Introduction

Frequently, problems encountered in the excavation of road and railway tunnels worldwide arise in those excavated under shallow overburden thicknesses of weak soils. Due to the strict technical standards for high-speed railways and expressways, i.e., due to the limited height of cutting excavation, the construction of shallow tunnels has become increasingly frequent [1]. The most common problems encountered in these tunnels are face shifts and discharges from the ceiling. Such problems are usually caused by the slippage of tunnel faces along these shallow tunnels. In such situations, tunnel excavation should be interrupted, and complex engineering approaches are required to safely pass through the collapse-prone zones; settlements along the tunnel route cause greater problems. Another important factor in the excavation of tunnels in weak ground is the interaction of the portal slopes with the ongoing tunnel excavation work. After the completion of the portal excavation, the deformations that may occur during tunnel excavation tend to affect the portal region and can cause stability problems of the tunnel and/or portals. A significant problem that occurs in shallow tunnels excavated through weak ground in residential areas is the negative effect of excavation under the buildings along the tunnel route. In such cases, excavation methods and tunnel supports that do not allow any deformations during the tunnel excavation phase should be implemented. If the tunnel is excavated based on the New Austrian Tunnelling Method (NATM) principles, face and ceiling supports must be implemented, in addition to ground reinforcement. Assis [2] stated the limitations and difficulties of urban tunnelling. In particular, he examined failure behaviour and surface displacements along shallow tunnels. Gupta [3] described the problems encountered on Line 3 of the Mumbai Subway. Hoek [4] investigated ground control strategies for underground structures. ‘Squeezing’ problems were encountered in Venezuela's Yacambu-Quibor Tunnel (squeezing occurred where the height of the overburden increased to 1270 m), and the tunnel passed through weak lithological units of graphitic phyllite. The problems were obviated by implementing 60-cm thick coatings containing sliding joints reinforced with steel shafts and steel ribs [4,5,6]. Rubiralta et al. [7] examined the problems encountered during the excavation with a tunnel boring machine (TBM) on the third line of Sofia Metro, an 8-km long project that included seven stations. An earth pressure balance (EPB) TBM was selected for the main tunnel excavation in this project.

Furthermore, Heslop [8] investigated design and construction issues in tunnels excavated beneath urban areas and explained their relevant problems. Li et al. [9] investigated the collapse factors of a shallow tunnel through Chaoyang Mountain of Qingdao, China, by simulation and field measurement. Astore and Pradella [10] studied the Anatolian Subway, which was constructed between Kadıköy and Kartal in Istanbul, along a length of 21.7 km with 16 stations. This subway is located mainly in the densely populated Anatolian part of İstanbul beneath the E5/D100 motorway. The tunnels are located under a cover thickness of 25–35 m. Taromi et al. [11] discussed the collapse and solution methods for the portal section of the 10.6-km long Sabzkuh water transmission tunnel. A collapse of the tunnel occurred following a 35-m tunnel excavation at the entrance portal using conventional methods (NATM) owing to geological conditions and inappropriate excavation procedures. The collapse in this section of the tunnel caused interactions between the portal and the tunnel. Within the scope of work conducted by Antony et al. [12], a 10.7-km-long section of the Hong Kong West Drainage Tunnel (HKWDT) with a diameter of 8.2 m was investigated. The units through which the tunnel passes are generally granite and tuff containing 30 potential fault zones; the tunnel route runs parallel to the Sandy Bay fault, and a double-shield TBM was selected for this project. In the fault zones, the TBM was converted to a single-shield TBM [12]. Kovari et al. [13] examined TBM usage under weak ground conditions beneath residential areas and stated that many large tunnels were being excavated with only a shallow cover under buildings, bridges, and roads, which could not only trigger settlements and large-scale collapses but also affect surface conditions.

The NATM, which aims to maximize the self-carrying capacity of overburden, was introduced in the 1960s by Rabcewicz [14,15,16]. The application range of the NATM is from weak ground to hard rock, and this method has been used in many tunnels, including tunnels that are currently under construction. Whittaker and Frith [17] summarized the factors affecting the problems of weak ground for select support systems. Goricki et al. [18] studied tunnel support systems for fault transitions and identified five main factors for support system selection and implementation. Sulem and Manh [19] and Bonini and Barla [20] examined the congestion problems of St-Martin-la Porte galleries excavated within the scope of the Lyon–Turin Railway Project and discussed the proposed solutions. The problems experienced in the Zhegushan, Laodongshan, Minyazi, Xiangshan, Yingfeng, and Yezhping tunnels excavated in China and the precautions taken against these problems are explained in detail by Wang et al. [21]. For the Bolu Tunnel of the Istanbul-Ankara Motorway, problems surfaced during excavation, including deformations in the support systems related to compression and swelling [22] and a collapse after the 12th November 1999 Düzce earthquake. In related studies, failed segments were identified, and revisions were made to the NATM method [22]. The causes of the collapse of the Bolu Tunnel after the Düzce earthquake were discussed by Aygar [23]. Aygar and Gokceoglu [24, 25] examined the effects of the squeezing and swelling characteristics of soil units and fault zones on tunnel support systems and stated the requirement of a rigid support system for those types of ground units. Aygar and Gokceoglu [26] have also emphasized that providing the stability of the tunnel face and ceiling is the most crucial factor of support systems for large-diameter urban railway tunnels excavated through weak units under a shallow overburden thickness. Additionally, the face stability of shallow tunnels excavated in weak ground conditions has been considered by several researchers [1, 27,28,29,30,31] due to the importance of face stability for tunnel stability. As mentioned by Morovatdar et al. [32], tunnelling at shallow depths in soft grounds gives rise to concerns associated with tunnel instability. Huang et al. [33] analysed the deformation response induced by surcharge loading above shallow shield tunnels in soft soil by employing 3D numerical analyses.

Based on the brief literature review described above, it can be stated that every tunnel project has complexities and requires specific methodologies. In other words, each tunnel case should be studied in detail considering its specific geological, geotechnical and project characteristics. The purposes of the present study are to analyse and compare the results obtained from analytical solutions and 3D numerical analyses of a shallow railway tunnel excavated in difficult ground conditions.

Tunnel specifications

The analyses in the study were performed on the entrance portal section of the T4 tunnel (1260 m) excavated within the scope of the Ankara-İzmir High Speed Railway Project in Turkey. T4 is a shallow tunnel drilled through weak ground conditions; therefore, it is important for tunnelling studies. The T4 tunnel was excavated beneath a maximum overburden thickness of 35 m. The tunnel passes mainly through interbedded gravel-sand-clay layers. Prior to project revisions, several tunnel face stability problems and deformations were observed along the tunnel route. Through a set of revisions and proposed solutions, tunnel excavations were completed successfully. A location map and an aerial view of the T4 tunnel are shown in Figs. 1 and 2. The project begins at the entrance portal (km: 209 + 615), continues at a slope of 1.6%, and ends at the exit portal (km: 210 + 875). The altitudes of the entrance and exit portals are 1223.95 m and 1243.73 m, respectively.

Fig. 1
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Map of the location of the T4 tunnel

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Fig. 2
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The portal plans of the T4 tunnel

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Geological and geotechnical conditions

As shown in the geological cross-section given in Fig. 3, the tunnel was excavated mainly through the lower Miocene aged Hacıbekir Formation comprising gravel in a silt–clay matrix, extremely weak sandstone, and mudstone–clayey sandstone [34]. Evaluation of the tunnel was performed via the mechanical properties of the rock at the entrance portal (km: 210 + 24), which is shallow overburden and cohesionless ground.

Fig. 3
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Geological cross-section of the tunnel route [34]

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In the present study, the entrance portal of T4 is analysed because this part of the tunnel presents serious geotechnical difficulties and requires special design. The section of the entrance portal at km: 210 + 150 demonstrates shallow tunnel characteristics with a minimum overburden thickness of 10 m, where weakly cemented sandstone is intercalated with clayey sand. Based on the material acquired from boreholes SK-246 + 415, SK-246 + 000, and SK-246 + 700 drilled in this section of the tunnel and site investigation data, geotechnical design parameters were determined for the units. There is a high potential of flow and slide cases either at the tunnel face or tunnel ceiling. At the parts of the tunnel through low-cohesion gravel in a silt–clay matrix (Figs. 4 and 5), the C4 rock class was specified according to the NATM method.

Fig. 4
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Core box photographs from SK-246 + 415 [34]

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Fig. 5
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Core box photographs from SK-246 + 700 [34]

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This section of the tunnel was excavated through low cohesive gravel in a silt–clay matrix; therefore, effective soil parameters were proposed. The standard penetration test (SPT) values obtained for boreholes SK-246 + 415 and SK-246 + 700 were not representative because of the gravel unit (Figs. 4 and 5). To achieve a safe design, a single parameter was assigned to the units. According to the SPT-N–effective shear strength relation introduced by Carter and Bentley [35], if the SPT-N value of clayey sand units is assumed to be 35, the corresponding angle of internal friction is 37°. Based on the clay content of the unit, the values were optimized as c' = 5 kPa and Ø' = 35°. The geotechnical parameters used in the analyses are given in Table 1, and the face, which is excavated in a silt–clay unit, is shown in Fig. 6.

Table 1 Geotechnical parameters used for the analyses
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Fig. 6
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A close view of the face excavated in the silt–clay unit

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Tunnel support design methods

There are basically 3 main methods used to determine tunnel support systems: empirical methods, analytical methods and numerical methods [36,37,38,39]. Each of these methods has its advantages and disadvantages; thus, support design can be performed by evaluating these three methods as a whole. Closed-form solutions can be used during preliminary design, but numerical programs should be used for detailed analysis. In this study, the FLAC3D [40] program was used to perform 3D analyses to determine the relationship between tunnel excavation levels. In addition, umbrella and face soil nails can be described into the model, and the face stability of the tunnel can be assessed. In 3D programs, the inner lining concrete can be defined in the interlayer concrete model, and changes that may occur during tunnel excavation can be examined. Additionally, analytical solutions were carried out, and the results were compared.

Evaluation of preliminary tunnel support systems

Zhang et al. [41] proposed a theoretical model for the stability analysis of a reinforced tunnel face in cohesive-frictional soils with the limit equilibrium method and strength reduction technique. The analytical model for face stability proposed by Zhang et al. [41] agreed well with the corresponding 3D numerical analysis results; hence, analytical models are extremely important for tunnel design and analysis. Lyu et al. [42] suggested an analytical approach to calculate the pressure distribution around a twin tunnel in layered strata. Fang et al. [43] proposed an analytical solution for loosening earth pressure above a shallow tunnel in unsaturated ground. As shown by these examples, analytical solutions are still useful tools for analysing tunnel deformations and ground reactions. In the present study, analytical solutions (closed-form solutions) are carried out to determine tunnel support systems and to investigate the ground and rock behaviour, presumably, for preliminary evaluation prior to numerical analyses [44,45,46]. In these analyses, it is assumed that the tunnel is circular and under hydrostatic conditions, where the in situ vertical and horizontal stresses are equal [45]. In Fig. 7, p0, the internal support pressure (pi), tunnel radius (r0) and plastic zone radius (rp) are shown under hydrostatic stress.

Fig. 7
figure 7

Plastic zone surrounding a circular tunnel [45]

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In Table 2 [44,45,46], closed-form solutions are given according to the Mohr–Coulomb failure criterion under hydrostatic stress.

Table 2 Closed-form solution equations [44,45,46]
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The ground parameters of the analysed tunnel portal section are given in Table 1. In this section, preliminary comments are made on the behaviour of the ground and tunnel support systems. The field stress is p0 = 0.020 × 14 = 0.28 MPa; σcm is calculated to be 0.02 MPa.

The ratio of rock mass strength (σcm = 0.02 MPa) to in situ stress (p0 = 0.28) (σcm/P0) is 0.07. In addition, the plastic zone radius is rp = 5.62 m according to Eq. 9 as shown in Table 2. If the unit strain occurring around the tunnel is Ɛ, it is calculated with Eq. 8 in Table 2. Here, Ɛ is 40%. Separately, ui = 2.65 m occurs in the unsupported state, indicating that the tunnel collapses in that state. In Fig. 8, the relationship between tunnel convergence and the ratio of rock mass strength to in situ stress for unsupported tunnels [7] is given, and in Fig. 9, the approximate relationship between the strain and the degree of difficulty associated with tunnelling through squeezing rock [7] is given. As seen from Figs. 8 and 9, the corresponding closure is not at an acceptable level; the tunnel should be closed at once, and this part of the tunnel falls within section E, as seen in Fig. 9. As mentioned above, face stability problems may emerge, so forepoling application and reinforcement of the tunnel face is required. If the strain levels exceed 5%, tunnel face problems emerge, which reveals that providing stability of the tunnel face and implementing the forepoling method are mandatory [47].

Fig. 8
figure 8

Plot of tunnel convergence against the ratio of rock mass strength to in situ stress for unsupported tunnels [47]

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Fig. 9
figure 9

Approximate relationship between strain and the degree of difficulty associated with tunnelling through squeezing rock. Note that this curve is for tunnels with no support [47]

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Rock support interaction analysis—characteristic curves

There are many uncertainties in determining tunnel support systems. Primary uncertainties arise due to the limited number of studies and thus the lack of approaches produced based on these studies. Today, many researchers are working on determining ground reaction curves (GRCs), support reaction curves (SRCs), and longitudinal deformation profiles (LDPs) [44, 48,49,50,51,52]. Among these studies, optimization of the supports were provided for certain conditions and cases. Deformations that occurred before the installation of the first supports were investigated. In other words, the most appropriate support system and the most economical method were researched for a specific time period. Because not all of the in situ stresses (P0) affect support systems, the main factor in identifying the most economical support system is estimating the Pi value. There are also many observational approaches for estimating the loads affecting supports [37, 38]. Clearly, the basic approach depends upon the principle of accurately predicting the future load on the supports and application of the most economic support systems within the specific time period.

For each section of the tunnel, the ground characteristic curve, longitudinal displacement profile and SRC are plotted. For plotting the GRC, Eqs. 4 and 7 in Table 2 are used. In addition, the plastic zone radius is calculated according to Eq. 6 in Table 2. The Vlachopoulos and Diederichs [51] equations are used for plotting the longitudinal displacement profiles.

$$u_{i} = \left\{ {\begin{array}{*{20}ll} {u_{im} \left[ {\frac{{u_{if} }}{{u_{im} }} \cdot e^{{{x \mathord{\left/ {\vphantom {x {r_{0} }}} \right. \kern-\nulldelimiterspace} {r_{0} }}}} } \right],} & {x < 0} \\ {u_{im} \left[ {\left( {\frac{{u_{im} }}{3}} \right)e^{{ - 0.15\left( {r_{pm} /r_{0} } \right)}} } \right],} & {x = 0} \\ {u_{im} \left[ {1 - \left( {1 - \frac{{u_{if} }}{{u_{im} }}} \right) \cdot e^{{\left( {{{ - 3x} \mathord{\left/ {\vphantom {{ - 3x} {r_{0} }}} \right. \kern-\nulldelimiterspace} {r_{0} }}} \right)/\left( {{{2r_{pm} } \mathord{\left/ {\vphantom {{2r_{pm} } {r_{0} }}} \right. \kern-\nulldelimiterspace} {r_{0} }}} \right)}} } \right],} & {x > 0} \\ \end{array} } \right.$$
(10)

Here, uif is the deformation in the tunnel face, and uim is the maximum displacement, which occurs at the rpm scale. While determining the tunnel support systems, the equations given in Table 3 are employed [44, 53]. Equations are given under the condition of a hydrostatic background stress state for steel shoring, shotcrete lining and bolts in a circular tunnel. The summary table of the support system selected in both parts of the tunnel is given in Table 4.

Table 3 Support capacity equations [44, 53]
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Table 4 Support properties between the portal and km: 210 + 150
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For the tunnel section, the ground reaction curve (Fig. 10), longitudinal displacement profile (Fig. 11) and SRC (Fig. 12) were plotted. In addition, the tunnel support system pressures and stiffness values are given in Table 5.

Fig. 10
figure 10

Characteristic curve for the studied section of the T4 tunnel

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Fig. 11
figure 11

LDP between the inlet portal and km: 210 + 150 employing the relation proposed by Vlachopoulos and Diederichs [51]

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Fig. 12
figure 12

GRCs and SRCs between the entrance portal and km: 210 + 150

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Table 5 Support pressure between entrance portal and km: 210 + 150
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The parameters used in the calculations are as follows: rpm/r0 = 2.83, tunnel face displacement uif = 0.04 m, maximum face displacement uim = 0.184 m, and face displacement/max displacement uif/uim = 0.21. Tunnel support systems should be established immediately after excavation when tunnels pass through very weak ground conditions. In this case, 4 cm of deformation occurs in the tunnel face; if the support system was constructed 1 m behind the tunnel face, 5 cm of deformation would occur (Fig. 11). In Fig. 10, the support pressures required to stabilize the deformation at the level of 5 cm are calculated as 0.03 MPa. A comparison of Fig. 10 and clearly shows that the deformation, which was observed immediately after the tunnel excavations, proceeded very rapidly due to the extremely weak ground conditions. The plastic zone radius exhibits a sudden increase with a plastic zone radius of 10.5–18 cm, whereas for the condition with the support system installed 1 m behind the tunnel face (in terms of deformation), all the overburden is in the plastic zone area. Slippage of the tunnel face and discharges from the tunnel ceiling are also possible because of the cohesionless ground conditions. For this reason, to increase the strength parameters of the ground (elastic modulus, cohesion and internal friction angle) in the tunnel ceiling and tunnel face, umbrellas are also required for the tunnel ceiling. In addition, the GRCs and SRCs with selected support elements (shotcrete, steel rib and bolts) are given in Fig. 12. In summary, tunnel support systems should be completed immediately to avoid deformation inside the tunnel. Otherwise, deformation develops very rapidly and can result in tunnel failure.

3D numerical analyses

3D numerical analyses are commonly used to analyse deformation and the performance of support systems [26, 27, 54]. 3D numerical analyses are performed to investigate not only tunnelling but also other construction processes [55,56,57,58,59,60]. Excavation for the T4 tunnel was initiated by a tunnel support system application. However, due to severe tunnel deformation and critical settlement, the excavation was interrupted. By adequately revising the support system, the tunnel excavation continued successfully. The main reason for the failure of the support is the implementation of Store-Norfers (SN) bolts and inadequate forepoling installation at the tunnel crown, together with the absence of support on the tunnel face. SN bolts are installed by first drilling a hole, grouting through it, and then mounting the bolt. When installing bolts through silty, sandy, and gravelly soils, it is possible that the holes fill with their constituent natural materials instead of the design grout mixture. In addition, due to the action of gravity, the grout on the tunnel ceiling may not be affixed, leading to insufficient grouting. Eventually, this may cause a malfunction of the bolts. If too short (L = 4 m), the 1.5′ diameter bolts proposed to stabilize the tunnel crown stability will be ineffective. As a consequence, flow and discharges occurred from the tunnel ceiling. To ensure stability of the tunnel face, fibre bolts and shotcrete should be applied.

As explained above, the gravel in the silty–clayey matrix units exhibits flow characteristics at the shallow tunnel location, causing issues for tunnel excavation. Accordingly, by taking these flow characteristics into account to determine an adequate support system, analyses were performed. The umbrella arch method, as a pre-reinforcement approach of tunnels in complex geological conditions, is widely used to maintain tunnel stability [32, 61].

The model to be used for the following 3D analyses is shown in Fig. 13. According to the symmetric conditions, half of the tunnel is modelled (Fig. 3). The centre of the tunnel is assumed to have the coordinates of (0,0,0). The boundary conditions selected are 5 times the diameter of the tunnel. The bottom of the model is 70 m long in the z direction, 70 m in the x direction and 100 m in the y direction (excavation face).

Fig. 13
figure 13

FLAC3D model of the tunnel between the inlet portal and km: 210 + 150

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First, analyses were carried out for the case in which no bolts were installed at the tunnel face, and the resulting displacements were examined. The tunnel numerical analyses were investigated in the sandy gravel units between the entrance portal and km: 210 + 150, which were considered low-cohesion units. In addition, since the cover thickness of the first section is shallow, analyses were performed for the 12–15 m section. The support systems were modelled with FLAC3D. In the model, a vertical plane of symmetry was assumed along the centre of the tunnel, so half of the tunnel is modelled. The total length of the tunnel is 100 m, the overburden is nearly 15 m, and the floor of the tunnel is located 22 m below the ground surface (Fig. 13).

The shotcrete was described with a shell element to the model. The inner concrete lining at the back of the tunnel was also defined as a different zone of the model. The soil nails applied at the tunnel were are defined as cable bolts. Tables 6 and 7 show the parameters used for modelling the shotcrete, inner concrete lining and cable bolts.

Table 6 Parameters used for modelling the shotcrete and interior lining concrete
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Table 7 Parameters used for modelling the cable bolts
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Umbrellas are described in the model with ‘pile’ elements. The numerical and analytical solutions during the description stage of umbrellas in the model refer to the work of Oke et al. [62,63,64,65,66], who stated that it is appropriate to define umbrellas as a pile element in FLAC3D. Table 8 summarizes the parameters used for modelling the umbrellas.

Table 8 Parameters used for modelling the umbrellas
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In the model, the cohesion and deformation modulus of the ground parameters around the tunnel were defined with the rock bolts in the tunnel. In other words, the ground parameters of the bolts and the soil units were estimated after the grouting procedure was completed. In this approach, the ground and rock bolts around the tunnel are represented as a single unit. In a sense, the reinforcement of the soil units around the tunnel were simulated by assigning new soil parameters (Table 9).

Table 9 Ground parameters for units reinforced with rock bolts (entrance portal to km: 210 + 150)
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In the 3D analysis, the top heading, bench and invert were modelled. In this work, the round lengths for the top heading, bench and invert sections were taken to be 1, 2 and 4 m, respectively, located at 100 m in the Y direction, 70 m in the X direction and − 70 m in the Z direction in the first modelling stage. The model is considered symmetrical. In the model, the loading condition is selected as the gravity method. The model is fixed at 0–100 m in the y direction, − 70 m in the Z direction, and 0–70 m in the x direction (Fig. 14). Additionally, the Mohr–Coulomb failure criterion is selected for the model. Tunnel excavation started at the top heading from 60 m. The top heading section was null until an advance of 60 m, while the bench section was null until 40 m, and the invert section was null until 36 m. The support system of this section was installed and entered into the model; additionally, it was assumed that the inner lining was constructed for the first 24 m section of the tunnel. Therefore, the required distance was secured for the top heading, bench, invert and inner lining (Fig. 15). After this stage, excavation steps proceeded in 1 m round lengths in the top heading. By first excavating the top heading for 2 m, then excavating the bench section for 4 m and finally completing the excavation of the invert section, the excavation stages were completed. The excavation process was continued in this way, and finally, a total of 8 m of excavation was completed in the top heading, bench and invert sections. Between the entrance section and km: 210 + 150, in the tunnel face, 12 m long and 4.0″ umbrellas were applied in the ceiling section, and 12 m long face soil nails accompanied by 40 cm shotcrete were installed to ensure the face stability. Between the entrance section and km: 210 + 150, 9 m long and 4.0″ umbrellas were applied in the ceiling section, and 9 m long face soil nails accompanied by 40 cm shotcrete were installed to ensure face stability. The face soil nails and umbrella applications are represented in Fig. 16.

Fig. 14
figure 14

FLAC3D model boundary conditions

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Fig. 15
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Top heading, bench and invert levels

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Fig. 16
figure 16

Support elements used in the tunnel excavation

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FLAC3D software uses the bulk modulus, K and shear modulus to represent the ground parameters in the model. These values are related to the deformation modulus (E) and Poisson’s ratio (υ) [40] and are presented in Table 10.

Table 10 Bulk, shear and deformation moduli
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Bulk Modulus: υ

$$K = \frac{E}{3(1 - 2\upsilon )}$$
(17)

Shear Modulus

$$G = \frac{E}{2(1 + \upsilon )}$$
(18)

In the analysis performed on this section of the T4 tunnel, the stresses in the model were estimated considering the gravity method, and the surface stresses remained constant. First, the deformation of the tunnel ceiling and tunnel face was examined. In the absence of face bolts and umbrellas on the tunnel ceiling and face, settlement occurred in the Z direction as the tunnel excavation continued to the surface, reaching 1.3 m at the crown (Fig. 17).

Fig. 17
figure 17

Displacement in Z direction

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In the tunnel face, it was observed that the deformation in the Y direction reached 70 cm (Fig. 18); in other words, a collapse occurred in the tunnel.

Fig. 18
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Displacement in the Y direction

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When the total displacement in the tunnel face was examined, it was observed that the collapse clearly reaches the surface (Fig. 19).

Fig. 19
figure 19

Total displacement developed at the studied section

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With the application of the soil nails and umbrella in the tunnel face and tunnel ceiling, the displacement occurring on the tunnel ceiling reflected a convergence of 2 cm towards the tunnel in the horizontal direction (Figs. 20 and 21). In addition, in the Z direction, vertical settlement occurred at approximately 10 cm, and the tunnel remained stable. Moreover, the surface displacement is approximately 2 cm at the tunnel face, while it is approximately 3 cm at the section where ring closure is realized.

Fig. 20
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Horizontal displacement in the Y direction

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Fig. 21
figure 21

Horizontal displacement in the Z direction

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When the top heading and bench distances were analysed with FLAC3D, it was observed that between the top heading and bench section, an approximately 10 m distance, approximately 10 cm of swelling takes place along the Z direction, which gradually increases after this point. In other words, the requirement of an intermediate temporary invert arises in the top heading section; additionally, the distance between the top heading and bench excavations should be secured at approximately 10 m (Figs. 22 and 23). As shown in Fig. 22 and Fig. 23, the deformations in the Z direction increase; hence, in this area, the intermediate invert is necessary for face and tunnel stability.

Fig. 22
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Swelling at the top heading section in the Z direction (without umbrella and forepoling)

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Fig. 23
figure 23

Swelling at the top heading section in the Z direction (with umbrella and forepoling)

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Discussion and conclusions

The T4 tunnel with a shallow overburden thickness was excavated through extremely weak (flowing) ground. For this type of ground condition, the risk of instability of the tunnel face and serious material flows from the tunnel ceiling is significant. Therefore, unsupported tunnel excavation should not be initiated, regardless of whether necessary measures are taken at the tunnel face and ceiling. In the present study, analytical solutions for tunnel support systems and corresponding 3D numerical analyses were performed, and the results obtained from these two methodologies were compared. Consequently, the conclusions obtained from the study can be drawn as follows:

SN bolts should not be applied through sandy and silty units since the holes drilled for placing those bolts are destroyed due to flowing soil features and lead to impractical conditions for grouting. Therefore, for this type of soil, a self-drilling bolt must be used. Then, grouting can be applied through the bolt openings, which will facilitate consolidation of the grout material around the tunnel. With successful grouting, no gaps will exist around the tunnel. This technique will help achieve the arch effect of the load distribution around the tunnel ceiling.

For tunnels with silty, sandy, and gravelly units, the tunnel stability is directly associated with the application of bolts and forepoling at the tunnel ceiling. In shallow tunnels where the soil characteristics are defined as flowing due to cohesionless features, potential face-flowing during excavation work may result in discharges at the tunnel ceiling, in turn increasing the risks of collapse inside the tunnel. This risk can extend to the ground surface and result in high re-excavation costs. Therefore, umbrellas (forepoling) at the tunnel ceiling should be at least 9–12 m long, and overlaps should be designed with a minimum ratio of 1/3. Additionally, high-pressure grouting should be maintained through the forepoling system until refusal is reached. This type of application will ensure face stability of the tunnels during excavation and will be useful in preventing potential collapses at the tunnel ceiling. For the tunnel face, a continuous installation of fibre-type rock bolts is required for establishing face stability, without which a possible sliding on the tunnel face would adversely affect the tunnel support systems.

The top heading, bench, and invert need to be close to each other. The distance between the top heading and bench can be a maximum of 20 m in length, whereas the distance between a bench and an invert can be as short as 10 m. Additionally, the excavation ring must be closed as quickly as possible. In the top heading, an intermediate invert is necessary after face excavation for face and tunnel stability.

The stability of tunnel faces should be progressively sustained through rock bolts and grouting applications. Additionally, discharge at tunnel faces should be prevented by using shotcrete. At the ceiling of the T4 tunnel, which was excavated through flowing material, the forepoling method had to be implemented to stabilize the ceiling sections; otherwise, discharge at the ceiling, a characteristic of shallow tunnels, may greatly increase the risk of collapse. To examine both the face stability and ceiling stability of the tunnel excavated through non-cohesive and low-cohesion flowing soils, it is necessary to perform 3D analyses. Through these 3D analyses, the features of the required umbrellas, such as their length, type and diameter, can be specified, and the size of the face soil nails can be determined.

According to the analytical solutions, if the support systems are not applied immediately after tunnel excavation, deformation develops very rapidly, and the plastic zone reaches the surface. Similarly, 3D analysis indicates that the deformation reaches 1.3 m and the plastic zone develops to the surface when there are no face bolts or forepolings.

Due to some assumptions considered in the analytical solutions, the calculated deformation results are greater than those of the 3D numerical analyses. Because all the support elements can be described in the 3D model, more optimistic results were obtained from the 3D numerical analyses.