model test cases in prototype.

According to the preset test conditions,the model test procedure is described as follows:

(1)Step 1:The drainage system is modeled and installed in the tunnel model in the model box.

(2)Step 2:The stratigraphic materials are made according to the preset proportion and filled into the model box.

(3)Step 3:The sensors are embedded or installed at the testing position.

(4)Step 4:The groundwater control system is set up and connected to the model box.

(5)Step 5:The conditions of the groundwater level and blockage degree change,and the test results for water discharge,EWP and structure displacement are monitored.

(6)Step 6:The model soils are removed,and the layout of the drainage system is changed.Steps 1 to 5 were repeated for the test in the next case.

4.Test results and engineering application

For convenience of comparison with actual engineering applications,these test results were increased according to their similarity ratios,i.e.the EWP and displacement were increased by 40 times,and the water discharge was increased by 1600 times.

Fig.9.Distribution of monitoring cross-sections and monitoring points:(a)Layout of monitoring cross-sections,(b)Measuring points of water pressure,and(c)Measuring points of structure displacement.

4.1.Test results for drainage system without drain blockage

4.1.1.Tunnel discharge

The drainage flow conditions of Case 1 to Case 4 for different groundwater levels are presented in Fig.12a and b.It was observed that under TDS,the groundwater discharging from external blind tubes flowed through the tunnel ditches(side ditches and central ditch)and finally discharged out of the tunnel,while for the tunnel with ODS,the additional buried pipe also participated in the tunnel drainage.With the increase in the groundwater level,the drainage flow of the two drainage systems increased gradually.There is a good agreement between the drainage characteristics of the model test and those of actual engineering applications.Fig.12c shows the variation curve of the total tunnel drainage of the two drainage systems.It was apparent that there were differences in the drainage volume and growth of the two drainage systems.First,due to the existence of buried drainage pipe,the drainage volume of the tunnel with ODS was significantly greater than that of the TDS,especially after the groundwater level was larger than 30 m.Second,as the groundwater level increased,the growth of the drainage volume of the two drainage systems slowed,but the TDS was more obvious.It was also investigated that reducing the spacing of annular blind tubes can increase the drainage volume.When the prototype spacing was reduced from 10 m to 5 m,the drainage volume of the tunnel with TDS and ODS at the 60 m groundwater level increased from 6.33 m3/(m d)to 9.04 m3/(m d)and 12.83 m3/(m d)to 14.1 m3/(m d),and the growth rates were 42.8%and 9.9%,respectively.This also indicates that reducing the spacing is more effective for the TDS to increase tunnel drainage.

Furthermore,the proportion of drainage sources under the ODS is depicted in Fig.12d.The tunnel drainage included water flow from tunnel ditches and buried drainage pipe.It can be concluded that the tunnel drainage at low groundwater levels is mainly dominated by the buried pipe,and as the groundwater level increases,the external blind tubes gradually play a role in drainage.In addition,reducing the spacing of the annular blind tube will increase the drainage volume of the external blind tubes,but it will also reduce the drainage volume of the buried drainage pipe.

4.1.2.Distribution of external water pressure(EWP)

Fig.13a-d shows the EWP distribution of different drainage systems under groundwater levels of 20 m,40 m and 60 m,and the variation curve of the average EWP at the tunnel bottom(WP-4,WP-5 and WP-6)and the tunnel arch(WP-1,WP-2 and WP-8)with increasing groundwater level is presented in Fig.13e.The characteristics of the distribution and growth of the EWP for different drainage systems or design parameters can be summarized as follows:

Fig.10.Layouts of tunnel drainage systems.

Fig.11.Loading procedure of groundwater level.

(1)There is a significant difference in the EWP at the tunnel bottom under the two drainage systems.For instance,under the TDS(Case 1),the average EWPs at the tunnel bottom of groundwater levels of 20 m,40 m and 60 m were 104.7 kPa,193.4 kPa and 346.5 kPa,respectively,with an increment of 241.8 kPa.However,these values of the tunnel with ODS(Case 3)were 10.8 kPa,31.2 kPa and 67.9 kPa,respectively,with an increment of 57.1 kPa.The average EWP at the tunnel bottom of the latter drainage system was 19.6%of the former when the groundwater level was 20 m,and as the groundwater level increased to 60 m,the ratio fell to only 10.3%.It was apparent that the EWP of the tunnel with ODS at the tunnel bottom is much lower than that of the TDS,and the higher the groundwater level is,the greater the difference in the EWP is.

(2)Reducing the spacing of the annular blind tubes has a limited effect on controlling the EWP at the tunnel bottom.For example,under a groundwater level of 60 m,the average EWPs of the regular spacing(Case 1)at the tunnel arch and tunnel bottom were 249.3 kPa and 344.4 kPa,while these values of the shortened spacing(Case 2)were 194.6 kPa and 321.7 kPa,respectively.This indicates that reducing the spacing of the annular blind tubes can reduce the EWP of the tunnel arch by 21.9%,but only by 6.6%at the tunnel bottom.

It was concluded that even if there is no drain blockage,the TDS has difficulty in controlling high water pressure at the tunnel bottom,especially under high groundwater levels,but the ODS can overcome this shortcoming.

4.1.3.Analysis of structure displacement

Fig.12.Test results of water discharge without drain blockage:(a)Drainage condition of Case 2,(b)Drainage condition of Case 4,(c)Total amount of water discharge,and(d)Proportion of water discharge of Cases 3 and 4.

Fig.13.Test results of EWP(kPa):Water pressure distributions of(a)Case 1,(b)Case 2,(c)Case 3 and(d)Case 4;and(e)Average water pressure at typical parts.

Fig.14 shows the variation curve of the vertical displacement of the tunnel structure,and a positive value represents uplift.There were different forms of structure displacement under the two drainage systems in the test.Under the TDS,as the groundwater level increased,the uplift of the bottom structure gradually increased,and there was a quantitative relationship of“tunnel bottom＞inner track＞outer track”.The increase in the uplift of the tunnel invert would also cause irregularity of the railway track.According to the Chinese specification for track smoothness in operating railway lines(GB/T25021-2010,2010;TB/T3355-2014,2015),once the uplift of the track exceeds 14 mm,the trains must pass through the Nanyang tunnel at a limited speed(normal speed is 250 km/h).Thus,it was also observed that when the groundwater level reached 40 m,the track uplift caused by the unstable invert exceeds the critical displacement,which means that the tunnel must operate at a limited speed after the groundwater level exceeds 40 m.Such test results can explain why the inverts of some railway tunnels,such as Burnley tunnel(Mothersille and Littlejohn,2012)and Gaotian tunnel(Ouyang,2018),are unstable and affect normal operation,especially at a large underwater depth or after heavy rainstorms.Furthermore,a comparison of the results for Cases 1 and 2 shows that reducing the spacing of annular blind tubes can lessen the uplift of the bottom structure,but the effect is limited.Even if the spacing was shortened(Case 2),the track uplift still exceeded the critical displacement under the groundwater level of 40 m.

As to the tunnels with ODS,the structure displacement was mainly caused by the settlement of the vault,and the settlement continued to increase as the groundwater level increased.Due to the effective control of the EWP at tunnel bottom,only a small settlement appeared in the invert structure.Even when the groundwater level reached 60 m,the maximum displacement of the track was only 1.2 mm and significantly smaller than the critical displacement,while uplift of the inner track was up to 35.2 mm under the same condition of tunnel with TDS(Case 1).Therefore,without considering drain blockage,the ODS can effectively control the EWP at tunnel bottom by enhancing the bottom drainage and finally overcome the invert instability problems of the TDS,even at a high groundwater level.

4.2.Test results of drainage system with drain blockage

4.2.1.Tunnel discharge

Fig.15a and b shows the water flow condition under different blockage degrees for the two drainage systems at the groundwater level of 40 m.It was apparent that as the blockage degree increases,the water flow at the outlets of the side ditches and central ditch gradually decreases,while the water flow of the buried pipe seems to increase.The comparison of the drainage volume between the no-blockage condition and total blockage condition is depicted in Fig.15c.There was also a significant difference in the change in tunnel discharge between the two drainage systems after drain blockage.In the tunnel with TDS,the total blockage of external drainage blind tubes represented almost no drainage.Under the ODS,although the decrease in drainage volume was gradually significant as the groundwater level increased,the drainage volume under the total blockage condition at the groundwater level of 60 m still reached 71.2% of the discharge under the no-blockage condition.Fig.15d further shows the effect of blockage on the drainage volume and its proportion under high groundwater levels.It was observed that as the blockage degree increases,the drainage volume of the external blind tubes(drain to tunnel ditches)decreases nonlinearly.For instance,from no-blockage to 50% blockage,the decrease in the drainage volume of the external blind tubes is small,approximately 17.2%-25.3%,while the blockage degree is greater than 50%,the drainage volume decreases sharply to almost 0.This indicated that the effect of the increased degree of drain blockage on the tunnel discharge is more serious at a higher degree than that at a lower degree.Moreover,it was also found that as the blockage degree increases,the drainage volume of the buried pipe gradually increases,and the buried pipe becomes the only drainage outlet of the whole tunnel.Specifically,after drain blockage,the drainage volume of the buried pipe increased from 6.68 m3/(m d)to 10.04 m3/(m d),with a growth rate of 50.3%.Thus,it was concluded that the blockage of drainage pipes has a great impact on the drainage of tunnels with TDS,but has little effect on that with ODS.

4.2.2.Distribution of EWP

Fig.16a and b shows the EWP distribution of the two drainage systems under a high groundwater level of 60 m,and Fig.16c and d shows the variation curves of the EWP at different groundwaterFig.14.Evolution of structure displacement of(a)Cases 1 and 2,and(b)Cases 3 and 4.levels with increasing blockage degree.The characteristics of the distribution and growth of the EWP can be summarized as follows:

(1)For the tunnel with TDS,the increase in the EWP caused by drain blockage was nonlinear,which should be related to the change in tunnel discharge.From no blockage to 50%blockage,the increase in the EWP was relatively small,but after reaching a 50% blockage,the EWP increased significantly.When the groundwater level was 60 m,the increments of the average water pressures at the tunnel bottom and tunnel arch in the previous stage were 76.6 and 64.5 kPa,while these values in the latter stage were up to 189.0 and 233.9 kPa.It was also observed that as the blockage degree deepens,the EWP gradually becomes the hydrostatic pressure of an undrained tunnel;that is,the deeper the groundwater is,the greater the EWP is.It should be noted that after drain blockage,the tunnel bottom is still the part with the highest EWP,and there is also a significant increase in the EWP compared with that of the no-blockage condition,which is a not beneficial for the instability of the invert.

(2)A certain increase in the EWP also appeared in the tunnel with ODS.Due to the different changes in the drainage volume of the external blind tubes and the buried pipe,the EWP at the tunnel arch and side wall experienced a relatively large increase,while the average EWP of the tunnel bottom was still controlled within 150 kPa.In addition,the increase in the EWP at the tunnel arch and side wall also showed the same nonlinearity,i.e.the increment of the EWP after 50%blockage was much greater than that when the blockage degree was less than 50%.Nevertheless,the ODS was still superior to the TDS in controlling the EWP at the tunnel bottom,and under the condition of a groundwater level of 60 m and complete blockage,the average EWP of the tunnel with ODS at tunnel bottom was 111.9 kPa,only 19.1% of that of the tunnel with the TDS.

4.2.3.Analysis of structure displacement

Fig.15.Test results of water discharge with drain blockage:(a)Drainage condition of Case 5 under 40 m groundwater level;(b)Drainage condition of Case 6 under 40 m groundwater level;(c)Total amount of water discharge with the rise in groundwater level;(d)Total amount and proportion of water discharge with the increase in blockage degree.

Fig.16.Test results of EWP with drain blockage:Water pressure distribution under 60 m groundwater level of(a)Case 5 and(b)Case 6,and water pressure of typical parts of(c)Case 5 and(d)Case 6.

The curves of track displacement that vary with the groundwater level and blockage degree are shown in Fig.17.It was apparent that after drain blockage occurs,there is a marked difference in the change in the track displacement of the tunnels with the two drainage systems.In the tunnel with TDS,due to the substantial increase in EWP at the tunnel bottom caused by pipe blockage,the uplift displacement of the track structure was further increased.As a result,the track displacements of the fully blocked tunnel were as high as 15.5 mm and 14.25 mm(inner track and outer track,respectively)at the groundwater level of 30 m,which both exceeded the critical displacement for the limit of the train speed.Thus,the blockage of external blind tubes will further aggravate the invert instability and cause invert anomalies of the operating railway tunnels even at low groundwater levels.Similar nonlinearity appeared in the increase in the track displacement.For instance,under the groundwater level of 60 m,the displacement of the inner track from the no-blockage condition to the condition of 50% blockage was 3.7 mm,while the value from the condition of 50% blockage to the condition of total blockage was as high as 8.6 mm.In addition,it was observed that the increase in track displacement was more significant at high groundwater levels.From the condition of no blockage to total blockage,the uplift of the inner track at groundwater levels of 20 m,40 m and 60 m was 3.5 mm,8.8 mm and 12.3 mm,respectively.It can be concluded that the deepening of the blockage degree has a more serious impact on the invert stability of tunnels with a high groundwater level or a deep blockage degree.More importantly,the drainage system blockage and groundwater level in actual engineering conditions often affect each other,for example,drain blockage might lead to an increase in the groundwater level and further cause more serious invert anomalies.

Fig.17.Test results of track displacement:(a)Track displacement with the rise of groundwater level,and(b)Inner track displacement with the increase in blockage degree.

Fig.18.On-site construction photos:(a)Groundwater gushing from the inclined shaft,and(b)Construction of the buried drainage pipe.

The tunnel invert with ODS was relatively stable in the test.It was found that as the groundwater level rises or the blockage degree increases,a small settlement appears in the track structure,which should be related to the increase in the EWP of the tunnel arch.However,even if the groundwater level reached 60 m and the external blind tubes were fully blocked,the maximum settlement of the railway track was only 1.8 mm,which can maintain the smoothness of the HSR track.Therefore,by effectively controlling the EWP at the tunnel bottom,the ODS can sustain the invert stability and ensure the normal operation of the railway tunnel,even in the case of high groundwater levels and serious drainage system blockage.

4.3.Engineering application

4.3.1.EWP monitoring during the construction period

Fig.19.Distribution of EWP at tunnel bottom tested on site(unit:kPa).

The construction of the Nanyang tunnel started in February 2015 and ended in September 2016.During the excavation of the karstdeveloped sections,the situation of groundwater gushing was relatively serious,as shown in Fig.18a.This verified the water richness of the stratum predicted by the geological survey,and also suggested the necessity of optimizing the tunnel drainage system.The ODS was adopted in the whole Nanyang tunnel.Compared with the TDS,the construction procedure of the ODS was slightly complicated.In the construction of the buried drainage pipe,the steps of trench excavation,trench cleaning,drainage pipe installation and permeable concrete pouring were carried out in sequence,as presented in Fig.18b.In addition,a test section was selected as shown in Fig.3,and seven osmotic manometers were embedded below the invert to measure the EWP at tunnel bottom.Fig.19 depicts the distribution of EWP after two heavy rainfalls during the construction period.It should be noted that a week of continuous heavy rain occurred before June 15,2015,and a heavy rainstorm occurred before July 4,2016.It was found that the on-site EWP of the invert is controlled at a low level,and the average EWP after the two rainstorms was only 38.2 kPa and 83.3 kPa,respectively.The field test results proved the effect of the ODS in reducing the water pressure at the tunnel bottom.Furthermore,it was noticed that the results of the model test and the field test exhibit good consistency in the distribution form of the EWP,which verifies the correctness of the model test.

4.3.2.Displacement monitoring during operation period

After the tunnel operation in 2017,in order to understand the stability state of the invert,manual monitoring of structure displacement was carried out periodically or during heavy rainfall in some sections with the risk of invert anomalies.In each test section,seven measuring points were arranged,as shown in Fig.20.Up to now,a total of three heavy rainfall events have occurred in the tunnel site area,including a torrential rainstorm with a 12-h rainfall of 112 mm in June 2017,a rainstorm with 24-h rainfall of 72.2 mm in July 2019,and a heavy rainstorm with a 12-h rainfall of 94.3 mm in July 2020.Although none of the three rainfall events triggered abnormal train operations,structure displacement monitoring was still carried out during the maintenance period from 0 to 4 a.m.Fig.20 depicts the test results in the EWP test section.Positive value means uplift,while negative value means settlement.The structure displacements in other sections of the tunnel also showed a similar pattern.It was apparent that during the heavy rain,the tunnel invert experiences an overall settlement,but the settlement displacements are relatively small and the maximum settlement of track slab is only 0.91 mm.According to the Chinese specification for the control parameters of operating track(TB/T3355-2014,2015),the vertical displacement of track in Nanyang tunnel with operating speed of 250 km/h shall not be greater than 5 mm.The settlement at the site was obviously lower than the control value,which was not enough to affect the safety of transportation.Meanwhile,it was noticed that the settlement of tunnel invert increases with the increase in rainfall intensity.This phenomenon should be caused by the more significant fluctuation of the groundwater level under high-intensity rainfall,and similar displacement patterns were observed in the model test.Comparing the results of field monitoring and model test,it can also be found that the distribution forms of settlement are relatively consistent and the settlement values show a good agreement.

Fig.20.Comparison of vertical displacement of tunnel invert between model test and field monitoring.

In summary,combined with the EWP test results during the construction period,the engineering application proves that even under heavy rainfall,ODS can effectively control the EWP at the tunnel bottom,maintain the stability of invert structure,and ensure the normal operation of the HSR line.

4.4.Discussion of the results

Some interesting conclusions about TDS can be obtained from the model tests.For a tunnel with TDS,due to the lack of drainage measures below the invert,the EWP at the bottom rapidly increases as the groundwater level rises,and even if the spacing of annular blind tubes is shortened,it is still difficult to effectively control the EWP at the bottom.Then,the uplift of the invert structure is triggered by the high EWP,which is the main reason for the instability of the tunnel invert.Meanwhile,due to the reduction of tunnel drainage,the blockage of external blind tubes also causes a further increase in the EWP and track uplift.Especially when the blockage degree exceeds 50%,the instability of tunnel invert is significantly aggravated.Therefore,based on these experimental results,some suggestions are proposed for operating railway tunnels that use TDS and are at risk of invert anomalies:

(1)Improving the drainage capacity at the tunnel bottom.By installing additional drainage pipes through the invert filling,high-pressure water under the tunnel invert can be discharged into the tunnel drainage ditches,which can reduce the EWP of invert structure.This concept has been validated in the existing studies,such as pin-hole drain method(Shin et al.,2009)and bottom-to-up drainage system(Li et al.,2018).

(2)Construction of auxiliary drainage channels in the strata.When the groundwater pressure is maintained at a high value,it is difficult to effectively reduce the EWP simply by adding new drainage pipes.The construction of a new drainage tunnel adjacent to the operating tunnel is a feasible option,which can lower the height of the groundwater level and thus control the EWP of the operating tunnel.Especially in karst development areas,this measure is widely used in tunnel treatment projects(Dai,2016;Ouyang,2018).

(3)Timely cleaning of blockages in the drainage system.The smoothness of the drainage system should be inspected regularly and the blockages should be cleared in time.When encountering heavy rainfall events,the frequency of inspection should also be increased to prevent blockage problems caused by mud and sand siltation.In particular,it is necessary to avoid the blockage degree of more than 50%,otherwise the resulting adverse effects are usually more serious.In practical engineering,mechanical cleaning and chemical treatment to remove blockages are the most commonly used methods(Chen et al.,2019).Specifically,mechanical cleaning is the use of scrapers or high-pressure water jets to clean up blockages in the drainage pipes,while chemical treatment is to inject mixed reagents to dissolve crystals in drainage pipes.

As to tunnels with ODS,some regularity conclusions were also obtained from the model tests.Tunnel drainage is mainly dominated by buried drainage pipe at a low groundwater level,and as the groundwater level rises,the external blind tubes gradually exert their drainage effect,even exceeding the buried drainage pipe.The EWP at the tunnel bottom is effectively reduced due to the buried drainage pipe,and thus invert instability under high groundwater levels does not appear.Meanwhile,when the external blind tubes are gradually blocked,the drainage volume of the buried drainage pipe increases,which ensures that the EWP of the tunnel bottom is controlled at a low level.However,it should be noted that blockage of external blind tubes leads to a significant increase in EWP at the arch,which is the main cause of water leakage problems at the tunnel arch.Therefore,in the application project of ODS,the setting of external blind tubes and its regular de-clogging are still necessary.Considering the experimental analysis and engineering economy,a spacing of 10-15 m is suggested for the circumferential blind tubes,which was adopted in the construction of Nanyang tunnel.

In the model test,even when the groundwater level was 60 m and the blind tubes were fully blocked,the average EWP at the tunnel bottom was 111.9 kPa,and the railway track experienced a settlement of only 1.8 mm.In the field engineering,under several heavy rainstorms,the maximum average EWP at the tunnel bottom was 83.3 kPa and the maximum settlement displacement of the track plate was only 0.91 mm.Therefore,both model test results and field applications validate that ODS is a feasible solution to prevent the instability of tunnel invert in water-rich areas,and suggest its application to new railway tunnels in water-rich areas.

5.Conclusions

In this study,invert stability of an operating HSR tunnel in a water-rich stratum was investigated by a series of model tests with 6 test groups and 110 test conditions.A variety of environmental and design factors commonly encountered in engineering practice were considered in the model tests,including different forms and layouts of the drainage system,groundwater level fluctuation and blockage of the drainage system.Meanwhile,3D printing technology was introduced to manufacture the scaled tunnel model to refine the detailed structure of the HSR tunnel and visualize the test process.During the test,the water discharge,EWP and structure displacement were measured to reveal the characteristics of the tunnel seepage and displacement fields.According to the test results and engineering application,the conclusions are drawn as follows:

(1)For operating railway tunnels,high EWP at the tunnel bottom causes uplift of the invert structure and then results in track irregularity,which is the occurrence mechanism of invert anomalies in water-rich areas.

(2)Due to the lack of drainage measures at the bottom,high EWP of the invert inevitably exists in the tunnels with TDS under high groundwater level.Even if the spacing of annular blind tubes is shortened,it is still difficult to effectively reduce the EWP,which is the main reason for the frequent occurrence of invert anomalies in HSR tunnels with TDS.

(3)In the tunnels with TDS,blockage of external blind tubes causes a significant decrease in the tunnel drainage and an increase in the EWP,which eventually aggravates the instability of the invert structure,especially when the blockage degree exceeds 50%.However,in tunnels with ODS,the effect of blockage is not as significant,due to the adequate drainage capacity of the buried drainage pipe.

(4)Owing to the additional and effective drainage path below the invert,ODS is able to control the EWP of the invert at a low value.The test results showed that even when the groundwater level was 60 m and the blind tubes were fully blocked,the average of the invert was 111.9 kPa and the railway track experienced a settlement of only 1.8 mm.

(5)The field application proves that ODS can sustain the invert stability and ensure the normal operation of the HSR tunnel.Furthermore,the distribution of EWP and invert displacement from the model tests are in good agreement with the field monitoring,which suggests that the introduction of 3D printing technology to model test is a reliable method to simulate the refined features of operating tunnel.

Limited by the test scheme,the model test explored some typical working conditions,however,some problems existing in the actual engineering may be ignored,such as the situation after the groundwater level exceeds 60 m,adaptability of ODS in different types of strata and possible blockage of the geotextile layer.These practical issues need to be further considered in future research by optimizing the test system and simulation methods.Besides,how to use brittle materials such as gypsum in 3D printing to simulate structural failure and deformation characteristics will also be of our interest.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was supported by the National Natural Science Foundation of China(Grant No.U1934211),the Open Foundation of National Engineering Research Center of High-speed Railway Construction Technology(Grant No.HSR202005),and Scientific Research Project of Hunan Education Department(Grant No.20B596).