Mechanism of Secondary Lining Cracking and its Simulation for the Dugongling Tunnel

Abstract

A large amount of lining cracks, pavement uplift and cable trench overturning occurred during the operation of the Dugongling tunnel, which finally led to the closure of the whole line. The study on the lining cracking mechanism is very important to ensure that the tunnel opens again early. First, the actual cracks of the lining were investigated in the field. According to the geological data, the expansion and softening of the surrounding rock is likely to be the main cause of lining cracking. To verify this inference, a corresponding research program was drawn up. Then, representative sections were selected and the back-analysis method was used to simulate the cracking characteristics of the lining. Based on the simulation results, the cracking mechanisms were studied. The research showed that the increased water content caused the expansion and softening of the surrounding rock, increased the uneven loading on the lining structure, and, finally, led to lining cracking and pavement uplift. Based on the cracking mechanism, progressive enhancement schemes were proposed for each section. The research results of this paper can provide a reference for the design and construction of this project and similar projects.

Introduction

Throughout history, as early as the first tunnel built by Chinese people in the Han Dynasty—the Shimen tunnel (EDCJHT 2015)—tunnels have played an important role in water conservancy and hydropower engineering, traffic engineering, industrial and civil engineering, and even military engineering (Hong 2015). Unfortunately, most tunnels suffer from deformation, leakage, or lining cracking to varying degrees during the construction or operation period. Some tunnels even endanger the safety of people during construction period (Liu et al. 2018; Li et al. 2018; Zuo et al. 2016; Zhu and Li 2017; Song et al. 2016a, b; Zhang et al. 2014; Shuai 2012; Liu et al. 2011a, b). During the construction of the Kuyu water diversion tunnel in Xinjiang, China, shotcrete cracking and steel arch distortion were caused by repeated water immersion (Liu et al. 2018). Plastic bulging appeared in the early supports near the F510 fault of the Youfangping tunnel of the Hu-Kun passenger dedicated line, and the deformation exceeded the clearance limit by more than 80 mm (Zuo et al. 2016). The Shiziya tunnel of former national highway 209 is located in an anhydrite rock layer. After the tunnel was opened to traffic, serious problems such as pavement cracking and lining collapse occurred (Liu et al. 2011a, b). The surrounding rock of the underground caverns of the Jinping I Hydropower Station was seriously deformed due to high in-situ stress, and shotcrete cracking and spalling appeared (Song et al. 2016a, b). The Wenchuan earthquake resulted in a large deformation and serious lining cracks of the Guxi tunnel (Zhang et al. 2014). For small-scale deformation, leakage, or lining cracking, only some simple measures, such as grouting, are required to meet the engineering requirements (Bian et al. 2016). However, for large-scale cases, it is necessary to carry out a special study on the causes and mechanisms of the damage, and then put forward appropriate treatment measures.

In view of the frequent occurrence of large deformation and structure cracking and the severity of accidents caused by such diseases, a large number of scholars have carried out studies on the mechanism and disposal measures of tunnels in the past decades (Meng et al. 2013a, b; Li et al. 2016a, b; Pérez-Romero et al. 2007; Zhang et al. 2017, 2019; Luo et al. 2018; Song et al. 2016a, b). The influence of the magnitude and direction of the second main stress on the large deformation and the failure of the surrounding rock in the main powerhouse of the Houziyan hydropower station has been discussed by Li et al. (2017). In terms of tunnel deformation theory, Wang et al. (2015) established a dynamic failure constitutive model that reflects the deformation and failure mechanism of deeply buried rock masses. Guo et al. (2015) pointed out that the reason for the deformation of soft rock roadways is that traditional support methods and materials cannot control large deformations of deep soft rock. With the help of infrared camera technology and strain monitoring systems, Sun et al. (2018) also studied the deformation mechanism of deeply buried soft rock tunnels.

In addition, deformation often leads to initial support or secondary lining cracking. The cracking mechanism of a tunnel lining under asymmetric loading was studied by Xiao et al. (2014). They pointed out that the burial depth was the main cause of the lining cracking. Cheng et al. (2018) monitored the lining cracking of Zhengzhou metro line 1 where shield construction was adopted. Xia et al. (2015) could effectively control the large deformation and the lining cracking of the Liangshui tunnel for the Chongqing railway by adopting a two-layer initial support and two-layer lining measures. Many tunnels do not deform during the construction period, but develop diseases such as lining cracking during the operation period. Therefore, some scholars have performed research on the cracking of tunnel linings during the operation period (Tan et al. 2018). Chiu et al. (2017) and Lee et al. (2013) studied the crack evolution process of tunnel lining during operation by adopting image mosaic technology. Yan et al. (2018) studied the cracking and failure of the segment lining of underwater tunnels under train impact loading. Wang (2010) has studied the lining cracking mechanism of a tunnel that adjacent to a moving slope based on a description of the spatial distribution, texture, and morphology of the lining cracks. Based on concentrated loss mechanics, Amorim et al. (2014) established a simplified model that can simulate the cracking of a tunnel lining under concentrated forces. Standing and Lau (2017) studied the factors controlling the lining response by establishing a small-scale physical model of a tunnel lining. Liu et al. (2011a, b) studied the tunnel structure damage mechanism of anhydrite in dolomite through a variety of experimental methods. Most of the current studies focus on the deformation of the surrounding rock during the construction period rather than the secondary lining cracking during the operation period. Therefore, it is of great importance to carry out research on tunnel diseases during the operation period, especially for the lining cracking mechanism, to prevent the further development of diseases and ensure the normal operating performance of the project.

Based on the Dugongling tunnel of the Changping expressway in Shanxi Province, the mechanism of lining cracking occurred during the operation period was studied in this paper, as well as the disposal measures. First, the characteristics, scope, and mode of cracking of the secondary lining were summarized through field investigation. Then, a research program was established based on the geological data and tunnel diseases. The cracking mechanism of the lining was studied by the methods of exclusion and back-analysis. Finally, the feasibility of the proposed disposal schemes was discussed and the relevant results were applied to practical projects.

Project Overview

The Changping expressway is an important part of the expressway network of the three-longitudinal, 12-horizontal and 12-ring in Shanxi Province, and it is also an important section of the expressway network of the three-connections and one-ring in Changzhi city. The Dugongling Tunnel is located in the main section of the Changping Expressway, between Qianyagou and Dalinggou Village of Pingshun County. The total length of the left tunnel is 2474 m and the maximum burial depth is 221 m. The total length of the right tunnel is 2515 m and the maximum burial depth is 231 m. The tunnel is a four-lane expressway with separate upstream and downstream traffic. The designed section has a height of 7.1 m, a width of 10.5 m, and a driving speed of 80 km/h. During the operating period and post-construction period, it was found that there were various diseases in the lining structures and pavement, which eventually led to the closure of the tunnel in July 2014.

Geography and Geological Structure

The tunnel site is located in the low and middle mountain areas. The highest point is located at Dugongling Mountain, with a ground elevation of 1498 m. The lowest point is located at the bottom of the Dalinggou ditch, with a ground elevation of 1198 m. The maximum elevation difference is 300 m. The main features of the terrain are that it is high in the middle and low in the east and west, and has a gradual decline from Dugongling to the east and west. The folds in the tunnel site are well developed, but the scales of the folds are not large. The fold is wide and the dip angle of the rock strata is small. K34 + 900 ~ K35 + 200 is composed of two synclines (S1, S3) and one anticline (S2), as shown in Fig. 1. The fault is orthogonal to K34 + 637 and YK34 + 648 of the tunnel. The extension length of the fault is approximately 300 m, and the fault distance is approximately 20 ~ 30 m on the surface of the tunnel site.

Fig. 1
figure1

The geological structures of the tunnel site

Formation Lithology

The stratum lithology of the tunnel site is mainly composed of slope-pluvial loess-like silty clay of the Holocene (Q4dl+pl), slope-pluvial gravel, and Malan loess of the upper Pleistocene (Q3dl+pl) and marlstone and limestone of the upper Majiagou formation in the Middle Ordovician (O2S1 and O2S2).

  1. 1.

    The Q4dl+pl is in a hard, plastic state, with well-developed pores. It is scattered in the tunnel entrance. The thickness is approximately 5 m. Calcareous nodules are sporadically distributed, with a diameter of 10–30 mm.

  2. 2.

    The Q3dl+pl is composed of gravel and Malan loess. The composition of the gravel is mainly limestone, followed by dolomite. The thickness of the gravel is 10–18 m. It is distributed along the roadside that is 50 m to the left of K35 + 550 ~ k35 + 580. The Malan loess is 4–20 m thick and distributed both at the entrance and exit of the tunnel.

  3. 3.

    The O2S2 is the thin-bedded limestone intercalated with thin-bedded marlstone. The mineral composition is mainly calcite with a small amount of dolomite. It contains high-dip fissures. The maximum thickness is 143.5 m. This stratum is mainly distributed in tunnel body and upper mountains.

  4. 4.

    The O2S1 is mainly thin-bedded marlstone with thin-bedded breccia limestone. The main mineral components are calcite and dolomite. Closed high-dip fissures are developed and filled with calcite veins. The maximum thickness is 21.8 m. O2S1 is the main surrounding rock of this tunnel.

Adverse Geological Conditions

The tunneling site mainly includes gypsum, softening marlstone, weakly corrosive groundwater, karst, abandoned mines, and other adverse hydrogeology.

  1. 1.

    Gypsum: At the north side of the tunnel exit to the village road of Dalinggou village, there is a layer of marlstone with a maximum thickness of 8.0 m. The gypsum is contained in the marlstone and the single layer is 1–2 m thick and 4–5 m long.

  2. 2.

    Softening marlstone: There are marlstones in section I of the upper Majiagou Formation in the Middle Ordovician around the tunnel. The marlstones will soften when exposed to water, but when it loses water, it will collapse and its strength will decrease.

  3. 3.

    Groundwater: The groundwater at the tunnel site is the perched water, which is replenished by precipitation. The ground water causes weak corrosion of the concrete and steel.

  4. 4.

    Karst: Karst ditches and grooves are developed in the surface of the tunneling site, but karst caves are not.

  5. 5.

    Mine pits: There are more than 100 abandoned iron ore pits distributed on the surface of section of K34 + 500 ~ K34 + 800. The visible depth is 1.5–9.0 m, which provides good conditions for precipitation infiltration.

Cracking Characteristics of the Secondary Lining

The Dugongling tunnel was damaged in the late construction and operation period (see Figs. 2, 3, 4). The main failure modes were cracking of the secondary lining, overturning of the cable trench, uplift, and cracking of the pavement. The damage to the left tunnel was more severe than that of the right tunnel.

Fig. 2
figure2

Photos of the cracking of the secondary lining: a longitudinal crack; b circumferential crack; and c oblique crack

Fig. 3
figure3

Photos of the overturning of the cable trench: a rupture failure; b overturning

Fig. 4
figure4

Photos of the uplift and cracking of the pavement: a longitudinal crack; b oblique crack; and c cavity

Failure Characteristics of the Left Tunnel

The failure characteristics of the left tunnel are described below.

  1. 1.

    Cracking of the Secondary Lining

The lining cracks are mainly longitudinal and transverse cracks, accompanied by some oblique cracks. The cumulative length of the cracks is 1580 m, accounting for 63.86% of the total length of the tunnel. Most of the cracks are distributed in the height range of 0–2 m of the tunnel wall. The cracks in the vault are less than that in the sidewalls, which are only distributed in the section of K35 + 050 ~ K35 + 185. In addition, the damage degree of the left and right walls of the secondary lining is basically the same.

  1. 2.

    Overturning of the Cable Trench

Overturning of the cable trench mainly occurs in the left side of the tunnel. There are 34 deformed segments of the cable trench, with a total length of 523.5 m. Among them, 25 segments are in the left of the tunnel, with a length of 391 m, and 9 segments are in the right of the tunnel, with a length of 132.5 m. The deformation features are mainly the inward inclination of the top surface of the cable trench. The damaged segments in the left side of tunnel are nearly three times as that in the right side. Moreover, the damage of the cable trench in the left side of the tunnel is more severe than that in the right side.

  1. 3.

    Uplift and Cracking of the Pavement

There are six instances of uplift of the pavement, with a total of 207 m, accounting for 13.1% of the total length of the tunnel diseases. There are 12 cracks in the pavement, ten of which are associated with the uplift of the pavement. In addition, the road surface has a drum deformation, and there are cavities under the road surface.

Failure Characteristics of the Right Tunnel

The failure characteristics of the right tunnel are described below.

  1. 1.

    Cracking of the Secondary Lining

Longitudinal and transverse cracks are the main ones which are accompanied by some oblique cracks. The cracks mainly occur in four segments, with a total length of 850 m, accounting for 33.80% of the tunnel length. Most of the cracks are in the height range of 0–2 m of the sidewalls and less are in the vault of tunnel. The lining damage degree is equally in the left and right walls.

  1. 2.

    Overturning of the Cable Trench

Overturning of the cable trench is mainly concentrated on the right side of the tunnel. There are 26 deformed segments of the cable trench, with a total length of 384 m. Among them, 16 segments are on the right side of the tunnel, with a length of 238.5 m, and 10 segments are on the left side of the tunnel, with a length of 145.5 m. The main deformation features are mainly the inward inclination of the top surface of the cable trench. Moreover, the inclination of the cable trench on the right side of the tunnel is more serious than that in the left side.

  1. 3.

    Uplift and Cracking of the Pavement

There are two instances of uplift of the pavement, with a total length of 60 m, accounting for 7.06% of the total length of the damaged tunnel. There are nine cracks in the pavement. For K34 + 980 ~ K35 + 010, the length of the uplifted pavement is 30 m, showing slight bilateral uplift and serious central uplift. The maximum uplift height is approximately 140 mm.

Study on the Lining Cracking Mechanism

Preliminary Study

According to past experience, the main causes of lining cracking are high geostress, increased creep deformation, excessive construction loads, unqualified lining, and expansion softening of the surrounding rock (Li et al. 2016a, b). Based on geological and quality inspection data, the cracking mechanisms of the lining are studied by a combination of exclusion and self-certification.

  1. 1.

    High Geostress

The maximum burial depth of the tunnel was approximately 230 m, and the surrounding rock was mainly of poor grade IV and V, belonging to weakly and moderately weathered rock mass. The fissures and karst were extremely developed. Karst caves and fissures in the rock mass provided a channel for groundwater seepage. The seepage rate in the tunnel during the construction was up to 31 m3/day. Besides, several boreholes in the tunnel exhibited airflow, which indicated that the fractures had a good connectivity with outside. Neither the seepage nor the good connectivity of the surrounding rock is the characteristics of high geostress strata. Moreover, the characteristics of high ground stress such as core cake were not found both in the detailed exploration stage and construction period.

In addition, although folds developed in the tunnel site, the scale is not large, and all the folds are open folds, with small dip angles and weak tectonic movement. The strength of marlstone at the sidewall of the tunnel is relatively low. The average uniaxial saturated compressive strength is only 16.8 MPa. The strength of marlstone at the bottom of the tunnel is relatively high. The average uniaxial saturated compressive strength is 56.8 MPa. According to geological data, the maximum horizontal principal stress is approximately 2.5–3.0 MPa, and the maximum vertical principal stress is approximately 5.0–6.5 MPa. With this, the strength–stress ratio of marlstone around the tunnel can be calculated both by the measured maximum principal stress value and the maximum principal stress value perpendicular to the tunnel axis. The strength–stress ratios of the sidewalls are 5.60 and 7.07, respectively, and the strength–stress ratio of the bottom of the tunnel is 17.48 and 22.01, respectively. Therefore, the marlstone of this tunnel is not within the range of high geostress no matter according to French and Japanese standards or domestic codes. The possibility of high geostress can be ruled out qualitatively and quantitatively.

  1. 2.

    Creep Deformation

Creep is a typical mechanical property of rock. Long-term creep after tunnel excavation can be the main causes of lining cracking. The large deformation caused by creep even affects the normal use of some tunnels. However, for the Dugongling tunnel, no large deformation was found during the construction period, and only a few diseases appeared in the late period of tunnel construction (i.e., after the lining was constructed). Therefore, creep is unlikely to be the main cause of lining cracks and other diseases. Besides, some creep tests were carried out to further explore the creep characteristics of the surrounding rock. Since the mechanical properties of limestone are obviously better than those of marlstone, creep tests were only carried out for the saturated marlstone, and some test curves are shown in Fig. 5.

Fig. 5
figure5

Creep curves of marlstone with gypsum at the a sidewall and b the bottom of the tunnel

From Fig. 5, it can be seen that for marlstone at the sidewalls of the tunnel, when the load is less than 8 MPa, the strain rate continues to decay until it tends to zero, while when the load is greater than 8 MPa, the creep rate remains constant and the creep deformation continues to develop. For the marlstone at the bottom of the tunnel, the creep effect is not obvious. When the load is close to the yield stress, brittle failure occurs very quickly. The results of the geostress test show that the vertical principal stress of the tunnel is only 5.0–6.5 MPa. It can be seen that neither the soft marlstone on the sidewalls nor the hard marlstone at the bottom of the tunnel will exhibit substantial creep deformation under the action of geostress. Therefore, based on the measured deformation and the creep test results, creep can be ruled out as the main cause of the lining cracking of the Dugongling tunnel.

  1. 3.

    Excessive Construction Loads on the Lining

According to the construction records, the secondary lining was applied after the deformation of the tunnel has reached stability, that is, 2 months after the initial support construction. This means that the lining does not bear the construction load. Therefore, the construction load can be excluded as a cause of the cracking of the lining and the uplift of the pavement.

  1. 4.

    Unqualified Lining

The design strength grade of the lining concrete was C25. According to the test results, the design strength of the second lining was basically the same as the conversion value of the ultrasonic strength. The concrete strength of each measuring area met the design requirements. The passing rate of 930 test points for the thickness of the secondary lining was 94.1%. The thickness of the secondary lining met the design requirement. There were 66 sections of supporting steel frame and 17 sections of reinforced concrete lining in the tunnel. Although the measured values for the spacing of steel frame or bars in a few sections were slightly larger than the design value, the remaining sections all met the design requirements. A total of 496 test points were taken for the pavement and the thickness of the concrete layer, with a passing rate of 98.8%. The tunnel pavement and the thickness of the concrete layer were assessed as qualified. The above test data showed that the construction quality of the tunnel lining was good. Therefore, the unqualified lining can be ruled out as the main cause of the lining cracking.

  1. 5.

    Expansion and Softening of the Marlstone with Gypsum

The Dugongling tunnel passes through marlstone with gypsum in the upper Majiagou formation in the Middle Ordovician (O2S1). To determine the content and distribution range of gypsum, drillings were carried out. It can be seen from the test results of the drilled rock samples that (1) the main components of the surrounding rock are calcite, dolomite, quartz, potash feldspar, plagioclase, and gypsum. Among them, the gypsum content is the largest, reaching more than 90% in some samples; (2) in 121 tunnel sections, 42 of them, accounting for 34%, have been tested to have gypsum, which has a discontinuous distribution; and (3) almost all marlstone strata of this project contain varying degrees of gypsum. In addition, laboratory tests show that both marlstone and gypsum have the characteristics of expansion and softening when exposed to water. The saturated free expansion of marlstone ranges from 0.16 to 0.94%, and the softening coefficient ranges from 0.20 to 0.65. The expansion force of gypsum is more than 90 times that of marlstone, and the softening coefficient is 0.8 times that of marlstone. It is obvious that the marlstone with gypsum, once exposed to water, will experience significant softening and uneven expansion, thus increasing the load on the lining structure.

According to the meteorological observation data from 2010 to 2013, the annual precipitation in 2013 was the highest, reaching 719.2 mm. In 2012, the annual precipitation was the smallest, which was only 491.8 mm. The relationship between the rainfall and water content of the surrounding rock of the Dugongling tunnel in 2013 is shown in Fig. 6.

Fig. 6
figure6

Curves of rainfall and water content of the surrounding rock in 2013

Figure 6 shows that the water content of the surrounding rock has a direct correlation with the rainfall. The monitoring data of the pressure box showed that the pressure of the surrounding rock increased obviously during the rainy season and reached a maximum value for the year; while in the dry season, the expansion force decreased obviously and reached a minimum value. Both the geological conditions and the hydrometeorological data indicated that the expansion and softening of marlstone with gypsum may be the main cause of lining cracking.

In addition, no large deformation or other problems occurred during the construction period. However, in October 2013, just 5 months after the opening for operation, cracks appeared in the tunnel lining. This process was not consistent with the deformation process caused by creep and high geostress, but was completely consistent with the expansion and softening process of marlstone when exposed to water. The underground water level of the tunnel was 400 m below the ground, and the maximum buried depth of the tunnel was only 230 m. Therefore, the groundwater around the tunnel was mainly the perched water from rainfall. After excavation, the seepage boundary changed, the groundwater was discharged into the tunnel, and the groundwater in the surrounding rock was lost. After the construction of the lining, the drainage channel was blocked, resulting in the accumulation of rainwater around the tunnel, and the water content of the surrounding rock gradually recovered. In addition, the 5 months after the tunnel opened happened to be a rainy season with the highest rainfall in recent years. Thus, the marlstone with gypsum expanded and softened, which might cause the lining cracking and other diseases.

Based on the above analysis, it was preliminarily concluded that the internal mechanism of the lining cracking, pavement uplift, and cable trench overturning of the tunnel was the expansion and softening of the marlstone with gypsum, and the external cause was the change of water content of the surrounding rock.

Numerical Simulation of Lining Cracking

The lining cracking of typical tunnel sections was simulated using the numerical simulation software FINAL. The cracking mechanism of the tunnel lining was demonstrated using the back-analysis method. The FINAL software is finite-element simulation software developed by professor Swoboda’s team in Austria. The software has 32 types of elements, which can simulate the dynamic and static problems of underground engineering, slope engineering, and foundation engineering. The software has been applied to a large number of practical projects, such as the London subway in the UK and the underground powerhouse of the Jinping Hydropower Station in China.

Representative Sections

Four representative sections, YK34 + 985, ZK34 + 721, ZK35 + 045, and ZK35 + 285, were selected according to the actual diseases, geological conditions, tunnel depth, and support structures, as shown in Table 1. The first representative section is used for the back-analysis and simulation of tunnel diseases, and the last three are used to verify the cracking mechanism of the lining. In the geological report, marlstone with high gypsum content is called marlstone with gypsum, while marlstone with low gypsum content is directly called marlstone. For the convenience of the following analysis, they are collectively referred to as marlstone with gypsum.

Table 1 Representative sections of the Dugongling tunnel

Parameters for the Numerical Simulation

  1. 1.

    Parameters of the Surrounding Rock

The parameters required for the numerical simulation were based on the geological drillings of the adjacent sections and relevant design manuals, as shown in Table 2. The locations of the geological drillings used for each representative section were ZK34 + 990, ZK34 + 822, ZK35 + 045, and ZK35 + 295. However, due to limited space, detailed information of each drilling was not given in this paper.

  1. 2.

    Expansion and Softening Parameters

Table 2 Physical and mechanical parameters of the surrounding rock

It is preliminarily inferred that the lining cracking was caused by the expansion and softening of the marlstone with gypsum. Therefore, the expansion and softening characteristics of marlstone with gypsum must be taken into account in the numerical simulation. The relevant parameters include the softening coefficient, expansion coefficient, and water content.

The tunnel excavation changed the seepage boundary of the groundwater, causing groundwater to drain into the tunnel. In the early stage of construction, the drainage volume was large, and the partial section reached 31 m3/day, but with the passage of time, the seepage volume gradually decreased. Since the groundwater around the tunnel was mainly perched water, the drainage volume of the tunnel increased during the rainy season every year. Just before the lining construction took place, that is, in spring 2012, the drilling data showed that the surrounding rock around the tunnel was basically dry. After the lining was constructed, the original leakage channels were blocked, and the surrounding rock gradually returned to a saturated state. Therefore, it was assumed that the initial water content of the marlstone with gypsum was zero, and the final water content was the saturated water content. The expansion-softening parameters of pure marlstone are shown in Table 3. Since the expansion of gypsum was much greater than that of marlstone, the expansion-softening parameters of marlstone with gypsum were obtained by back-analysis.

Table 3 Expansion and softening parameters of the pure marlstone

According to the definition of the expansion coefficient α, it can be expressed as:

$$ \alpha = \frac{{e_{{\text{p}}} }}{{W_{{\text{H}}} - W_{0} }}, $$
(1)

where ep is the expansion rate, WH is the saturated water content, and W0 is the initial water content.

According to Table 3, the mean values of the softening coefficient and free expansion rate of marlstone are 0.425 and 0.55%, respectively. According to formula (1), the mean values of the free expansion coefficient is 0.088.

  1. 3.

    Parameters of the Support Materials

The material parameters of the supporting structure are mainly based on The Highway Tunnel Design Code (JTG D70-2004), as shown in Table 4.

Table 4 Material parameters of the support and pavement structures

Back-Analysis Method

The expansion-softening parameters of marlstone with gypsum are not given in Table 3, which could be obtained by the back-analysis method. The back-analysis process is performed as follows: (1) the support structures and expansion-softening process of the tunnel are simulated in the way of geometry and mechanics; (2) the stress field, the deformation field, and the stress and deformation laws of support structures are studied; and (3) the simulation results are compared with the actual deformation and stress, and then, the analysis parameters are fed back and adjusted until the difference between the numerical results and the measured values is within a reasonable range. The reasonable difference for this theory can be expressed as:

$$ \Phi_{\min } = \sum\limits_{i = 1}^{n} {(U_{m}^{i} - U_{c}^{i} )^{2} } , $$
(2)

where i is the key point number on the secondary lining; Umi is the target value of point i, that is, the deformation monitoring value or design strength of the lining; and Uci is the numerical value corresponding to Umi. When Φ = Φmin, the optimal solution of the parameters is obtained.

According to the FINAL software, the softening and expansion of the surrounding rock were considered using the softening coefficient k, the expansion coefficient α, and the change value of the water content △ω. When the surrounding rock expands, the expansive stress can be expressed as follows:

$$ \sigma = E \cdot \alpha \cdot \Delta \omega \cdot V_{0} , $$
(3)

where σ is the expansion stress, E is the deformation modulus, α is the expansion coefficient, △ω is the change value of the water content, and V0 is the initial volume of the rock mass.

When expansion occurs, the equivalent expansion load is:

$$ \left\{ {F_{ex} } \right\} = \sum\limits_{i = n}^{m} {\int\limits_{Si} {\left[ B \right]_{i}^{T} \left\{ \sigma \right\}{\text{d}}A} } , $$
(4)

where {σ} is the expansive stress field and [B]i is the geometry matrix of unit i.

In addition, curved beam element was used to simulate the shotcrete and lining structure, and bar element was used to simulate the system bolt and random bolt. The grouting effect was simulated by increasing the deformation modulus and strength parameters of the surrounding rock. The reinforcing effect of the steel mesh and steel arch frame was simulated by increasing the modulus and strength of the relevant concrete. Because the left and right line spacing of the Dugongling tunnel was more than 20 m, which was more than two times the tunnel diameter, the interaction between the left and right tunnels was not considered in the numerical simulation (Ng et al. 2004). The surrounding rock adopt the Mohr–Coulomb constitutive model and the lining adopt the elastic constitutive model. The geostress was simulated according to the measured value in the geological survey report. The key points of the back-analysis are illustrated in Fig. 7.

Fig. 7
figure7

The key points for the back-analysis

Simulation and Results of the Lining Cracks

In this section, the representative section of YK34 + 985, located in YK34 + 930 ~ YK35 + 095 of the right tunnel, was selected to demonstrate the cracking mechanism of the lining using the back-analysis method. The main diseases in this section were the dense distribution of cracks. These were primarily longitudinal cracks, accompanied by a small number of transverse and oblique cracks. The cracks were mainly distributed in the height range of 0–2 m of the sidewalls. The widths of the cracks were 0.2–2.5 mm. The damage degrees of the left and right sides of the tunnel were similar. The pavement uplift showed a trend of high on the left and low on the right. The maximum value of the pavement uplift was approximately 140 mm.

  1. 1.

    Geological and Numerical Model

The section of YK34 + 985 is on the east side of anticline S2 and the west side of syncline S1. The occurrence of the strata is 122°∠25°. The dip angle of the strata on the section of YK34 + 985 is 21.58°. The geological model is shown in Fig. 8. The finite-element model and its detailed diagrams are shown in Fig. 9.

  1. 2.

    Simulation Results of the Lining Cracks

Fig. 8
figure8

The geological model of the section of YK34 + 985

Fig. 9
figure9

The numerical model of the section of a YK34 + 985 and b its details

The parameters in Tables 2, 3, and 4 were used as the initial values to simulate the deformation and cracking of the lining and pavement. The simulated deformation of the lining is shown in Fig. 10.

Fig. 10
figure10

Simulated lining deformation of the section of YK34 + 985

From Fig. 10, it can be seen that the left part and the middle part of the pavement show uplift deformation, and the uplift in the left arch foot is higher than that in the middle. Convergent deformations appear in the sidewall and the left arch foot. There are cavities between the pavement surface and cushion, the cushion and backfill, and the backfill and inverted arch. The left cable trench is separated from the lining, and the sidewalls of the cable trench on both sides of tunnel are inclined. There is substantial tensile stress in the sidewalls, the right arch foot, and the middle point of the pavement. The maximum tensile stress is on the right sidewall, which is approximately 1.25 MPa. The simulated disease features is coincided with the actual diseases in Table 1, indicating that the main cause of the lining cracking is probably the expansion and softening of the marlstone with gypsum.

To further verify the cracking mechanism of the lining, the expansion coefficient and softening coefficient were inverted based on the monitored deformation and the design strength of the lining. When the expansion coefficient of the marlstone with gypsum is 0.10–0.12 and the softening coefficient is 0.4–0.6, the simulated deformation and stress are shown in Table 5.

Table 5 Stress and deformations at the key points of the section of YK34 + 985

From Table 5, it can be seen that there is a large tensile stress on the sidewall and arch foot of the lining, while other parts are mainly subjected to compressive stress. The tensile stress of the sidewall is greater than the designed tensile strength of C25 concrete. Especially for the right sidewall, the tensile stress is even greater than the ultimate tensile strength. The tensile stress value of the right arch foot is approximately 1.21 MPa. Although this value is less than the designed tensile strength, there is still a trend of cracking. The diseases inferred from the lining stress is consistent with the actual diseases described in Table 1. The simulated deformation values of the midpoint of the pavement and left sidewall are 91.38 mm and 24.56 mm, respectively. The deformation of the left sidewall is approximately 26.9% that of the pavement. From October 5, 2014 to May 31, 2015, the measured uplift deformation of the midpoint of the pavement is 24.3 mm, and the convergence value of the left sidewall is 6.3 mm. The latter is approximately 25.9% of the former. The measured values are basically equal to the simulation results for the deformation ratio of the sidewall to the pavement. The difference in the absolute values is mainly due to the late installation of the monitoring points and only partial deformation was collected. In addition, the maximum value of the monitored deformation of the pavement is approximately 140 mm, which is coincided with the simulated deformation of 130.56 mm. When the surrounding rock is at different saturation, the simulated deformation and cracks of the lining are shown in Fig. 11.

Fig. 11
figure11

Deformation of the secondary lining under the expansion and softening of the surrounding rock at saturations of a 0%, b 20%, c 40%, d 60%, e 80%, and f 100%

As shown in Fig. 11, with increasing saturation, the expansion-softening effect of the surrounding rock gradually develops, which is reflected in the deformation process of the sidewall and pavement. When the surrounding rock is saturated (Fig. 11f), the uplift of the pavement is very severe. Moreover, there is a large convergence deformation from the sidewall to the arch foot. The simulation results are in good agreement with the actual diseases described in Table 1.

In conclusion, under the back-analysis parameters, both the overall failure mode of the tunnel and the stress and deformation of the key points are in good agreement with the measured results. The mechanism of lining cracking and pavement uplift of the section of YK34 + 985 is really the expansion and softening of marlstone with gypsum around the tunnel.

Study on the Mechanism of Lining Cracking

The expansion-softening effect has been proven to be the main cause of lining cracking of YK34 + 985, but whether it is applicable to the whole tunnel still needs further verification. In this part, three representative sections of ZK34 + 721, ZK35 + 045, and ZK35 + 285 are selected in the left tunnel to further verify the aforementioned failure mechanism. Due to space limitations, the detailed simulation process of the ZK35 + 285 is given, while only the simulation results are given for the other two sections.

Geological and Numerical Model

The section of ZK35 + 285 is not in the fold zone, so the strata have a near-horizontal distribution. The geological model is shown in Fig. 12. The numerical model and its detailed diagrams are shown in Fig. 13.

Fig. 12
figure12

The geological model of the section of ZK35 + 285

Fig. 13
figure13

The numerical model of the section of a ZK35 + 285 and b its details

Simulation Results of the Lining Cracks

According to the above cracking mechanism, the simulated deformation and cracks of the lining are shown in Fig. 14. The inversion values of the expansion and softening coefficient are 0.09–0.116 and 0.35–0.52, respectively.

Fig. 14
figure14

Lining deformation of the section of ZK35 + 285 by back-analysis

From Fig. 14, it can be seen that the pavement of this section is severely damaged. There are cavities between the different layers of pavement and there are cracks along the tunnel axis. The sidewall is deformed outwards, but the vault is almost undeformed. The cable trench is inclined outwards seriously. The above diseases indicate that the simulation results are in good agreement with the actual diseases in Table 1. In addition, for better explanation, the simulated stress and deformation of key points of lining structure are shown in Table 6.

Table 6 Stress and deformations at key points of the section of ZK35 + 285

From Table 6, it can be seen that tension stress occurs at the arch foot of the lining and the vault as well as at the midpoint of the pavement. The tension stress at the arch foot and arch bottom is no more than 0.30 MPa. However, the tension stress in the middle of the pavement is as high as 4.08 MPa, which exceeds the designed tensile strength of C25 concrete. This results in substantial longitudinal cracks in the middle of the pavement. Table 6 shows that the ratio of the convergence of the right sidewall to the pavement uplift is approximately 19.6%. From September 12, 2014 to May 31, 2015, the measured convergence of the right sidewall and the uplift of the pavement are 14.7 mm and 132.2 mm, respectively, with a ratio of 18.8%. The measured values are basically equal to the simulated results regarding the deformation ratio of the sidewall to the pavement. The difference in the absolute values is mainly due to the late deployment of the monitoring points and the fact that only part of the deformation values was collected. In addition, the monitoring value of uplift deformation in the middle of the pavement was approximately 138.6 mm, which is in good agreement with the simulated value of 135.27 mm.

The simulated diseases of the ZK34 + 721 and ZK35 + 045 sections under the action of expansion and softening of the surrounding rock are shown in Fig. 15.

Fig. 15
figure15

Lining deformation of the sections of a ZK34 + 721 and b ZK35 + 045

It can be seen from Fig. 15 that the simulated cracking and deformation of the lining are in good agreement with the actual diseases in Table 1. The main diseases of the ZK34 + 721 section are lining cracking and floor caving. The measured deformation of the pavement is 38.7 mm, while the simulated value is 40.2 mm. The section of ZK35 + 045 has long and wide longitudinal cracks, and the pavement uplift and floor void are very severe. The measured deformation of the pavement is 130 mm, while the simulated deformation is 138.0 mm.

In conclusion, based on the simulation results for the above four typical sections, it can be concluded that both the overall failure mode of the tunnel and the stress and deformation of the key points are in good agreement with the measured results, which fully proves that the main cause of the lining cracking is the expansion and softening of the marlstone with gypsum.

Discussion on the Cracking Mechanism

Combined with the geological data and lining test results, the possibilities of lining cracks caused by high geostress, creep deformation, construction loading, and unqualified lining were excluded. It was inferred that the lining cracking was caused by the expansion and softening of the marlstone with gypsum in the presence of water. The representative section of the right tunnel was simulated by the software of FIANL. The simulation results were in good agreement with the field investigation and the measured values. Then, the mechanism was extended to the left tunnel, and good simulation results were also obtained. The simulation results proved the correctness of the inference that the mechanism of the cracking of the lining and the uplift of the pavement was the expansion and softening of the marlstone with gypsum.

The expansion and softening of the marlstone around the tunnel was triggered by the increase of water content. According to the geological data, the underground water level of the tunnel was 400 m below the ground, and the maximum buried depth of the tunnel was only 230 m. Therefore, the groundwater around the tunnel was mainly the perched water from rainfall. After the excavation, the seepage boundary changed, resulting in a decrease of the water content of the surrounding rock and dry shrinkage deformation of the marlstone with gypsum. However, after the lining was constructed, the seepage boundary was blocked, resulting in a gradual increase of the water content and a gradual softening and expansion of the marlstone with gypsum. As a result, the non-uniform load acts on the lining structure. The increasing process of the lining load is in good agreement with the development process of tunnel diseases obtained by field statistics, as shown in Figs. 16 and 17.

Fig. 16
figure16

Statistical chart of the diseases length of the Dugongling tunnel in past years

Fig. 17
figure17

Statistical chart of the overall conditions of the Dugongling tunnel

According to Fig. 16, there were almost no diseases in the tunnels during the excavation stage when the seepage passage was not blocked. However, diseases developed gradually after the initial support was applied. In particular, after pouring the secondary lining, the diseases developed rapidly, and showed a tendency of fast first and then slow. The length of the tunnel diseases developed fastest in 2013 and 2014. In those 2 years, the increased length was approximately 1765 m, accounting for 76% of the total length of the diseases. Then, the length of the diseases tended to a fixed value. According to Fig. 17, the diseases were becoming more and more serious over time. The tunnel length of class 1 and 2 decreased year by year from 2014 to 2017, with total decreases of 66 m and 70 m, respectively. The length of class 5 increased gradually over 3 years, increasing by 215 m and 86% in total. Among them, from 2014 to 2015 and 2015 to 2016, the fastest increase occurred, with an annual increase of more than 80 m. In particular, from February to July 2014, the cracking length of the lining increased from 157 to 215 m, with an increase of nearly 40%, which was consistent with the time of rainfall in this region. The development process of the damage to the tunnel was closely related to the construction and operation process of the tunnel. There was a functional relationship between the diseases and the changes of water content of surrounding rock.

It can be concluded that the lining cracking and the pavement uplift were caused by the increase in the uneven load. The uneven load was caused by the expansion and softening of the marlstone with gypsum. The expansion and softening of the marlstone with gypsum was caused by the increase of the water content after the construction of support structure. Similar diseases also occurred in the Shiziya tunnel in the Yiba segment of the Hang-Lan highway (Liu et al. 2011a, b). When the tunnel opened to traffic, there were many diseases such as pavement cracking, side ditch deformation, lining collapse, and so on. Liu et al. (2011a, b) pointed out that part of the tunnel was located in the dolomite layer, which contained high-purity gypsum. The lateral expansion rate was 1.7–2.3%. The average annual rainfall in this area was 1117.9 mm. Thus, the tunnel diseases were occurred. In addition to the expansion of the gypsum, the marlstone in the Dugongling tunnel also exhibited the characteristics of expansion and softening. Moreover, the karst ditches and mining pits provided good conditions for precipitation infiltration. It is very similar in the diseases and mechanisms of the Dugongling tunnel and the Shiziya tunnel. This is another proof of the mechanism of lining cracking proposed in this paper.

Due to the lack of some experimental data, some numerical parameters, such as the expansion and softening parameters, were not accurate. Therefore, the expansion and softening parameters of the surrounding rock were studied using the back-analysis method. These parameters mainly included the water content, expansion coefficient, and softening coefficient. In view of the fact that too many inverted parameters would lead to multiple solutions, the water content of the marlstone was assumed according to the climate and geological conditions. It was assumed that the water content of the marlstone with gypsum before the lining construction was zero. At the same time, it was assumed that the expansion coefficient and softening coefficient had the same varying tendency. In the back-analysis, the criterion for judging the cracking of the lining was the designed tensile/compressive strength of the concrete. The deformation criteria mainly were the deformation ratio between the sidewall and the pavement. Although the stress and deformation of the key points obtained by the numerical simulation were in good agreement with the criterion values, the previous assumptions lead to the inconsistency between the simulated and measured values. In addition, the monitoring sections were not the representative section and the cumulative monitoring time was relatively short. Therefore, the parameters obtained by the back-analysis method were not the actual parameters, but equivalent parameters to meet the needs of engineering accuracy. According to the previous analysis, the cracking mechanisms and back-analysis parameters can meet the needs of this project, and can be used to study the disposal measures.

Disposal Measures of the Lining Cracks

Based on the cracking mechanism and original design scheme, several disposal schemes were proposed. The feasibility of disposal schemes for each section under the action of expansion and softening was studied using numerical methods. Due to space limitations, only two sections of YK34 + 985 and ZK35 + 285 are given below.

Disposal Schemes

(1) YK34 + 985

A. Replace the inverted arch and secondary lining

First, the lining, inverted arch, and pavement were removed, and then replaced them with concrete of equal strength and thickness.

B. Replace the inverted arch and secondary lining, and install prestressed bolts

First, the lining, inverted arch, and pavement were removed, and then replaced them with concrete of equal strength and thickness. In addition, five prestressed bolts with a prestress of 10 ton, a length of 6 m, and a spacing of 1 m × 1 m were applied to the sidewalls.

(2) ZK35 + 285

A. Replace the inverted arch

First, excavated the inverted arch and pavement, and then replaced them with concrete of equal strength and thickness.

B. Replace the sidewalls and install prestressed bolts

The original sidewalls were removed and replaced with C25 reinforced concrete. The thickness of the reinforced concrete was 50 cm. The inverted arch would not be demolished, but would be reinforced by grouting with five D42 tubes. The length of the D42 tube was 8 m. In addition, seven prestressed bolts with a length of 10 m and a diameter of 28 mm were installed under the arch waist.

Lining Stress

Under the action of expansion and softening of the surrounding rock, the stresses of the lining structure are shown in Table 7 when the disposal schemes are adopted.

Table 7 Stresses at the key points of the lining structures under different disposal schemes

As seen from Table 7, when the section of YK34 + 985 adopts scheme A, the tensile stresses at the left- and right-side walls of the lining are 1.57 MPa and 1.47 MPa, respectively, which are greater than the ultimate tensile strength of C25 concrete. When scheme B is adopted, the tensile stresses at the left- and right-side walls of the lining structure are reduced to 1.36 MPa and 1.21 MPa, respectively. However, the tensile stress of the left wall is slightly greater than the designed tensile strength of C25 concrete.

In the scheme A of the section of ZK35 + 285, the tensile stress values of the arch roof and the arch shoulder increase slightly compared to those before treatment, while the tensile stresses of the key points of the pavement are substantially reduced. The tensile stresses in the whole section are less than the design strength. When scheme B is adopted, the stress distribution of the lining structure is substantially adjusted. The tensile stresses of the arch roof, the arch shoulder and the middle point of the pavement are reduced compared to scheme A. Although there are some tensile stresses at the arch bottom and the arch foot, they are all less than the design strength. Therefore, both the schemes A and B can ensure the safety of section of ZK35 + 285.

Evaluation of the Disposal Measures

For the section of YK34 + 985, the lining stress is slightly greater than the design value when adopting scheme B, but considering the role of reinforcing bars, it still can meet the design requirements. For the section of ZK35 + 285, the safety reserve of scheme B is larger than that of scheme A. Therefore, disposal scheme B is recommended as the final disposal plan for both sections. The recommended scheme was applied to the actual disposal of the Dugongling tunnel. The disposal scheme of the section of YK34 + 985 was carried out on May 15, 2017 and the section of ZK35 + 285 was carried out on December 15, 2017. The deformation of the representative sections were monitored, as shown in Fig. 18.

Fig. 18
figure18

Deformation curves of the lining structures after reinforcement and disposal: a YK34 + 985 and b ZK35 + 285

As shown in Fig. 18, when the disposal measures were implemented, the deformation of the lining developed slightly at the initial stage and then tended to stabilize. The deformation of the section of YK34 + 985 tended to be stable after 8 months, and the maximum deformation was not more than 4 mm. The deformation of the section of ZK35 + 285 tended to be stable within 1 month, and the maximum deformation was also less than 4 mm. The disposal schemes designed according to the cracking mechanism in this paper met the engineering requirements, further proving the correctness of the cracking mechanism.

Conclusions

Based on the actual condition of the Dugongling tunnel of the Changping expressway, the main cause of lining cracking was studied by means of exclusion and back-analysis. The main conclusions were obtained as follows:

  1. 1.

    Based on the field investigation, the main failure modes of the Dugongling tunnel during its operation period were summarized, including lining cracking, pavement uplift, and cable trench overturning.

  2. 2.

    Combined with the geological data and test results, the possibilities of lining cracks caused by high geostress, creep deformation, construction loading, and unqualified lining were excluded. It was pointed out that the lining cracking was caused by the expansion and softening of the marlstone with gypsum in the presence of water.

  3. 3.

    The expansion and softening coefficients of the representative sections were obtained by means of back-analysis. On this basis, the diseases of the tunnel were simulated and the cracking mechanism of the tunnel lining was revealed according to the numerical results. That is, the increased water content caused the expansion and softening of the marlstone with gypsum, increased the uneven loading on the lining structure, and, finally, led to lining cracking and pavement uplift. The cracking mechanism can be applied to similar projects in this region.

  4. 4.

    In view of the actual cracking situation and cracking mechanism, a progressive disposal scheme was proposed. When scheme B was adopted, the lining stress of each section met the design requirements. Therefore, the scheme B was considered as the final disposal scheme, which was applied to the actual disposal of the Dugongling tunnel in May 2017. The monitored deformation showed that the disposal scheme could ensure the safety of lining, and the lining structure showed no further cracking.

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Acknowledgements

We would like to express our gratitude to the two anonymous reviewers for their constructive comments and suggestions. This research was supported by the Talent-technology Foundation (Grant no. RC1804) and Special Funds of the Natural Science Foundation (Grant no. ZR18017) of Xi’an University of Architecture and Technology, the Shaanxi Natural Science Foundation (Grant no. 2019JQ-756), the Special Scientific Research Project of Shaanxi Education Department (Grant no. 19JK0452), and the China Postdoctoral Science Foundation (Grant no. 2019M663648).

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Liu, N., Li, N., Xu, C. et al. Mechanism of Secondary Lining Cracking and its Simulation for the Dugongling Tunnel. Rock Mech Rock Eng (2020). https://doi.org/10.1007/s00603-020-02183-3

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Keywords

  • Highway tunnel
  • Lining cracking
  • Pavement uplift
  • Expansion and softening
  • Cracking mechanism