11 multistage tunnel excavation and support · 11 multistage tunnel excavation and support ... an...

Multistage Tunnel Excavation and Support 11 - 1

11 Multistage Tunnel Excavation and Support

11.1 Problem Statement

Construction of large railroad, subway and road tunnels often involves multiple stages of excavationand support, particularly if the tunnels are located at shallow depth and/or in weak ground. A typicalexample for construction conditions and sequence of a shallow tunnel are illustrated in Figure 11.1and Figure 11.2.

In this example, the construction sequence is divided into four major excavation stages:

Stage I: right-side excavation;

Stage II: left-side excavation;

Stage III: top-heading excavation; and

Stage IV: bench excavation.

Each excavation stage is accomplished in three construction steps:

Step a: initial excavation;

Step b: installation of rockbolt support; and

Step c: installation of a shotcrete lining.

The three steps occur at different times during the advancement of the tunnel face. Consequently,the loads acting on the tunnel will be changed at the time the support is installed, as a function ofthe tunnel advancement.

The stress and displacement fields in the vicinity of a tunnel construction change in the direction ofthe advancing tunnel face, and this is most rigorously analyzed using a three-dimensional program,such as FLAC3D (Itasca 2012). However, advancing tunnel problems are often analyzed in twodimensions by neglecting displacements normal to the tunnel cross-section.

An important issue in the design of supports is the amount of change in the tunnel load that takesplace, due to the tunnel advancement, before the support is installed. If no change is assumed tooccur, the loads acting on the support will be overpredicted. If complete relaxation at the tunnelperiphery is assumed to occur, zero load will develop in the support at the installation step, providedthat the relaxation state is at equilibrium. In reality, some relaxation takes place. However, it isdifficult to quantify relaxation with a two-dimensional program, because this depends on the distancebehind the face at which the support is installed. One way to model the relaxation is to decreasethe elastic moduli of the tunnel core, equilibrate, install the support and remove the core. Thisapproach is typical of finite element codes. The main problem then becomes estimating how muchto reduce the moduli.

FLAC Version 8.0

11 - 2 Example Applications

Figure 11.1 Construction conditions for a multistage tunnel excavation andsupport

FLAC Version 8.0


Figure 11.2 Construction sequence for a multistage tunnel excavation andsupport

An alternative approach to model the relaxation is based on the relation of the closure of theunsupported tunnel to the distance to the face. Panet (1979) published such an expression. (Alsosee Section 8.) Tunnel closure can be related to traction forces acting on the tunnel periphery viaa ground reaction curve. Thus, the tunnel relaxation as a function of the distance to the face canbe specified in terms of tractions defined by a ground reaction curve, and an expression relatingclosure to distance to the face.

In order to simulate the relaxation, tractions are first applied to the tunnel boundary to providean equilibrium condition at zero relaxation; then the tractions are gradually decreased to a valuecorresponding to a tunnel closure value that is related to a specified distance to the face. Thesupport is then installed at this relaxation state. In this example, the rockbolt support is installed atan excavation stage corresponding to 50% relaxation of the tunnel load, and the shotcrete is installedat a stage corresponding to 75% relaxation, as illustrated in Figure 11.1.

FLAC Version 8.0


11.2 Modeling Procedure

11.2.1 Model Setup

FLAC is well-suited to model sequential excavation and construction problems. In this example, thefour excavation stages and three construction steps within each stage are simulated as 12 sequentialsolutions. A procedure that demonstrates the process to develop a ground reaction curve for thismodel is also included. The project file, “mstunnel.prj”, contains all of the command data for eachsolution stage in this example.

The FLAC mesh is defined with the grid distorted to align with the boundaries of the four segmentsof the tunnel excavation. The Build / Generate / Geometry Builder tool is used to create the tunnel geometrywith a fine mesh in the vicinity of the tunnel and a radially graded mesh extending to the modelboundaries. The tunnel stage boundaries are defined in an imported geometry file, “tunnel.dxf”.This file can be directly obtained from a CAD drawing or drawn by hand in the Sketch tool. TheFLAC grid for this example is shown in Figure 11.3. A close-up view of the four excavation stagesis shown in Figure 11.4.

The rock behavior is represented by the Mohr-Coulomb model assigned the properties listed inFigure 11.1. The rockbolts are modeled using rockbolt elements, and the shotcrete is simulatedwith liner elements. Note that the structural element logic is a plane-stress formulation, so the valuespecified for the Young’s modulus, E, is divided by (1−ν2) to correspond to the plane-strain model(see Section 1.2.2 in Structural Elements).

The model is brought to an initial force-equilibrium state under gravitational loading, with the topboundary of the mesh representing the ground surface. The initial stage is identified as Step 0 inFigure 11.1.

FLAC Version 8.0


FLAC (Version 8.00)

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29-Jun-15 15:06 step 0 -5.556E+01 <x< 5.556E+01 -8.556E+01 <y< 2.556E+01

Grid plot

0 2E 1

-7.000

-5.000

-3.000

-1.000

1.000

(*10^1)

-4.000 -2.000 0.000 2.000 4.000(*10^1)

JOB TITLE : Multistage Tunnel Excavation and Support

Itasca Consulting Group, INC. Minneapolis, MN, USA

Figure 11.3 FLAC grid for a multistage tunnel construction

FLAC (Version 8.00)

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28-Jul-15 11:41 step 0 -1.510E+01 <x< 1.640E+01 -4.587E+01 <y< -1.437E+01

User-defined Groupsmstunnel:rock’mstunnel:left side’mstunnel:bench’mstunnel:top heading’’mstunnel:right side’

Grid plot

0 5E 0

-4.250

-3.750

-3.250

-2.750

-2.250

-1.750

(*10^1)

-1.250 -0.750 -0.250 0.250 0.750 1.250(*10^1)


Itasca Consulting Group,INC Minneapolis, MN

Figure 11.4 Close-up of excavation stage groups for multistage tunnel con-struction

FLAC Version 8.0


11.2.2 Ground Reaction Curve

Before conducting the sequential excavation/support analysis, unsupported tunnel calculations areperformed in order to develop ground reaction curves for this model. This procedure is demonstratedfor the excavation of the entire tunnel in one stage. Separate ground reaction curves can also bedeveloped for each tunnel segment.

The ground reaction curve is developed by measuring the force on the tunnel boundary at zero relax-ation and applying an incrementally decreasing amount of this force as a traction while measuringthe corresponding tunnel closure. The command APPLY relax performs this relaxation procedureautomatically.

The APPLY relax command is applied to gridpoints along the entire tunnel boundary in this example.When the command is executed, x- and y-reaction forces at these gridpoints are recovered and thenapplied as tractions (with an opposite sign) at the same gridpoints. The nsteps keyword then definesthe number of intervals over which the tractions are reduced. In this example, nsteps = 10, i.e.,the tractions are reduced in 10% increments from the zero relaxation state. The keyword rstop setsthe final reduced value of the traction. Tractions are defined as dimensionless relaxation factorsbetween 1.0 and 0.0. For this example, the ending relaxation factor rstop is set to 0.2. If a lowervalue is specified, the tunnel collapses.

Tunnel closure is monitored as a history. The FISH function closure calculates the verticalclosure of the tunnel. The closure is then recorded as grhist = 1 in the APPLY relax command. Theground reaction curve, which plots the reduction in relaxation factor versus the closure, is writtento a table specified by grtable = 1 in the APPLY relax command. Figure 11.5 displays the resultfor load relaxation of the entire tunnel boundary from a relaxation factor of 1.0 to 0.2. This is theground reaction curve.

By also relating the tunnel closure to the distance to the tunnel face (e.g., see Figure 8.6 in Section 8),relaxation factors can be selected to correspond to selected distances to the tunnel face.

For this multistage tunnel excavation/construction example, we do not relate the relaxation factorsto specific distances to the tunnel face. We arbitrarily choose a relaxation factor of 0.5 (50%relaxation) to define the tunnel loading state at which the rockbolt support is installed. The factoris then reduced to 0.25 (75% relaxation) to develop loads in the rockbolts. The relaxation factorof 0.25 corresponds to the state at which the shotcrete is installed, and then complete relaxation(100% relaxation) is allowed to develop loads in the shotcrete.

FLAC Version 8.0


FLAC (Version 8.00)

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29-Jun-15 15:06 step 10388 ground reaction curverelax factor vs vert. closure

0 5 10 15 20 25 30 35 40

(10 )-03

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000



Figure 11.5 Ground reaction curve: relaxation factor versus vertical closure

11.2.3 Construction Simulation

The construction steps of the excavation/support analysis follow the same sequence for each exca-vation stage. First, the excavation segment is nulled and the APPLY relax command is applied overthat segment boundary to reduce the tractions in 20% increments (nsteps = 5) until the tractionsare 50% of their starting value (rstop = 0.5). The model is brought to force equilibrium at 50%relaxation. This is Step a, as shown in Figure 11.1.

At this state, the rockbolt elements are added, representing the rockbolt support. The locationsof the rockbolts are defined by a sketch of the rockbolt pattern. This geometry is imported intoFLAC from the Build / Sketch tool as the file “rockbolts.dxf”. (The geometry can be imported as aCAD drawing or drawn in the Sketch tool.) Using the sketch as a background image, the rockboltsare located around the boundary of each excavation, as shown in Figure 11.1. Each rockbolt iscomposed of five segments, which is sufficient to locate a rockbolt node within every zone alongthe bolt length.

The tunnel tractions around the excavation are now reduced again using APPLY relax. The relaxationincrement, nsteps = 5 and the end factor rstop = 0.5. This results in the tractions relaxing anadditional 50%. The model is then brought to force equilibrium at 75% relaxation. This is Step bin Figure 11.1.

FLAC Version 8.0


At this state, the liner elements are added to represent installation of the shotcrete lining. The tunneltractions are reduced by using APPLY relax with nsteps = 5 and rstop = 0.0. The tractions are nowrelaxed 100% and the model is brought to equilibrium.

Loads that develop in the rockbolts result from tunnel-load relaxation from 50% to zero, and theloads that develop in the shotcrete result from relaxation from 25% to zero.

By applying the relaxation in a five-step reduction (nsteps = 5), the effects of transient wavesare minimized, and a gradual excavation of the tunnel is simulated. This is demonstrated byFigure 11.6, which displays vertical stress histories at the springline of the tunnel. The historiesshow gradual changes in the stresses; if the relaxation loads were applied suddenly (i.e., in one step),sudden changes would be observed in these histories, and a different final state could result. (SeeSection 3.10.3 in the User’s Guide for further discussion on path-dependency effects of loading.)

FLAC (Version 8.00)

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29-Jun-15 15:06 step 254190 HISTORY PLOT Y-axis : 1 Ave. SYY ( 58, 38)

2 Ave. SYY ( 19, 37)

X-axis :Number of steps

5 10 15 20 25

(10 ) 04

-1.100

-1.050

-1.000

-0.950

-0.900

-0.850

-0.800

(10 ) 06



Figure 11.6 Vertical stress histories at the springline

FLAC Version 8.0


11.3 Results

Typical results for this analysis are shown in Figures 11.7, 11.9, 11.10 and 11.11. The settlementprofile of the ground surface at the end of the analysis is shown in Figure 11.7. The profile iscreated with FISH function settle; y-displacements at the gridpoints along the top of the modelare stored in table 2.

The axial forces in the rockbolts at the end of each excavation stage are shown in Figure 11.9, andthe axial forces in the shotcrete are shown in Figure 11.10. Note that the sense of the axial forceplot depends on the order in which the structural elements are created. The sense can be changedby assigning a maximum value with opposite sign following the max keyword when issuing thecommand PLOT structure axial. Figure 11.8 shows the Plot Item Switches dialog, in which themaximum value is set to −800000.0 to change the sense of the liner axial force plot.

FLAC (Version 8.00)

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29-Jun-15 15:06 step 254190 settlementvert. displ. vs dist.

-50 -40 -30 -20 -10 0 10 20 30 40

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

(10 )-02



Figure 11.7 Final settlement profile

FLAC Version 8.0


Figure 11.8 Plot Item Switches dialog; use the Maximum switch to changethe plot sense

FLAC Version 8.0


FLAC (Version 8.00)

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29-Jun-15 15:06 step 55881 -1.298E+01 <x< 1.298E+01 -4.298E+01 <y< -1.702E+01

Rockbolt Plot

Axial Force onStructure Max. Value# 1 (Rockb) -1.615E+04# 2 (Rockb) -4.879E+04# 3 (Rockb) -7.257E+04# 4 (Rockb) -8.105E+04# 5 (Rockb) -7.681E+04# 6 (Rockb) -7.937E+04# 7 (Rockb) -6.099E+04# 8 (Rockb) -3.963E+04# 9 (Rockb) -1.484E+04 Marked Gridpoints

-4.000

-3.500

-3.000

-2.500

-2.000

(*10^1)

-1.000 -0.500 0.000 0.500 1.000(*10^1)



(a) right-side excavation

FLAC (Version 8.00)

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29-Jun-15 15:06 step 114535 -1.298E+01 <x< 1.298E+01 -4.298E+01 <y< -1.702E+01

Rockbolt Plot

Axial Force onStructure Max. Value# 1 (Rockb) -1.465E+04# 2 (Rockb) -4.940E+04# 3 (Rockb) -7.429E+04# 4 (Rockb) -8.062E+04# 5 (Rockb) -7.490E+04# 6 (Rockb) -7.803E+04# 7 (Rockb) -5.951E+04# 8 (Rockb) -3.710E+04# 9 (Rockb) 9.513E+03#11 (Rockb) -1.835E+04#12 (Rockb) -5.753E+04#13 (Rockb) -8.529E+04#14 (Rockb) -9.029E+04#15 (Rockb) -8.798E+04#16 (Rockb) -8.709E+04#17 (Rockb) -6.962E+04

-4.000

-3.500

-3.000

-2.500

-2.000

(*10^1)

-1.000 -0.500 0.000 0.500 1.000(*10^1)



(b) left-side excavation

FLAC Version 8.0


FLAC (Version 8.00)

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29-Jun-15 15:06 step 232653 -1.298E+01 <x< 1.298E+01 -4.298E+01 <y< -1.702E+01

Rockbolt Plot

Axial Force onStructure Max. Value# 1 (Rockb) -2.151E+05# 2 (Rockb) -1.505E+05# 3 (Rockb) -1.533E+05# 4 (Rockb) -9.614E+04# 5 (Rockb) -6.661E+04# 6 (Rockb) -7.084E+04# 7 (Rockb) -7.250E+04# 8 (Rockb) -8.958E+04# 9 (Rockb) -5.394E+04#11 (Rockb) -1.468E+05#12 (Rockb) -1.478E+05#13 (Rockb) -1.217E+05#14 (Rockb) -8.849E+04#15 (Rockb) -7.572E+04#16 (Rockb) -7.978E+04#17 (Rockb) -8.090E+04

-4.000

-3.500

-3.000

-2.500

-2.000

(*10^1)

-1.000 -0.500 0.000 0.500 1.000(*10^1)



(c) top-heading excavation

FLAC (Version 8.00)

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29-Jun-15 15:06 step 254190 -1.298E+01 <x< 1.298E+01 -4.298E+01 <y< -1.702E+01

Rockbolt Plot

Axial Force onStructure Max. Value# 1 (Rockb) -2.159E+05# 2 (Rockb) -1.520E+05# 3 (Rockb) -1.538E+05# 4 (Rockb) -9.934E+04# 5 (Rockb) -7.557E+04# 6 (Rockb) -1.073E+05# 7 (Rockb) -1.121E+05# 8 (Rockb) -1.065E+05# 9 (Rockb) -1.804E+05#11 (Rockb) -1.479E+05#12 (Rockb) -1.482E+05#13 (Rockb) -1.222E+05#14 (Rockb) -9.097E+04#15 (Rockb) -8.276E+04#16 (Rockb) -1.108E+05#17 (Rockb) -1.134E+05

-4.000

-3.500

-3.000

-2.500

-2.000

(*10^1)

-1.000 -0.500 0.000 0.500 1.000(*10^1)



(d) bench excavation

Figure 11.9 Axial forces in rockbolts at 100% relaxation for each excavationstage

FLAC Version 8.0


FLAC (Version 8.00)

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29-Jun-15 15:06 step 55881 -1.486E+01 <x< 1.575E+01 -4.530E+01 <y< -1.470E+01

Liner Plot

Axial Force onStructure Max. Value#10 (Liner) 6.034E+05 Marked Gridpoints

-4.250

-3.750

-3.250

-2.750

-2.250

-1.750

(*10^1)

-1.000 -0.500 0.000 0.500 1.000 1.500(*10^1)



(a) right-side excavation

FLAC (Version 8.00)

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29-Jun-15 15:06 step 114535 -1.486E+01 <x< 1.575E+01 -4.530E+01 <y< -1.470E+01

Liner Plot

Axial Force onStructure Max. Value#10 (Liner) 1.057E+06#20 (Liner) 6.899E+05 Marked Gridpoints

-4.250

-3.750

-3.250

-2.750

-2.250

-1.750

(*10^1)

-1.000 -0.500 0.000 0.500 1.000 1.500(*10^1)



(b) left-side excavation

FLAC Version 8.0


FLAC (Version 8.00)

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29-Jun-15 15:06 step 232653 -1.486E+01 <x< 1.575E+01 -4.530E+01 <y< -1.470E+01

Liner Plot


-4.250

-3.750

-3.250

-2.750

-2.250

-1.750

(*10^1)

-1.000 -0.500 0.000 0.500 1.000 1.500(*10^1)



(c) top-heading excavation

FLAC (Version 8.00)

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29-Jun-15 15:06 step 254190 -1.486E+01 <x< 1.575E+01 -4.530E+01 <y< -1.470E+01

Liner Plot


-4.250

-3.750

-3.250

-2.750

-2.250

-1.750

(*10^1)

-1.000 -0.500 0.000 0.500 1.000 1.500(*10^1)



(d) bench excavation

Figure 11.10 Axial forces in shotcrete at 100% relaxation for each excavationstage

FLAC Version 8.0


Figure 11.11 plots a moment-thrust diagram for the shotcrete liner at 100% relaxation at the lastexcavation stage. The plot indicates that all segments along the liner have a factor of safety greaterthan 1.4.

FLAC (Version 8.00)

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2-Jul-15 11:01 step 254190 -1.486E+01 <x< 1.575E+01 -4.530E+01 <y< -1.470E+01

moment thrust diagram Safety Factors 1.0

1.2

1.4

-8 -6 -4 -2 0 2 4 6 8

(10 ) 04

0.000

0.500

1.000

1.500

2.000

2.500

3.000

(10 ) 06



Figure 11.11 Moment-thrust diagram (tensile yield strength = 1 MPa, com-pressive yield strength = 10 MPa) for shotcrete liner at 100%relaxation at the last excavation stage

FLAC Version 8.0


11.4 References

Itasca Consulting Group, Inc. FLAC3D (Fast Lagrangian Analysis of Continua in 3 Dimensions),Version 5.0. Minneapolis: ICG (2012).

Panet, M. “Time-Dependent Deformations in Underground Works,” in Proceedings of the 4thISRM Congress (Montreux), Vol. 3, pp. 279-289. Rotterdam: A. A. Balkema and the SwissSociety for Soil and Rock Mechanics (1979).

FLAC Version 8.0

11 multistage tunnel excavation and support · 11 multistage tunnel excavation and support ... an...

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