Tunnels

Abstract

Tunnelling is an indispensable part of infrastructure services. Some of the factors affecting the tunnel design can be listed as the characteristics of the soil or rock mass, tunnel excavation method, tunnel dimensions and the structures located on the tunnel route. Field studies (geological-geotechnical evaluations) during the design phase are one of the most important factors in tunnel design. All studies to be carried out after this stage are based on the determined geological model. The determination of the tunnel support system is made with detailed analytical and numerical solutions. In this study, empirical, analytical and numerical solutions, geotechnical measurements, swelling and squeezing phenomena in tunnels, tunnel support capacity equations, weak rock in tunnelling and tunnel support types are explained briefly.

1. Introduction

Today, the number of tunnel projects has increased significantly due to the developing infrastructure projects. Tunnels are used in most large highways, railways, water, metro and mining projects. Depending on the increasing number of infrastructure projects, the total number being constructed is gradually increasing. As a consequence of this increase, tunnel design and construction works are also gradually increasing. Project design studies carried out after the determination of project routes are of great importance. It is extremely important to determine the rock and ground support classes, excavation methodology and support elements within the project design studies. Although there are different tunnel project approaches today, all designs are based on the principles of rock and soil mechanics; for this reason, the correct determination of soil and rock parameters is the main factor in determining tunnel design. In addition, the correct realisation of the geological model of the route through which the tunnel will pass is another factor that will directly affect the tunnel design. In addition to all of these, surface structures also affect the design. While deformation is not allowed in tunnels to be excavated under towns and cities, a certain amount of deformation is allowed in mountain tunnels. The design of the support system is affected by natural structures such as streams on the surface. This design effort can be divided into empirical, analytical and numerical methods for the project work to be done. Although these three methods are used separately most of the time, they should be evaluated together for a healthy tunnel project. During the tunnel excavations, tunnel projects should be compared with predicted and encountered geological conditions. If necessary, tunnel projects should be revised according to the encountered geological conditions. It should be well known that the predicted geological conditions and the actual geological conditions encountered will never be the same. For this reason, geotechnical measurements such as geological face maps, convergence measurements and deformation measurements should be made during the tunnel excavation in order to make the necessary revisions and updates. If necessary, the support system and rock mass parameters should be revised with a back-analysis. In addition, laboratory tests made from the boreholes taken during the excavation and rock mass parameters should be re-evaluated.

2. Rock mass classification system

The most important factor when designing a tunnel is to define the geological conditions that the tunnel will pass through. Based on this definition, rock mass classification systems are made by determining the strength parameters of the rock mass and the geological conditions. With these methods, the units that the tunnel will pass through are classified providing detailed information before the tunnel project commences. Rock mass classification systems have been developed in detail since the 1940s, and this process has been refined by different researchers until the present day. A main one of these methods, developed by Terzaghi [1] in 1946 made a classification for steel supports depending on the rock load. In later processes, Lauffer [2] developed a classification based on unsupported standup time, Rabcewicz [3, 4, 5], Rabcewicz and Golser [6] introduced the principles of the New Austrian Tunnelling Method, Deere et al. [7] in 1967, the direction of Rock Quality Designation (RQD), and Wickham et al. [8] developed the Rock Structure Rating system. The Rock Mass Rating (RMR) system, which is one of the most well-known systems today, was developed by Bieniawski [9, 10, 11] and was last modified in 1989. Barton et al. [12, 13, 14] improved the rock classification system known as the Q system. In 1995, Palmstrom [15] developed the Rock Mass Index (RMI) system. All of these methods emerged as empirical studies in the field.

While making rock mass classifications, uniaxial compressive strength of intact rock, condition of discontinuities (spacing, orientation, roughness, etc.), in situ stresses, groundwater condition, tunnel size and rock quality designation are all evaluated. The biggest problem when working with rock mass classification systems is that they are made according to interpretations that vary from person to person, since they are empirical. While one researcher defines discontinuities in a particular way, another researcher may make different interpretations under the same conditions. In addition, incomplete data collection in studies is an important factor. Since the boreholes, from which the main input parameters are obtained, are often not done properly, problems are created in terms of the accuracy of the data. When drilling, the length of the run, sampling and the application of the correct drilling technique will directly affect the results. For this reason, although all rock mass classification systems contain very important and valuable information when describing the rock mass, the results should always be viewed with suspicion. No rock mass classification system specifies a definite support system for the design, it just gives a range. While designing, these support systems should be considered as an initial step in analytical and numerical solutions, and never be considered absolute truth.

2.1 Rock load theory

Rock Load Theory, developed by Terzaghi [1] for sizing steel rib systems, started to be applied in railway tunnels opened in the United States in 1946. Terzaghi considered the pressure exerted by the loose soil (Hp) on the steel rib on the tunnel (Figure 1). For this purpose, Terzaghi [1] divided the rock mass into nine main categories. These categories range from solid-intact rock to swelling ground. He calculated the pressure coming to the steel supports depending on Hp Eq. (1). In Table 1, rock mass classes and rock load factors are given.

Figure 1.

Rock load concept [1].

Rock class	Rock condition	Rock load factor (Hp)	Remarks
I	Hard and intact	Zero	Light lining is required only if spalling or popping occurs
II	Hard stratified or schistosite	0–0.5B	Light support is mainly for protection against spalling. The load may change erratically from point to point
III	Massive moderately jointed	0–0.25B	No side pressure
IV	Moderately blocky and seamy	0.25B–0.35(B + Ht)	No side pressure
V	Very blocky and seamy	(0.35–1.10)(B + Ht)	Little or no side pressure
VI	Completely crushed but chemically intact	1.10(B + Ht)	Considerable side pressure.; Softening effects of seepage toward the bottom of the tunnel require either continuous support for the lower ends of ribs or circular ribs.
VII	Squeezing rock moderate depth	(1.10–2.10)(B + Ht)	Heavy side pressure invert struts are required. Circular ribs are recommended.
VIII	Squeezing rock moderate depth	(2.10–4.50)(B + Ht)	As above
IX	Swelling rocks	Up to 250 ft. (80 m) irrespective of the value of (B + Ht)	Circular ribs are required. In extreme cases, the use of yielding support is recommended.

Table 1.

Rock load in tunnels within various rock classes [1].

$$p=\mathit{Hp}\ast \gamma \ast H$$E1

2.2 Stand-up time

Lauffer [2] defined the relationship of stand-up time to rock mass quality depending on the tunnel diameter in unsupported condition. The rock mass is classified from very good rock (A) to very weak rock (G). Here, the unsupported period is 100 years in the A rock class, while it ranges from 1 minute to 10 minutes in the G rock grade (Figure 2). This classification is valid for a span of 5 m. Stand-up time indicates the time during which the tunnel remains stable in unsupported conditions. Lauffer applied the stand-up time approach to the Bieniawski RMR rock classification system.

Figure 2.

Relationship between active span and stand-up time and rock mass classes [2].

2.3 New Austrian tunnelling method (NATM)

The principles of the New Austrian Tunnelling Method (NATM) were introduced by Rabcewicz [3, 4, 5] in the 1960s. The NATM method is based on the principle of increasing the carrying capacity of a mountain with a flexible outer belt by allowing deformations around the tunnel. It is divided into rock classes, from very solid rock to swelling soils. In subsequent years very serious criticisms were made of NATM and this process continues today.

According to NATM principles, the rock is divided into three main groups stable (A), friable (B) and stress failure, squeezing (C). These rock classes are again subdivided into subclasses (Table 2).

Main rock class	Rock classes
A (stable to overbreak)	A1 (stable)	A2 (friable)
B (friable)	B1 (friable)	B2 (very friable)	B (ravelling)
C	C1(rock bursting)	C2 (squeezing)	C3 (heavily squeezing)	C4 (flowing)	C5 (swelling)

Table 2.

NATM rock classes.

2.4 Rock quality designation

Deere et al. [7] made a classification according to the core samples obtained from the borehole. Here rock quality is defined by dividing the core samples larger than 10 cm by the run size. The RQD value remained as a preliminary approach but has continued to be used as one of the most important data inputs to the other developed rock classification systems. The RQD value is shown in Eq. (2). In the classification made according to the RQD value, the rock mass is divided into five main categories (Table 3).

RQD	Rock mass quality
<25	Very poor
25–50	Poor
50–75	Fair
75–90	Good
99–100	Excellent

Table 3.

Rock mass quality classification classes [7].

$$\mathit{RQD}=\left(\mathit{\text{Total length core pieces}}>10\mathit{cm}/\mathit{\text{total length of the core}}\right)\ast 100\%$$E2

2.5 Rock structure rating (RSR)

Wickham et al. [8] developed the RSR system based on their work in small-diameter tunnels. They established a relationship between the parameters determined according to the geological conditions and the construction parameters. RSR value Eq. (3) is also given:

$$\mathrm{RSR}=\mathrm{A}+\mathrm{B}+\mathrm{C}$$E3

Parameter (A) depends on the rock hardness, geological structure and rock type origin.

Parameter (B) depends on the discontinuity pattern which derives from joint spacing, joint orientation and direction of the tunnel drive.

Parameter (C) depends on the joint condition and water inflow.

2.6 Rock mass rating system (RMR)

Rock Mass Rating System is a method developed by Bieniawski [9, 10, 11] between 1973 and 1989 on the basis of mine galleries and road tunnels. Bieniawski classified the rock mass according to six parameters.

1. Uniaxial compressive strength (UCS)

2. Rock quality designation (RQD)

3. Spacing of discontinuities

4. Condition of discontinuities

5. Groundwater conditions

6. Orientation of discontinuities

The RMR system was developed in line with the data obtained from horseshoe tunnels with a diameter of 5–12 m. In this method, there is a rating value for each parameter. The support system is determined according to the RMR score calculated according to these determined values (Table 4).

Rock mass class	Excavation	Rock bolt (20 mm diameter, fully grouted)	Shotcrete	Steel sets
I—Very good rock; RMR: 81–100	Full face, 3 m advance	Generally, no support is required except spot bolting
II—Good rock; RMR: 61–80	Full face, 1–1.5 m advance. Complete support 20 m from face	Locally, bolts in crown 3 m long, spaced 2.5 m with occasional wire mesh	50 mm in crown where required	None
III—Fair rock; RMR: 41–60	Top heading and bench. 1.5–3 m advance in top heading. Commence support after each blast. Complete support 10 m from face	Systematic bolts 4 m long, spaced 1.5–2 m in crown and walls with wire mesh in crown.	50–100 mm in crown and 30 mm in sides.	None
IV—Poor rock; RMR: 21–40	Top heading and bench 1–1.5 m advance in top heading. Instal support concurrently with excavation, 10 m from face	Systematic bolts 4–5 m long, spaced 1–1.5 m in crown and walls with wire mesh	100–150 mm in crown and 100 mm in sides	Light to medium ribs spaced 1.5 m where required
V—Very poor rock; RMR: <20	Multiple drifts 0.5–1.5 m advance in the top heading. Instal support concurrently with excavation. Shotcrete as soon as possible after blasting	Systematic bolts 5–6 m long, spaced 1–1.5 m in the crown and the walls with wire mesh. Bolt invert	150–200 mm in the crown, 150 mm in sides and 50 mm on the face	Medium to heavy ribs spaced 0.75 m with steel lagging and forepoling if required. Close the invert

Table 4.

Guidelines for excavation and support of 10 m span rock tunnels in accordance with the RMR system [11].

2.7 Tunnelling quality index (Q)

Barton et al. [12, 13, 14] proposed a Tunnelling Quality Index (Q) system for underground structures. The Q method was developed in Scandinavia in 212 tunnels excavated in solid rock. The Q value is logarithmic, ranging from 0.001 to 100. According to the Q value, the rock mass is divided into nine main categories between exceptionally good and exceptionally poor. The Q value depends on a total of six parameters. These are;

RQD: Rock quality designation.

Jn: Joint set number.

Jr: Joint roughness number.

Ja: Joint alteration number.

Jw: Joint water reduction factor.

SRF: Stress reduction factor.

According to these parameters, the Q value is calculated with Eq. (4).

$$Q=\left(\mathit{RQD}/\mathit{Jn}\right)\ast \left(\mathit{Jr}/\mathit{Ja}\right)/\left(\mathit{Jw}/\mathit{SRF}\right)$$E4

The (RQD)/Jn) value used in the equation corresponds to the rock mass geometry and the block/wedge size. The Jr/Ja value refers to the inter-block shear strength condition and the Jw/SRF value to the active stress incorporation water pressures and flows condition.

In addition to the Q value, the equivalent dimension (De) value is needed for the tunnel support details. This value is determined by dividing the tunnel diameter by the excavation support ratio. The details of the support system are determined by crossing these two values in the chart in Figure 3 and Table 5.

Figure 3.

Q excavation and support system chart [14].

1.	Unsupported	6)	Fibre-reinforced shotcrete and bolting, 9–12 cm
2.	Spot bolting	7.	Fibre-reinforced shotcrete and bolting, 12–15 cm
3.	Systematic bolting	8.	Fibre-reinforced shotcrete, >15 cm; Reinforced ribs of shotcrete and bolting
4.	Systematic bolting (and unreinforced shotcrete, 4–10 cm.	9.	Cast concrete lining
5.	Fibre-reinforced shotcrete and bolting, 5–9 cm

Table 5.

Q support system details [14].

2.8 Section conclusion

The main purpose of all rock mass classification systems developed empirically is to describe the rock mass. There are many parameters as inputs in all studies. While making the evaluations, the comments that each engineer will make in the field may be different. Since these evaluations are empirical, they directly affect the determination of the rock class. Another important factor in rock classification is the evaluation of boreholes, which is one of the basic input parameters and perhaps the most important one. Consideration should be given to the sampling and run lengths required while drilling. Errors made during these processes will directly affect the design. Since the wrong calculation of the RQD value will be a direct input parameter in the rock mass parameters, borehole quality is extremely important. The number and location of drillings is another important factor. The insufficient number of boreholes will significantly increase the uncertainty in determining the tunnel rock classes. The uniaxial compression test or point load test, also appears as direct input parameters. During laboratory experiments, sampling, transportation or errors seriously affect the rock mass classification systems.

It is unwise to accept the results of the rock classification system as invariably correct, even when there are great uncertainties in determining the rock parameters.

Each of the researchers, on the other hand, aimed to make rock mass classifications according to the support systems that were successful in the field. Each method has its own limitations. Terzaghi [1] only offered suggestions for steel supports for tunnels excavated in solid rock. Bieniawski determined the intervals as 20 units in the determination of the RMR system. This situation often brings with it uncertainties. When the RMR value is calculated as 41, the rock class is medium rock, and when it is 39, it is weak rock. According to this situation, one should be very careful in recommending support. As stated, in cases where the rock mass parameters are purely empirical and relative, specifying and applying the support elements directly according to the determined RMR values may lead to wrong results.

Since similar limitations are valid for all rock mass classification systems, taking the rock mass classification systems as invariable correct will give extremely inaccurate results. Rock mass classification systems are, however, extremely important for the preliminary evaluation and preliminary design of the unit that the tunnel will pass through. In light of these obtained data, it is necessary to dimension the support systems with analytical and numerical methods.

Because the support systems determined according to all rock mass classification systems are given within a range a clear and precise sizing cannot be given. For this reason, these approaches are only a guide in terms of tunnel design.

3. Closed-form solutions-rock support interaction

It is often difficult to determine how the rock mass is deformed during tunnel excavation to determine the interaction of rock support systems because there are many uncertainties in defining the rock. Most of the time, such approaches give results on a homogeneous medium, but in a complex situation, they should be evaluated with numerical analysis.

In addition to empirical methods, closed-form solutions are used in the determination of tunnel support systems. Closed-form solutions calculate the plastic behaviour of the rock mass and determine the deformations that occur according to the support pressures. The interaction of the ground and support systems is revealed by drawing the ground interaction curve and support interaction curves in the tunnel.

The assumptions made in the analysis are;

• The tunnel is circular

• In situ stresses are considered hydrostatic

• The rock mass is homogeneous and isotropic.

4. Analysis of tunnel behaviour during construction

Figure 4 shows the deformation vectors and the plastic zone in the tunnel propagation direction in weak rocks. Figure 5 gives a summary of the deformations that occur in the tunnel. The elastic deformations that occur in the tunnel start at a distance of two tunnel diameters in front of the tunnel and reach the maximum level after two tunnel diameters behind the tunnel face [16]. The maximum displacement occurring in the tunnel face is one-third of the total displacements (Figure 5).

Figure 4.

Vertical section through a three-dimensional finite element model of the failure and deformation of the rock mass surrounding the face of an advancing circular tunnel [16].

Figure 5.

Radial displacements around the tunnel [17].

The unsupported deformation situation for the rock-soil interaction is given in Figure 6. If the uniaxial compressive strength of the rock mass is σ_cm > 2p_o (p_i = 0), the displacements are elastic and continue linearly. If a failure occurs, the displacements are plastic and are curved in Figure 6.

Figure 6.

Graphical representation of relationships between support pressure and radial displacement of tunnel walls [16].

Ground reaction curve or characteristic line depends on the convergence occurring in the tunnel with the internal support pressure.

Here, the tunnel radius is taken as r₀, the hydrostatic pressure p₀ and the support pressure as p_i (Figure 7).

Figure 7.

Plastic zone surrounding a circular tunnel.

If the support pressure p_i is less than the critical pressure p_cr, the rock mass will fail. If the pi pressure is greater than p_cr, no failure occurs around the tunnel and the rock mass behaves elastically. The critical support pressure is given in Eq. (5):

$$\mathit{Pcr}=\frac{2p0-\mathit{\sigma cm}}{1+k}$$E5

Elastic displacement is given in Eq. (6):

$$\mathit{uie}=\frac{r0\left(1+\vartheta \right)\left(p0-\mathit{pi}\right)}{\mathit{Em}}$$E6

Here E_m is the rock mass deformation modulus and ν is Poisson’s ratio.

If the support pressure (p_i) is less than the critical pressure p_cr, failure occurs around the tunnel and a plastic zone is formed. In this case, plastic deformation and plastic zone radius are defined by Eq. (7). The resulting plastic deformation is given in Eq. (8):

$$\mathit{rp}=\mathit{ro}\left[\right(\frac{2\left(p0\left(k-1\right)+\mathit{\sigma cm}\right)}{\left(1+k\right)\left(\left(k-1\right)\mathit{pi}+\mathit{\sigma cm}\right)}]^\frac{1}{k-1}$$E7

$$\mathit{uip}=\left(\frac{\mathit{ro}\left(1+\vartheta \right)}{\mathit{Em}}\right)\left[2\left(1-\vartheta \right)\left(p0-\mathit{pcr}\right){\left(\frac{\mathit{rp}}{r0}\right)}^2-\left(1-2\vartheta \right)\left(p0-\mathit{pi}\right)\right]$$E8

The graph of radial displacement with Pi to the support pressure drawn with the help of the given equations is given in Figure 8. Here,

Figure 8.

Response of support system to tunnel wall displacement resulting in the establishment of equilibrium [16].

if p_i = p_o, no deformation occurs,

p_i > p_c elastic deformation occurs,

p_i < p_crise plastic deformation occurs.

After the support installation, the deformations continue elastically. Maximum elastic deformation is defined as u_sm and maximum support pressure is defined as p_sm.

Support interaction analysis depends on three main parameters. These are

• Deformations that occur before support are made

• Support stiffness

• Support capacity

In the support reaction curve, elastic deformations occur in the tunnel after the tunnel excavation. The support reaction curve has reached equilibrium if the ground reaction curvature crosses the curve before deformations in the rock mass increase substantially. However, if the deformations that occur develop very quickly and the reinforcements are insufficient, failure occurs and balance cannot be achieved.

Equations for the stiffness and capacity of supports have been published by Hoek and Brown [18] and Brady and Brown [19]. The equations are given in Table 6.

Steel set
σys is the yield strength of the steel (MPa); Es is the Young’s modulus of the steel (MPa); As is the cross-sectional area of the section (m^2); sl is the set spacing along the tunnel axis (m); ro is the radius of the tunnel (m); Pssmax is the maximum support pressure; Kss is the stiffness	$\mathit{\text{Pssmax}}=\frac{\mathrm{As}\ast \mathit{\sigma ys}}{\mathit{sl}\ast \mathit{lro}}$ (9); $\mathit{\text{Kssmax}}=\frac{\mathrm{Es}\ast \mathit{As}}{\mathit{sl}\ast \mathit{lr}{o}^2}$ (10)
Rock bolts
db is the rockbolt or cable diameter (m); l is the free length of the bolt or cable (m); Es is the Young’s modulus of the bolt or cable (MPa); sc is the circumferential bolt spacing (m); sl is the longitudinal bolt spacing (m); Tbf is the ultimate bolt or cable load; Psbmax is the maximum support pressure; Kss is the stiffness	$\mathit{\text{Psbmax}}=\frac{\mathit{Tbf}}{\mathit{sl}\ast \mathit{sc}}$ (11); $\mathit{Ksb}=\mathit{Es}\ast \pi \ast \frac{d{b}^2}{4\mathit{\text{lslsc}}}$ (12)
Concrete or shotcrete
σcc is the uniaxial compressive of the concrete or shotcrete (MPa); Ec is the Young’s modulus of the concrete or shotcrete (MPa); υ is the Poisson ratio of the concrete or shotcrete; tc is the thickness of the lining (m); ro is the radius of the tunnel (m); Pscmax is the maximum support pressure; Kss is the stiffness	$\mathit{\text{Pscmax}}=\frac{\mathit{\sigma cc}}{s}\ast \left[1-\frac{{\left(\mathit{ro}-\mathit{tc}\right)}^2}{r{o}^2}\right]$ (13); $\mathit{Ksc}=\left(\mathit{Ec}\ast \frac{r{o}^2-{\left(r0-\mathit{tc}\right)}^2}{2\ast \left(1-{\vartheta }^2\right)\ast \left(r0-\mathit{tc}\right)\ast r{o}^2}\right)$ (14)

Table 6.

Support capacity equations [18, 19].

5. Numerical methods

In tunnel design, empirical solutions and analytical solutions do not always give exact results. Numerical analysis and solutions are required for complex geological structures and complex underground structures. The Finite Element Method, Finite Difference Method and Discrete Element Methods are used as common numerical analysis methods. Numerical analysis methods are used both in 2D and 3D. Numerical programs have been increasingly used in tunnel design in recent years. In numerical programs, in-situ conditions, geological units and boundary conditions can be reflected exactly. In addition, while creating the models, the tunnel geometry, excavation stages and support details can be entered into the model exactly.

In numerical methods, the stresses and strains occurring in the ground can be calculated and the cross-sectional effects on the support systems can also be determined. Thus, much more accurate results can be obtained compared to empirical and analytical solutions for design.

6. Weak rock tunnelling-soil tunnelling

In the evaluations of rock mass classification systems, support details for weak rocks are usually detailed as cast lining or ring closure of the inverted section with rigid lining. However, in tunnels defined as weak rock or soil, dimensioning support details is often not possible according to rock mass classification systems. In these sections, the dimensioning of support systems can be detailed as a result of analytical solutions and numerical solutions. According to ISRM classification systems, sections with a value of less than 1 MPa are considered soil. In addition, special support system solutions emerge in weak rocks, especially in units with weak strength such as clay, claystone and schist. The squeezing mechanism that develops under high overburden affects the long-term performance of the support systems. For this reason, both squeezing and swelling potential are the most important factors in tunnels excavated in weak rocks and soils. Two different tunnel support system approaches are used for tunnels excavated in weak rocks and soils [19, 20, 21, 22]. These are called the passive method and the active method. While the passive method is based on the principle of increasing the support pressure by allowing deformations in the tunnel, in the active method, the support systems are dimensioned without allowing such deformations. However, for the passive approach in squeezing ground, the long-term deformations that may occur in real projects were often unsuccessful and an active approach was adopted in the revisions made. For this reason, it is very important to determine and evaluate the squeezing mechanism, which is one of the most important factors in weak ground.

6.1 Squeezing in tunnels

In the evaluations for the squeezing mechanism, Jethwa et al. [23], Sakurai [24], Singh et al. [25], Goel et al. [26], Hoek and Marinos [27], Aydan et al. [28] approaches are quite common. In these approaches, the uniaxial compressive strength of the rock mass, unit weight and overburden height appear as the main factors.

Singh et al. [25] defined according to the Q value. If the H value determined according to Eq. (15) is greater than $350\ast Q^{1/3}$, squeezing is expected, while if the H value is less than $350\ast Q^{1/3}$, squeezing is not expected (Figure 9):

Figure 9.

Squeezing conditions regarding Q and H values [25].

$$H=350\ast Q^{1/3}$$E15

Goel et al. [26], on the other hand, defined the squeezing state similarly according to the Q value. He stated the calculated value of the Q value according to the stress-free conditions as N (rock mass number). If the H value (Eq. (16)) calculated according to this value is greater than the thickness of the overburden height, squeezing will occur, and if it is small, there will be no squeezing. In Figure 10, Goel et al. [26] the squeezing condition is shown according to the N value:

Figure 10.

Squeezing conditions according to Goel et al. [26].

$$H=\left(275N^{0.33}\right)B^{-1}\left(\mathrm{m}\right)$$E16

Sakurai [24] classified the compression mechanism according to the strain value calculated based on the uniaxial compressive strength of the rock mass. He proposed Eq. (17) to determine the strain value:

$$\mathit{\epsilon pc}=1.073\mathit{\sigma c}{m}^{-0.318}$$E17

The relationship between the uniaxial compressive strength of the rock mass depending on the strain value is given in Figure 11.

Figure 11.

Relationship between uniaxial compressive strength of strain and rock mass [24].

Jethwa et al. [23] classified the compression according to the N coefficient. Nc coefficient (competency factor) is given in Eq. (18):

$$\mathit{Nc}=\mathit{\sigma cm}/\mathit{Po}$$E18

P_o is the in situ stress and σ_cm is the uniaxial compressive strength of the rock mass. The compression status according to the calculated Nc value is given in Table 7.

Degree of squeezing	Ranges (N)
High	<0.4
Moderate	0.4–0.8
Slightly	0.8–2
Non-squeezing	>2

Table 7.

Squeezing degree according to Jethwa et al. [23].

Hoek and Marinos [27] defined the squeezing according to the strain value depending on the relationship between the uniaxial compressive strength of the rock and the in-situ stress. The strain value is given in Eq. (19):

$$\epsilon =0.2\ast {\left(\mathit{\sigma cm}/\mathit{Po}\right)}^{-2}$$E19

The squeezing mechanism is given in Figure 12 depending on the calculated strain value and the ratio of the compressive strength of the rock mass to the in situ stress.

Figure 12.

Approximate relationship between strain and the degree of difficulty associated with tunnelling through rock [27].

While evaluating the squeezing mechanism, the critical factors are the height of the overburden, the unit weight and the uniaxial compressive strength of the rock mass.

6.2 Swelling in tunnels

Swelling soils can cause failures in the support systems due to unexpected loads. Most of the time, it can cause failures and swell even in the sections where inner lining and invert concrete are completed in tunnels. For this reason, the swelling potential of the ground should be evaluated during tunnel design. Support systems should be designed to carry these new loads that may occur. Einstein and Bischef [29] suggested a design procedure for swelling soils. First of all, the process can be listed as determining the primitive stress state of the current situation, determining the swelling soils around the tunnel and performing the swelling tests (odometer). In addition, they suggested closing the ring with invert, draining the water in the tunnel and closing the surface with steel-wire shotcrete (SFRS) after excavation.

Komornik and David [30, 31] proposed Eq. (20) for the analytical determination of the pressure that will occur due to the swelling:

$$\text{logps}=2.132+0.0208\mathit{\omega L}+0.000665\mathit{\gamma d}-0.0269\mathit{\omega n}$$E20

where.

ps = selling pressure (kg/cm²) at zero swelling strain.

$\mathit{\omega L}$=liquid limit (%).

γd = natural dry density (kg/m³) and.

$\mathit{\omega n}$=natural moisture content (%).

7. Tunnel support details for classical tunnelling

Support systems in tunnels are generally divided into two main parts.

1. Outer lining

   • Shotcrete

   • Steel rib

   • Bolt

   • Forepoling/Umbrella

2. Inner lining

The outer lining used in the tunnel is made to ensure the stability of the tunnel after the tunnel excavation.

Shotcrete: Shotcrete is used in tunnels as a basic carrier element. Shotcrete applied immediately after the excavation not only prevents the ground from loosening by preventing atmospheric effects but also has the feature of carrying the loads coming from the ground. Shotcrete application is divided into dry and wet in tunnels.

Steel rib: With the increase in the thickness of shotcrete in tunnels, it acts as reinforcement in the concrete and can resist the first deformations that will occur after excavation in the tunnel. Steel rib can be divided into I type, H type, lattice girder and TH type (sliding rib).

Rock bolt: The rock bolt is an integral part of the external support as a support system. It is a support system that is necessary both to prevent block slipping due to discontinuities in rocks and to connect the plastic zone to the elastic zone in weak rocks. Rock bolts are used passively in tunnels. It is divided into SN, PG, swellex and self-drilling bolt (IBO). Rock bolt diameters are generally used between 28 mm and 51 mm depending on the soil type.

In SN-type bolt applications, firstly the hole is drilled, then the borehole is filled with injection and finally, the bolt is placed into the hole (Figure 13).

Figure 13.

SN-type rock bolt.

In PG-type bolts, after the hole is drilled, the PG bolt is driven into the hole. In the last stage, the grout is pumped into the hole using the grout pipe (Figure 14).

Figure 14.

PG type bolts.

Swellex-type bolts are used in tunnels opened in rocks with water ingress. After drilling the hole, the swellex bolt is placed. Afterwards, high pressure is applied from the bolt mouth, allowing the bolt to swell and hold onto the rock (Figure 15).

Figure 15.

Swellexs type rock bolt.

IBO (injection boring outside) is known as self-drilling bolts. In the application, the hole is drilled with the help of the bit attached to the bolt and the bolt remains in the borehole. In long bolts, bolts connected with coupling are added every 3 or 4 m and placed in the hole together with the drill (Figure 16). The injection process is completed by filling the entire drilling through the IBO bolts.

Figure 16.

IBO type bolts.

Forepoling/umbrella: Forepolings are not basically considered as a carrier element. The main purpose of the forepoling is to provide the stability of the ceiling in order to prevent slips that may occur during the excavation (Figure 17). Forepoling diameters and types vary depending on the ground.

Figure 17.

Umbrella type forepoles.

Inner Lining: The inner lining concrete is made after the completion of the outer supports of the tunnel in order to give the tunnel its final form and to provide an architectural view. In general, inner-lining concrete is not considered as a load-bearing element. However, in weak or very weak rock conditions, it has recently been designed as a carrier element. The inner lining concrete is a necessary structure for the placement of drainage pipes required for tunnel drainage, as well as for the placement of ventilation fans and electro-mechanical devices to be used in the tunnel (Figure 18).

Figure 18.

Tunnel inner lining section (a) tunnel section (b) application in site.

8. Tunnel excavation systems

Circular tunnel cross-section is always the most accurate method for tunnel stability and stress distribution (Figure 19). However, in most cases, this is not possible. Horseshoe section is often applied in mine galleries and water tunnels (Figure 20).

Figure 19.

Circular tunnel section.

Figure 20.

Horseshoe tunnel section.

As a tunnel excavation method, it is preferred that it is completed as a full section, and the stress distributions are created once, in terms of tunnel stability. However, in large-diameter tunnels, the excavation process is carried out gradually. While tunnel excavation is divided into top heading and bench in solid rock, invert excavation is also carried out in weak rocks (Figure 21).

Figure 21.

Tunnel excavation section (a) longitudinal section (b) front view.

In solid rocks, the distance between the top heading and the bench can be longer due to the low deformations. This distance can be up to 70–100 m in solid rocks. On weak grounds, the top heading, bench and invert distance should be minimum to complete the ring. The distance between the top heading and the bench is between 15 and 25 m in weak ground conditions. Temporary invert is performed to prevent deformations that may occur in the top heading in very weak soils. Thus, deformations are limited by closing the ring in the top heading.

In addition, the ADCEO-RS (The Analysis of Controlled Deformation in Rocks and Soils) method also suggests a near-full cross-section excavation in both rocks and weak soils [32, 33]. In this method, the tunnel face and ceiling section are reinforced with fibre bolts, and the tunnel excavation can be done as a full section (Figure 22). Thus, the tunnel is excavated close to the circular, and the ring is closed immediately.

Figure 22.

ADECO-RS full-face excavation method.

Tunnel excavation in long tunnels (L > 5 km) can be conducted using a Tunnel Boring Machine (TBM). It is generally preferred in metro tunnels and water tunnels (Figure 23). The TBM machine carries out the excavation with mechanical excavation and segments or supports are placed right behind it.

Figure 23.

Hard rock TBM section for water tunnels.

The type and selection of TBM completely depend on the type of soil or rock. While open TBM is preferred for solid rocks, earth pressure balanced (EPB) type TBMs are preferred for very weak rocks. TBM types are summarised in Table 8 [34].

Face support	Full face excavation	Partial face excavation
None or passive	Open hard rock TBM or Main Beam TBM	Digger shield
	Single shield hard rock TBM	Auger or road header
	Double shield Hard Rock TBM
Active	Earth Pressure Balanced TBM (EPB-TBM)	Digger shield with compressed air
	Slurry TBM	Auger or road header with compressed air
	Compressed Air Shields
Combination	Dual or Multimode-TBMs, combining for example hard rock excavation with EPB-and/or Slurry mode

Table 8.

Most common TBM with or without face support [34].

9. Geotechnical measurements

Studies carried out during the design phase can never give a definitive result. Because the research studies for tunnel design are limited and the acceptances to be made require that tunnel projects always be controlled with the measurements made during the tunnel excavation. This is because not all the works carried out during the tunnel design phase reflect the tunnel behaviour exactly. Every tunnel project requires revision during tunnel excavation. For this purpose, geotechnical measurements made during the tunnel excavation are of great importance and it is an indispensable condition of tunnelling.

A correct programming of measurements during the tunnel excavation will both prevent uncertainties in the tunnel project and contribute to the formation of a safer and more economical outcome. The geotechnical measurements to be made in the tunnel are:

1. Deformation measurements.

2. Convergence measurements.

3. Extensometer measurements.

4. Inclinometer measurements.

5. Stress cell-pressure measurements.

6. Strain gauge measurements.

7. Piezometric measurements.

8. Geotechnical face maps.

9.1 Deformation measurements

During the tunnel excavation, deformation measurements should be carried out every 10 or 20 m for solid rocks and every 2 m for weak rocks. Deformation measurements are made by electronically reading targets placed along the tunnel section with a theodolite. These measurements provide extremely important information regarding tunnel behaviour. According to the results of the measurements, the deformations in the tunnel can be determined and the support systems and the excavation sequence can be revised. The measurement frequency can be adjusted on-site according to the deformation rate occurring in the tunnel. If the measurements made during the first week after the excavation remain constant, they are continued weekly, while in cases where the deformation increases daily, two readings can be made daily (Figure 24).

Figure 24.

Deformation target points in circular tunnel.

9.2 Convergence measurements

During tunnel excavation, convergence measurements should be made with tape extensometers (Figure 25) to see the closures in the tunnel. In addition to deformation measurements, convergence measurements are also made to determine on which side and how much the closure is.

Figure 25.

Tape the extensometer section in the tunnel.

9.3 Extensometer measurements

Extensometer measurements are made in the tunnel in order to see the plastic zone thickness around the tunnel (Figure 26). They play an important role in determining the length of the bolts by detecting the loosened zone thickness around the tunnel. In addition, they give information about the magnitude of the loads that will come to the outer lining depending on the loosened zone thickness. Extensometer lengths are determined according to the tunnel diameter. Extensometers can be applied individually as well as in single, double or triple types. Measurements are started immediately after the placement of extensometers and are made daily or weekly depending on the frequency of movement.

Figure 26.

Extensometer measurements in tunnel (a) installation section in tunnel, (b) in tunnel application and (c) triple type extensometer.

9.4 Inclinometer measurements

Inclinometer measurements are made from the surface to see possible movements in the portal sections or on the tunnel route (Figure 27). The inclinometer is selected according to the thickness of the land movement or possible loose zone in the drilled boreholes and generally goes down to the level of the tunnel. By means of inclinometers, possible movements in the portal section are determined and the necessary information is provided for the portal design, and it can be determined whether possible movements on the tunnel route affect the tunnel structure.

Figure 27.

Inclinometer typical section (a), measurements on site (b).

9.5 Stress cell

Stress cells are placed on the ground or concrete after excavation to see the stresses acting on the supports. In addition, stress cells are placed in the inner lining of concrete and the stresses that occur in the lining are determined. With the determination of the incoming loads, necessary revisions can be made in the shotcrete or inner lining concrete design/implementation. Because, when the assumptions made in tunnel lining calculations often differ with the site conditions, it is extremely important to determine the incoming loads on site. The lining thicknesses can be determined by making back analyses by means of the loads determined in the field. Stresses can be measured by placing the stress cell in both the radial and tangential directions (Figure 28).

Figure 28.

Stress cell and strain gauge application on site.

9.6 Strain gauge measurements

Strain gauges are placed in shotcrete or interior lining concrete to see the strains in the lining and to detect the incoming stresses (Figure 28).

9.7 Piezometric measurements

Piezometric measurements can be carried out to measure the water pressure or the water level around the tunnel. These measurements are of great importance for inner lining design, especially in the long term.

9.8 Geotechnical face maps

After the tunnel excavation, the geological units should be defined and perimetric maps should be made. The changes in geological conditions with these maps are extremely important in terms of evaluating the changes in geological conditions between those envisaged in the project and the geological conditions actually encountered. If there is a difference between the encountered geological conditions and the predicted geological conditions, the tunnel design may need to be revised according to the new conditions.

9.9 Conclusion

Acceptances and geotechnical investigations carried out during the tunnel design phase are limited. All tunnel projects are made with these deficiencies and in a sense, they are in the form of a preliminary project. It should never be possible to go with uncertainties and to implement the same support systems made in the design phase. Geotechnical measurements and project data should be continuously evaluated and revised according to the encountered geological conditions.

10. Conclusion

Empirical, analytical and numerical approaches should be used together in tunnel design. Empirical methods provide preliminary information for the rock mass and support design during the design phase. The details of support systems should be complemented by numerical analysis.

Each tunnel reaches its final design status during the process of tunnel excavation. All the acceptances made during the design phase should be considered as preliminary assumptions. Based on the geological-geotechnical research carried out during the design phase, the tunnel behaviour cannot be fully revealed. For this reason, measurements such as geological and geotechnical evaluations, deformation measurements, convergence measurements and pressure cells should be done to revise the tunnel design according to the encountered geological conditions.

During the tunnel excavation, geological-geotechnical measurements, face maps and horizontal boreholes, if necessary, should be carried out continuously.

TBM selection and design are completely dependent on geological conditions. The wrong TBM selection can be made because of the geological profile that is not determined correctly. This situation causes very serious project problems in the tunnel.

While determining the tunnel excavation method, tunnel opening and ground conditions are some of the most important factors. In large-diameter tunnels, the tunnel is usually divided into top heading, bench and invert if necessary. It is obligatory to close the ring (top heading, bench and invert) as soon as possible when excavating in weak rock conditions and soils. Otherwise, serious deformations can be observed in the tunnel. The most correct approach for tunnel section is circular or near-circular type section.

Acknowledgments

The author would like to thank Fugro Sial Geosciences Engineering Ltd.

Conflict of interest

The author declares no conflict of interest.