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Technical Manual for Design and Construction of Road Tunnels - Civil Elements

Appendix F - Sequential Excavation Method Example

The calculation example involves the tunneling analysis and lining design of a typical two-lane highway tunnel using the finite element code Phase2 by Rocscience, Inc. The calculation is carried out in stages and follows the approach laid out in 9.7.2.3 above and evaluates ground reaction as indicated in 9.7.2.4 and evaluates support elements as described in 9.7.2.5 and 9.7.2.6.

In this example, homogeneous, isotropic ground conditions are assumed. The constitutive model is based on the Mohr-Coulomb failure criterion. Table 9-6 displays each calculation stage in a left column, typical output graphics in the middle column and further explanations and comments in the right column. The calculation is for a SEM tunnel that uses a top heading and bench excavation sequence. After each excavation step (top heading and bench) the initial support elements are installed and consist of rock dowels and an initial shotcrete lining.

After establishing the initial, geostatic stress conditions in Stage 1, the excavation and installation of initial support is carried out in stages 2 through 5. The tunnel final lining installation occurs in stage 6. For simplicity, it is assumed that the initial lining will deteriorate completely and all ground loads will be imposed onto the final lining in stage 6. No other loading conditions such as ground water loads or seismic loading are included in this example.

The structural capacity of the initial and final linings is evaluated using so called Capacity Limit Curves or "CLCs." The calculated section force combinations N-M, i.e., initial or final lining normal forces N and lining bending moments M are graphed onto charts where the CLCs denote the capacity of the structural lining section in accordance with ACI 318.

Section force combinations N-M are obtained from each finite element included in the representation of the lining (beam or shell) in the numerical modeling. The capacity of the lining is displayed in accordance with ACI 318 considering lining thickness, concrete (shotcrete) design strength, and structural reinforcement of the lining section. Steel fibers are used for the structural reinforcement of the shotcrete initial lining and conventional, deformed bars are used for the reinforcement of the concrete linings.

The example is presented in a tabulated format (Table F-1) as follows. Note the last row of Table F-1 represents the capacity limit curves for both the initial shotcrete and final concrete linings. All N-M (normal force-bending moment) combinations represented by dots fall well within the enveloping CLCs indicating that in this example the linings as designed will provide sufficient capacity for the anticipated ground conditions and associated ground loads.

TABLE F-1 SEM Calculation Example for a Two-Lane Highway Tunnel in Rock
Stage 1: This stage assesses the in-situ, geostatic stress conditions prior to the tunnel construction. It considers the unit weight of the ground material, lateral loads dictated by the lateral earth pressure coefficient, any tectonic stresses and overburden loads. Main input parameters involve unit weight (γ), modulus of elasticity (E), friction angle (φ), cohesion (c) and Poisson's Ratio (v). This stage is considered to be the 'initial stage' of the model prior to any tunnel excavation.
Stage 1Stage 1

Stage 1: Geostatic Stress Conditions

Output Options: Ground Stresses and Deformations

Output Shown: Major Principal Ground Stress Sigma 1

Stage 2: The tunnel excavation causes ground relaxation and ground deflection related to it occurs ahead of the advancing tunnel construction face and around the tunnel. While this relaxation causes ground deflection and surface settlements near excavations, the ground movement also mobilizes shear resistance in the ground. This ground relaxation due to the excavation process before support installation associated with the excavated round length is approximated by "softening" the material within the top heading; the ground material within the top heading is softened by reducing the stiffness of the material by 0.4 – 0.6 times the actual ground modulus (Eactual).
Stage 2Stage 2

Stage 2: Excavation of the Top Heading

Output Options: Ground Stresses and Deformations

Output Shown: Major Principal Ground Stress Sigma 1 (Note stress relaxation above the tunnel and stress concentration around top heading sidewalls and temporary invert)

Stage 3: In this step the ground elements in the top heading are removed and the initial support elements including shotcrete and rock dowels/bolts are inserted. This leads to a new equilibrium where the initial support elements support the tunnel opening. The shotcrete is modeled using beam elements and the dowels/bolts are modeled using elements that may be loaded in axial loading only. To simulate the early age of the shotcrete its elastic modulus is reduced to one third (1/3) of its final, 28-day design strength. The shotcrete reaches its full strength in the next stage. The initial shotcrete lining capacity is verified in accordance with ACI 318 using Capacity Limit Curves.
Stage 3Stage 3
Stage 3
Stage 3

Stage 3: Installation and Loading of Initial Support in the Top Heading (Shotcrete and dowels/bolts)

Output Options: Ground Stresses, Deformations of Ground and Linings, Section Forces (N, M) in Shotcrete Lining, Loads in Rock Dowels/Bolts

Output Shown:

- Major Principal Ground Stress Sigma 1

- Shotcrete Lining Force Diagram:

- N – Axial Force

- M – Bending Moment

- Dowel/Bolt Forces:

- N – Axial Force

Stage 4: Similar to Stage 2 the tunnel excavation in the bench will cause ground relaxation and ground deflection. This ground relaxation due to the excavation process before support installation is approximated by "softening" the material within the bench; the ground material within the bench is softened by reducing the stiffness of the material by 0.4 – 0.6 times the actual ground modulus (Eactual).
Stage 4Stage 4

Stage 4: Excavation of the Top Heading

Output Options: Ground Stresses, Deformations of Ground and Linings, Section Forces (N, M) in Shotcrete Lining (Top Heading), Loads in Rock Dowels/Bolts (Top Heading)

Output Shown: Major Principal Ground Stress Sigma 1

Stage 5: Similar to Stage 3 the ground elements in the bench are removed and the initial support elements including shotcrete and rock dowels/bolts are inserted in the bench.
Stage 5Stage 5
Stage 5
Stage 5

Stage 5: Installation and Loading of Initial Support in the Bench (Shotcrete and dowels/bolts) Output Options: Ground Stresses, Deformations of Ground and Linings, Section Forces (N, M) in Shotcrete Lining, Loads in Rock Dowels/Bolts

Output Shown:

- Major Principal Ground Stress Sigma 1

- Shotcrete Lining Force Diagram:

- N – Axial Force

- M – Bending Moment

- Dowel/Bolt Forces:

- N – Axial Force

Stage 6: This stage involves installation of the concrete final lining beam elements. These are inserted into a stress free state as all ground loads are supported by the initial support elements. A "slip" layer is simulated between the shotcrete and concrete lining beam elements. This layer will allow transfer of radially acting forces only thus representing the waterproofing membrane layer between the linings that is incapable of transferring shear forces. In this example it is assumed that over time, the initial shotcrete lining and rock dowels/bolts deteriorate and all loads need to be supported by the final lining. To simulate this phenomenon, the initial lining elements (i.e. shotcrete and rock dowels/bolts) are removed from the model thus loading the final lining. The final concrete lining capacity is verified in accordance with ACI 318 using Capacity Limit Curves.
Stage 6Stage 6
Stage 6

Stage 6: Installation and Loading of Final Concrete Lining by Removing all Initial Support elements in the Top Heading and Bench (Shotcrete and dowels/bolts)

Output Options: Ground Stresses, Deformations of Ground and Linings, Section Forces (N, M) in Shotcrete Lining

Output Shown:

- Major Principal Ground Stress Sigma 1

- Concrete Lining Force Diagram:

- N – Axial Force

- M – Bending Moment

- Dowel/Bolt Forces:

- N – Axial Force

Stage 3: Initial Lining Limit Capacity Curve as per ACI 318-99.Stage 6: Final Lining Limit Capacity Curve as per ACI 318-99.

Concrete tunnel lining design to ACI318-99: M-N Interaction Chart

Concrete tunnel lining design to ACI318-99: M-N Interaction Chart

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Updated: 06/19/2013
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