Ground load on tunnels built using new Austrian tunneling method: study of a tunnel passing through highly weathered sandstone

Abstract

The ground load acting on a tunnel is an important issue in tunnel design, especially when the tunnel passes through highly weathered sandstone. A systematic field-monitoring campaign was performed to investigate the ground loads on a tunnel structure, the behavior of the composite support system, and the deformation of the tunnel boundaries. The monitoring results were analyzed and compared with those of various theories, such as the whole-soil column theory and those of Terzaghi, Bierbaumer, Xie Jiaxiu, and Protodyakonov. The ground load on a highway tunnel in highly weathered sandstone does not conform to current theoretical methodologies. It was confirmed that Terzaghi’s theory is suitable for estimating the peak magnitude of the vertical ground load, but differs from the field-monitoring results for ground load distribution profile. To facilitate tunnel design, a potential profile for ground loads is proposed, in which the vertical load component is ‘mountain’-shaped and the horizontal component adopts a ‘folded-line’ pattern. The roof rockbolts are subjected to compression and should be replaced by pipe grouting that is capable of providing enhanced reinforcement and accelerating the construction schedule. The bending moments acting on the lining were found to form a ‘butterfly’ shape. Supplementary finite-element modeling was undertaken to explore the mechanical behavior of the tunnel lining. These results indicated that steel rebar needs to be pre-installed in both the intrados of the lining roof and extrados of the spandrels to improve the lining tensile strength.

Appendix A Theories typically used to calculate ground load

Whole-soil column theory

At shallow depths, the excavation-induced failure plane extends to the surface of the ground and frictional resistance is not considered. Consequently, the uniform vertical ground load q on the tunnel structure increases linearly with increasing buried depth:

$$ q=\gamma h $$

(A1)

where γ denotes the unit weight of the ground and h represents the vertical distance from the ground surface to the tunnel roof.

Xie Jiaxiu’s theory

The failure plane is assumed to be inclined at an angle β to the horizontal, as shown in Fig. 17. In this figure, the settlement of ground block GEFH (above the roof opening) would cause potential movement of lateral blocks FDB and ECA. According to Xie Jiaxiu’s theory (China Railway Eryuan Engineering Group 1997; Song et al. 2007), the vertical ground load, q, can thus be expressed as:

$$ \Big\{{\displaystyle \begin{array}{c}q=\gamma\;H\left(1-\frac{H}{2a}\lambda\;\tan \theta \right);\\ {}\lambda =\frac{\tan \beta -\tan {\varphi}_0}{\tan \beta \left[1+\tan \beta \left(\tan {\varphi}_0-\tan \theta \right)+\tan {\varphi}_0\tan \theta \right]};\\ {}\tan \beta =\tan {\varphi}_0+\sqrt{\frac{\sec^2{\varphi}_0\tan {\varphi}_0}{\tan {\varphi}_0-\tan \theta }},\end{array}} $$

(A2)

where a is half the span of the excavation, λ is the lateral ground pressure coefficient (defined as the ratio of the horizontal to vertical ground loads) acting on the tunnel structure, β is the angle of inclination of the failure plane with respect to the horizontal direction, φ₀ is the computational friction angle, θ is the friction angle of the sliding surface l_FH or l_EG, and the other parameters are as previously defined.

Fig. 17

Schematic diagram of the tunnel in Xie Jiaxiu’s theory

Terzaghi’s theory

Terzaghi (1946) assumed that the ground acts as a granular material. Thus, once the tunnel is excavated, the medium above the opening space is able to deform downwards. A sliding surface l_OAB is assumed to be formed (Fig. 18). Accordingly, Terzaghi found that the vertical ground pressure on the tunnel support is given by:

$$ q=\frac{\gamma b}{\tan \varphi \cdot K}\left[1-\exp \left(-K\tan \varphi \cdot \frac{h}{b}\right)\right]. $$

(A3)

Fig. 18

Diagram illustrating the parameters involved in Terzaghi’s theory

As the tunnel depth h increases, the second term in the square brackets gradually vanishes due to its exponential form, and Eq. (A3) simplifies to:

$$ q=\frac{\gamma b}{\tan \varphi \cdot K} $$

(A4)

Protodyakonov’s theory

This theory takes into consideration the arch effect hypothesized for deep tunnels, which leads to the formation of a parabolic profile above the tunnel roof (Myrianthis 1975; Szechy 1970). The weight of loose ground below the parabolic curve is referred to as the ‘ground load’ and is thus related to the dimensions of the tunnel (Fig. 19). The vertical ground pressure acting on the supporting structure is then calculated from the weight of the ground under the parabolic curve:

$$ \Big\{{\displaystyle \begin{array}{c}{a}_t=a+{H}_t\times \tan \left(45-\varphi /2\right);\\ {}{h}_k={a}_t/f=\frac{a_t}{\left(\tau /\sigma \right)}={a}_t\cdot \sigma /\left(\sigma \tan \phi +c\right)={a}_t/\tan \varphi; \\ {}q=\gamma \times {h}_k,\end{array}} $$

(A5)

where a_t is half the width of the collapse arch, a is half the span of the tunnel, H_t is the net height of the opening, φ is the friction angle of the ground, and h_k is the height of the collapse arch. It should be noted that the expressions in Eq. (A5) are not suitable for the condition where the buried depth of tunnel is less than five times the opening span (10a).

Fig. 19

Illustration showing the basis of Protodyakonov’s theory

Bierbaumer’s theory

Engineering practice shows that the ground load exerted on the structure of a tunnel is always less than the weight of the covering strata. By considering the forces of resistance (due to internal friction) and cohesion on the failure plane (Fig. 20), Bierbaumer (1913) theorized that the vertical load on the roof of the tunnel is:

$$ {q}_b=\gamma {H}_{\mathrm{t}}\left[1-\frac{H_{\mathrm{t}}}{2{a}_1}{K}_1-\frac{c}{\gamma {a}_1}\left(1-2{K}_2\right)\right], $$

(A6)

where a₁ = a + H_t tan(45^∘ − φ/2), K₁ = tan φ tan²(45^° − φ/2), K₂ = tan φ tan(45^° − φ/2).

Fig. 20

Scheme used in Bierbaumer’s theory