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

Chapter 6 - Rock Tunneling

6.6.3 Numerical Methods

Another powerful design tool is an elasto-plastic finite element or finite difference stress analysis. Finite element or finite difference analysis has been used for a wide range of engineering projects for the last several decades. Complex, multi-stage models can be easily created and quickly analyzed. The analyses provide complex material modeling options and a wide variety of support types can be modeled. Liner elements, usually modeled as beam elements, can be applied in the modeling of shotcrete, concrete layers, and steel sets. A typical finite element analysis layout to design support system is presented in Figure 6-30.

Design of Support System in FE Analysis (o: Yield in Tension, x: Yield in Compression)

Figure 6-30 Design of Support System in FE Analysis (o: Yield in Tension, x: Yield in Compression)

Almost every project undertaken today requires numerical modeling to predict behavior of structures and the ground, and there is no shortage of numerical analysis programs available to choose from. Perspectives on numerical modeling in tunneling fields have changed dramatically during the last several decades. In the past, numerical modeling was generally thought to be either irrelevant or inadequate. The focus has now shifted to numerical computations as numerical techniques advance. There are a number of commercial computer programs available in the market—the problem is in knowing how to use these programs effectively and in having an understanding of their strengths and weaknesses.

All the programs require the user to have a sound understanding of the underlying numerical models and constitutive laws. The user interface is improving with the most recent Windows programs, although the learning curve for all the programs should not be underestimated. A number of numerical methods have been developed in civil engineering practice. The methods include finite element method (FEM), finite difference method (FDM), boundary element method (BEM), discrete element method (DEM) and hydrocodes. The numerical modeling programs commercially available in tunnel design and analysis are briefly introduced in Table 6-12.

Continuum Analysis FEM, FDM and BEM are so-called continuum analysis methods, where the domain is assumed to be a homogeneous media. These methods are used extensively for analysis of underground excavation design problems. To account for the presence of discontinuities, mechanical and hydraulic properties of rock mass were reduced from those measured from intact samples. (Refer to section 6.3.6)

Table 6-12 Numerical Modeling Programs used in Tunnel Design and Analysis
  • A two-dimensional finite difference code
  • Widely used in general analysis and as a design tool applied to a broad range of problems
  • Using user-defined constitute models and FISH functions, it is well suited for modeling of several stages, such as sequential excavation, placement of supports and liners, backfilling and loading.
  • As an option, this program enables dynamic analysis, thermal analysis, creep analysis, and two-phase flow analysis.
  • The explicit solution process of finite difference code enables numerical calculations stable, however, requires high running time when complex geometry and/or sequence modeling is involved.
  • Mechanical behavior of soils and rock mass
  • Coupling of hydraulic and mechanical behavior of soils
  • Well suited for tunneling or excavation in soil
  • Global overview of engineering solution in rock mass, where equivalent properties of the rock mass should be properly evaluated
  • Seismic analysis
  • Three-dimensional version of FLAC
  • Meshing generation software is recommended for complicated geometry.
  • Complex three-dimensional behavior of geometry
  • Suitable for interaction study for crossing tunnels
  • A finite element packages for two-dimensional and three-dimensional analysis
  • Automatic finite element mesh generator
  • User Friendly
  • Tunneling and excavations in soil
  • Coupling of hydraulic and mechanical behavior
  • Modeling of hydrostatic and non-hydrostatic pore pressures in the soil
  • Two-dimensional elasto-plastic finite element stress analysis
  • Well suited for rock engineering
  • Automatic finite element mesh generator
  • Easy-to-use
  • Tunneling and excavations in rock
  • Global overview of engineering solution in rock mass
  • A finite element code for analyzing groundwater seepage and excess pore-water pressure dissipation problems within porous materials
  • Available from simple, saturated steady-state problems to sophisticated, saturated-unsaturated time-dependent problems
  • Both saturated and unsaturated flow
  • Steady state and transient groundwater seepage analysis for tunnels and excavations
  • Equivalent properties of the rock mass should be properly evaluated
  • A modular finite difference groundwater flow model
  • Most widely used tool for simulating groundwater flow
  • To simulate aquifer systems in which (1) saturated flow conditions exist, (2) Darcy's Law applies, (3) the density of groundwater is constant, and (4) the principal directions of horizontal conductivity or transmissivity do nor vary within the system
  • Three-dimensional steady state and transient flow
  • Modeling of heterogeneous, anisotropic aquifer system
  • Fate and transport modeling for geoenvironmental problems with available package
  • A two-dimensional discrete element code
  • Well suited for problems involving jointed rock systems or assemblages of discrete blocks subjected to quasi-static or dynamic conditions
  • Modeling of large deformation along the joint systems
  • The intact rock (blocks) can be rigid or deformable blocks
  • Full dynamic capability is available with absorbing boundaries and wave inputs
  • Joints data can be input by statistically-based joint-set generator
  • Coupling of hydraulic and mechanical modeling
  • Tunneling and excavation in jointed rock mass
  • Well suited if dominating weak planes are well identified with their properties properly quantified
  • Hydrojacking potential analysis for pressure tunnels, which requires details of joint flow, aperture and disclosure relationships
  • Seismic analysis
  • Three-dimensional extension of UDEC
  • Specially designed for simulating the quasi-static or dynamic response to loading of rock mass containing multiple, intersecting joint systems
  • Full hydromechanical coupling is available
  • Complex three-dimensional behavior of geometry
  • Suitable for interaction study for crossing tunnels in jointed rock mass
  • Hydrojacking potential analysis for pressure tunnels
  • Pseudo-three-dimensional wedge generation and stability analysis for tunnels
  • Simple safety factor analysis
  • Three joint sets are required to form wedges
  • Conceptual analysis tool for tunnel support design
  • A parametric study for wedge loading diagrams for tunnel
  • Pseudo-three-dimensional surface wedge analysis for slopes and excavations
  • An easy to use analysis tool for evaluating the geometry and stability of surface wedges
  • Wedges formed by two intersecting discontinuity planes and a slope surface
  • Conceptual design of slopes
  • A parametric study for wedge loading diagrams for slopes and excavations
  • A general purpose transient dynamic finite element program
  • It is optimized for shared and distributed memory Unix-, Linux-, and Windows-based platforms
  • Coupling of Euler-Lagrange non-linear dynamic analysis
  • Widely used in impact and dynamic analysis
  • Impact analysis
  • Blast/explosion analysis
  • Seismic/vibration analysis
  • Modeling of computational fluid dynamics
  • A finite difference, finite volume and finite element-based Hydrocode
  • Coupling of Euler-Lagrange non-linear dynamic analysis
  • Convenient material library
  • Widely used in dynamic analysis
  • Blast/explosion analysis
  • Impact analysis
  • Seismic/vibration analysis
  • Modeling of computational fluid dynamics

The continuum analysis codes are sometimes modified to accommodate discontinuities such as faults and shear zones transgressing the domain. However, inelastic displacements are mostly limited to elastic orders of magnitude by the analytical principles exploited in developing solution procedures. FLAC, PHASES, PLAXIS, SEEP/W, and MODFLOW are widely used programs for continuum analyses. Figure 6-31 presents an example of contour plot on the strength factor (SF) on a circular tunnel in gneiss from Finite Element Analysis (Choi et. al., 2007). Based on SF contour plots presented in Figure 6-31, the minimum SF against shear failure near the tunnel is 40, which means the rock mass strength is 40 times the induced stresses, indicating that the entire domain is not over-stressed and no stress-induced stability problems are anticipated.

Strength Factor Contours from Finite Element Analysis

Figure 6-31 Strength Factor Contours from Finite Element Analysis (from Choi et. al., 2007)

Discrete Element Analysis If the domain contains predominant weak planes and those are continuous and oriented unfavorably to the excavation, then the analysis should consider incorporating specific characteristics of these weak planes. In this case, mechanical stiffness (force/displacement characteristics) or hydraulic conductivity (pressure/flow rate relationship) of the discontinuities may be much different from those of intact rock. Then, a discrete element method (DEM) can be considered to solve this type of problems. Unlike continuum analysis, the DEM permits a large deformation and finite strain analysis of an ensemble of deformable (or rigid) bodies (intact rock blocks), which interact through deformable, frictional contacts (rock joints). In hydraulic analysis, the DEM permits flow-networking analysis, which is suitable in ground water flow analysis in jointed rock mass.

The coupled hydromechanical analysis is another powerful strength of DEM analysis because a flow in jointed rock mass is closely related to applied loading. This type of analysis requires details of joint flow, aperture and closure relationships and is suitable only if dominating weak planes are well identified with their properties properly quantified. UDEC and 3DEC are the most predominant programs, while UNWEDGE and SWEDGE are good alternatives for conceptual design purposes. An example of discrete element analysis is presented in Figure 6-32.

Graphical Result of Discrete Finite Element Analysis

Figure 6-32 Graphical Result of Discrete Finite Element Analysis

6.6.4 Pre-Support and Other Ground Improvement Methods

Pre-support is used in both rock and soil tunnels, perhaps somewhat more frequently in soil tunnels. In rock tunnel applications pre-support may be called for when the tunnel encounters zones of badly weathered and/or broken rock. In such rock, the stand up time may be too short to install the usual support system.

Pre-support may include a number of techniques. For example, spiles and forepoling typically are installed through and ahead of the tunnel face. These members are driven or drilled as shown schematically in Figure 6-21 and pass over the support nearest the face and under or through the next support back from the face. Thus, overlapping "cones" of spiles are formed and this results in a sawtooth pattern to the opening profile. These spiles are usually selected based upon experience and judgment as there is no known design method. Therefore, successful application usually rests on the workers in the field because they are at the face and have to make the decisions in real time and in short time as the ground is exposed and its behavior observed.

6.6.5 Sequencing of Excavation and Initial Support Installation

As shown in Section 6.4, the three principal excavation methods for rock tunnels are as follows:

  • Drill and blast (including SEM/NATM) for full face or multiple heading advance of any shape in any rock.
  • Roadheader for full face or multiple heading advance of a shape in rock up to moderate strength.
  • TBM for full face (generally round only) in any rock.

When an excavation is made in intact rock by any method there is an adjustment (or redistribution) in the stresses and strains around that excavation. This adjustment, however, quickly dissipates such that the change is only about six percent at a clear distance of three radii from the wall of the opening. The insitu stresses in the rock are generally low for most highway tunnels because those tunnels are at relatively shallow depth. Thus, in intact rock the ("elastic") stresses resulting from this redistribution do not exceed the rock strength so stability is not a concern.

However, rock in reality is a jointed (blocky) material and it is the behavior of a blocky mass that nearly always governs the behavior of the tunnel. Evert Hoek describes this behavior as follows (Hoek, 2000): "In tunnels excavated in jointed rock mass at relatively shallow depth, the most common types of failure are those involving wedges falling from the roof or sliding out of the sidewalls of the openings. These wedges are formed by intersecting structural features, such as bedding planes and joints, which separate the rock mass into discrete but interlocked pieces. When a free face is created by the excavation of the opening, the restraint from the surrounding rock is removed. One or more of these wedges can fall or slide from the surface if the bounding planes are continuous or rock bridges along the discontinuities are broken.

Unless steps are taken to support these loose wedges, the stability of the back and walls of the opening may deteriorate rapidly. Each wedge, which is allowed to fall or slide, will cause a reduction in the restraint and the interlocking of the rock mass and this, in turn, will allow other wedges to fall. This failure process will continue until natural arching in the rock mass prevents further unraveling or until the opening is full of fallen material.

The steps which are required to deal with this problem are:

Step 1: Determination of average dip and dip direction of significant discontinuity sets.
Step 2: Identification of potential wedges which can slide or fall from the back or walls.
Step 3: Calculation of the factor of safety of these wedges, depending upon the mode of failure.
Step 4: Calculation of the amount of reinforcement required to bring the factor of safety of individual wedges up to an acceptable level."

The concepts for and applications of sequencing of excavation and initial support installation are generally based on drill and blast excavation, but also apply to roadheader excavation. These concepts can be summarized in "one sentence" as follows: do not excavate more than can be quickly removed and quickly supported so that ground control is never compromised.

6.6.6 Face Stability

In general, face stability is not as great a concern in rock tunnels as in soil tunnels because the rock stresses tend to arch to the sides and ahead of the face. However, in low strength rock, in areas where the rock is broken up or where the rock is extremely weathered face stability may be an issue. As discussed in Chapter 7 and in Section 6.6.5 the secret to successful tunneling where face stability may be an issue is to assure that individual headings are never so large that they cannot be quickly excavated and quickly supported. In addition, where groundwater exists it should be drawn down or otherwise controlled because, as noted by Terzaghi, unstable ground is usually associated with or aggravated by groundwater under pressure.

6.6.7 Surface Support

Surface support in a rock tunnel may be supplied by ribs and lagging as discussed above, or, more frequently now, by shotcrete in combination with rock bolts or dowels, steel sets, lattice girders, wire mesh or various types of reinforcement mats. For the most part modern rock tunnels are supported by shotcrete and either rock bolts or lattice girders.

Either system provides a flexible support that takes advantage of the inherent rock strength but that can be stiffened simply and quickly by adding bolts, lattice girders and/or shotcrete. In addition, lattice girders provide a simple template by which to judge the thickness of shotcrete. For other situations wire mesh or reinforcement mats have proven to successfully arrest and hold local raveling until sufficient shotcrete can be applied to knot the whole system together and hold it until the shotcrete attains its strength.

6.6.8 Ground Displacements

For the most part, ground displacements around a rock tunnel can be estimated from elastic theory or calculated using any of a number of computer programs. Elastic theory allows an approximate calculation of the ground displacements around a round tunnel in rock, as shown in Figure 6-33. The approximate radial displacement at a point directly around a tunnel in elastic rock is given by:

u is equal to Pz multiplied by 1 plus v divided by E then multiplied by a squared divided by r.


u= Radial movement, in.
Pz= Stress in the ground
υ= Poisson's ratio
E= Rock mass modules
a= Radius of opening
r= Radius to point of interest as presented in Figure 6-33.

Elastic Approximation of Ground Displacements around a Circular Tunnel in Rock

Figure 6-33 Elastic Approximation of Ground Displacements around a Circular Tunnel in Rock

For any shape other than circular, one can usually sketch a circle that most nearly approximates the true opening and use the radius of that circle in the above solution for an approximate displacement. However, in the rare case where the precise value of movement might be a concern, then it should be determined by numerical analysis. Displacement contours induced by two tunnel excavation, calculated by Finite Element Method, are presented in Figure 6-34.

Ground Displacement Contours Calculated by Finite Element Method

Figure 6-34 Ground Displacement Contours Calculated by Finite Element Method

6.7 Groundwater Control During Excavation

Groundwater control in rock can take many forms depending on the nature and extent of the problem. In fact, for many cases experience has proven that a combination of control methods may be the best solution. For a given tunnel it may also be found that different solutions apply at different locations along the alignment.

6.7.1 Dewatering at the Tunnel Face

Dewatering at the tunnel face is the most common method of groundwater control. This consists simply of allowing the water to drain into the tunnel through the face, collecting the water, and taking it to the rear by channels or by pumping. It then joins the site water disposal system. Note that if there are hydraulic or other leaks or spills at the TBM or other equipment in the tunnel such contaminants are in this water.

6.7.2 Drainage Ahead of Face from Probe Holes

Probe holes ahead of the tunnel may be placed to verify the characteristics of the rock and hence to provide information for machine operation and control. These holes will also predrain the rock and provide warning of (and drain) any methane, hydrogen sulfide or any other gas, petroleum, or contaminant that may be present. In areas where there are such known deposits of gas or other contaminants it is common (and recommended) practice to keep one or more probe holes out in front of the machine. When such materials are encountered, the probes alert the workers to the need to increase the frequency of gas readings, to increase the volume of ventilation or to take other steps as required to avoid the problem of unexpected or excessive gas in the tunnel.

6.7.3 Drainage from Pilot Bore/Tunnel

Pilot tunnels can provide a number of benefits to a larger tunnel drive, including:

  • Groundwater drainage
  • Gas or other contaminant drainage
  • Exploratory information on the geology
  • Grouting or bolting galleries for pre-support of a larger opening
  • Rock behavior/loading information for design of the larger opening

The question of location and size of pilot tunnel always leads to a spirited discussion such that no two are ever the same. They are typically six to eight feet in general size and may be located at one or more of several locations. As one example, on the H-3 project in Hawaii there was concern that huge volumes of water might be encountered. This is a 36 ft + highway through the mountain to the opposite side of the island. Borings were limited, but did not indicate huge volumes of water. However it was common knowledge that similar sites contained water-filled cavities large enough for canoe navigation and there was concern that a similarly large volume would be found in the H-3 tunnel. The pilot tunnel, proved that water was not a major concern and at the same time provided a second, unexpected benefit: by being able to see and analyze the rock for the whole tunnel bore, the winning contractor determined that he could perform major parts of the excavation by ripping with state-of-the-art large rippers in lieu of using drill and blast techniques. Because of this evaluation he was able to shave off millions of dollars in his bid and accelerate the construction schedule by several weeks. As an added benefit, the pilot tunnel was enlarged slightly and now is the permanent access (by way of special drifts) for maintenance forces to access the entire length of tunnel with small pickups without using the active traffic lanes.

6.7.4 Grouting

Groundwater inflow into rock tunnels almost exclusively comes in at joints, bedding planes, shears, fault zones and other fractures. Because these can be identified grouting is the most commonly used method of groundwater control. A number of different grout materials are used depending on the size of the opening and the amount of the inflow.

The design approach is first to detect zones of potentially high groundwater inflow by drilling probe holes out in front of the tunnel face. Second, the zones are characterized and, hopefully, the major water carrying joints tentatively defined. Then, third, a series of grout holes are drilled out to intercept those joints 10 feet to a tunnel diameter beyond the tunnel face or wall. Fourth, using tube-a-machetes, cement and/or water reactive grouts are injected to seal off the water to a level such that succeeding holes are drilled as the fifth step and injected with finer, more penetrating grouts such as micro-fine or ultra-fine cements and/or sodium silicate can be injected to complete the sealing off process. Based on evaluation of the grouting success additional holes and grouting may be required to finally reduce the inflow to an acceptable level. Typically it will be found that steps four and five must be repeated, trial and error, until the required reduction in flow is achieved.

6.7.5 Freezing

On rare occasions, it may become necessary to try freezing for groundwater control in a tunnel in rock. This might occur, for example, at a shaft where it was necessary to control the groundwater locally for a breakout of a TBM into the surrounding rock. If upon beginning excavation of the TBM launch chamber it were found that the water inflow was too great the alternative control methods would be to grout as discussed above or perhaps to freeze.

The authors are not aware of any examples in the U.S. where freezing has been used in a rock tunnel, probably for a very simple reason that high inflow encountered into a rock tunnel would be concentrated at the joints present in the rock. The concentration would usually result in a relatively high velocity of flow. Such velocity would typically exceed six feet per day, the maximum groundwater velocity for which it is feasible to perform effective freezing. Thus, for the most part freezing would not be used in rock tunneling except very locally, as discussed above, and even then it might be necessary to use liquid nitrogen to perform the freezing.

6.7.6 Closed Face Machine

A closed face machine could be used for rock tunneling in high groundwater flow conditions over short lengths. In reality such a machine would be more like an earth pressure balance (EPB) machine with sufficient rock cutters installed to excavate the rock. For any extended length (greater than a few hundred feet) this would typically be uneconomical. The machine would have to grind up the rock cuttings and mix, the resulting "fines" with large quantities of conditioners and the existing water to result in a plastic material. This is necessary for the EPB to control the face in front of the bulkhead and to bring the material from its pressurized state at the face down to ambient by means of the EPB screw conveyor (See Chapter 7).

For these reasons, one would not normally plan to build a closed face rock machine but to equip an EPB with rock cutters for driving short stretches in rock within a longer soft ground tunnel. An exception to this general statement would be a rock tunnel in weak or soft rock such as chalk, marl, shale, or sandstone of quite low strength such that it essentially behaved as high strength soft ground.

6.7.7 Other Measures of Groundwater Control

The groundwater control methods discussed above probably account for more than 95% of the cases where such control is required in a tunnel in rock. For the odd tunnel (or shaft) where something else is required the designer may have to rely on experience and or ingenuity to come up with the solution. A few suggestions are given here, but really inventive solutions may have to be developed on a case-by-case basis.

Compressed Air once was a mainstay for control of groundwater or flowing or squeezing ground conditions but it is used very infrequently in modern construction. Where the tunnel (or shaft) can be stabilized by relatively low pressures (say 10 psi or less) it may still be used. However, it requires compressor plants, locks, special medical emergency preparation and decompression times.

Panning may be attractive in some cases where the water inflow is not too excessive and is concentrated at specific points and/or seams. In this case pans are placed over the leaks and shotcreted into place. Water is carried in chases or tubes to the invert and dumped into the tunnel drainage system

Drainage Fabric is now frequently used in rock tunnels. These geotechnical fabrics can be put in over the whole tunnel circumference or, more often, in strips on a set pattern or where the leaks are occurring. Fastened to the surface of the rock with the waterproof membrane portion facing into the tunnel, this fabric is then sandwiched in place by the cast-in-place concrete lining. The fibrous portion of the fabric provides a drainage pathway around and down the tunnel walls and into a collection system at the tunnel invert.

6.8 Permanent Lining Design Issues

6.8.1 Introduction

For many tunnels the principle purpose of the final lining is to prepare the tunnel for its end use, for example, to improve its aesthetics for people or its flow characteristics for water conveyance. Thus, the final lining may consist of cast-in-place concrete, precast concrete panels, or shotcrete.

On the Washington DC subway for example both cast-in-place concrete and precast concrete panels were used. For downtown stations a variety of initial support schemes were used but a final lining of cast-in-place concrete, with a "waffle" interior finish was used for final support and lining. For outlying stations both initial support and the final structural lining were provided by rock bolts, embedded steel sets and shotcrete all installed as the stations were excavated. The precast concrete segmental inner lining (with waffle finish) that was installed at the outlying stations is architectural only - it carries no rock load. Precast concrete segments are more common in soil than in rock tunnels because in soil they are both initial and (sometimes) final support and they provide the reaction for propelling the machine forward. In rock tunnels the machine typically propels itself by reaction against grippers set against the rock.

6.8.2 Rock Load Considerations

As discussed in section 6.6, rock loads can be evaluated empirically or analytically. The calculated rock loads are often times described as roof load, side load, and eccentric load, where roof load and side load are uniformly distributed (Figure 6-35). It is recommended that the permanent lining is designed based on the uniform loads (roof and side loads) and checked by eccentric load case. Detailed load considerations are presented in Chapter 10 "Tunnel Lining."

Rock Loads for Permanent Lining Design: Uniform Roof and Side LoadsRock Loads for Permanent Lining Design: Eccentric Load

Figure 6-35 Rock Loads for Permanent Lining Design: (a) Uniform Roof and Side Loads; (b) Eccentric Load

The question of what "loads" to use for design of the permanent lining of a tunnel in rock always raises interesting challenges. Fundamentally, three conditions are possible:

  1. If initial support(s) are installed early and correctly, it can be showned, that they will not deteriorate within the design life of the structure, and if the opening is stable, then a structural final lining is not required. (Figure 6-36).
  2. If initial support(s) are installed early and correctly, the opening is stable (with no continuing loosening), but it cannot be demonstrated that the initial supports will remain completely effective for the design life of the structure, then the load(s) on the final lining may be essentially equal to those of the initial support. An example of this situation is the H-3 tunnel in Hawaii where initial support is provided by 14-ft rock bolts and the load on the final lining was assumed to be 14 feet of rock, analyzed in three ways:
    • Uniform load across the entire tunnel width
    • Uniform load across half of the tunnel width
    • Triangular load across the entire tunnel width with the maximum at the centerline.
  3. If initial support(s) are providing a seemingly stable opening but it is known that additional support is required for long term stability then that support must be provided by the final lining. An example of this situation is the Superconducting Super Collider where tunnels in chalk were initially stabilized by pattern rock bolts in the crown and spot bolts elsewhere. Months later, however, slaking (and perhaps creep) resulted in linear wedges (with dimensions up to approximately by one-third the tunnel diameter) "working" and sometimes falling into tunnels driven and supported months earlier. To be stable long-term, a lining or additional permanent rock bolts capable of supporting these wedges or blocks would have been necessary.

Unlined Rock Tunnel in Zion National Park, Utah

Figure 6-36 Unlined Rock Tunnel in Zion National Park, Utah

As illustrated by the above, determination of the requirement for and value of "loads" to be used for design of final linings in tunnels cannot be prescribed in the manner that is possible for structural beams and columns. Rather, the vagaries of nature must be understood and applied by all on the design and construction team.

6.8.3 Groundwater Load Considerations

For conventional tunnels, the groundwater table is lowered by tunnel excavation, because the tunnels act as a drain. When the undrained system is considered, the groundwater lowering measures are disrupted after the final lining is placed and the groundwater table will reestablish its original position. For a drained system, the groundwater is lowered and will lowered so long as rainfall or at the project site seepage is not sufficient to raise the groundwater table. For underwater tunnels, the groundwater table keeps constant due to the water body above the tunnels and full hydrostatic water pressure should be considered with an undrained system unless an intensive grouting program is implemented in the surrounding ground.

This section discusses factors affecting groundwater flow regime and interaction with concrete lining, and methods to estimate groundwater loadings in the lining design including empirical method, analytical solution, and numerical method. Factors on the Lining Loads due to Water Flow

Groundwater loadings on the underwater tunnel linings can be reduced with a drained system while the groundwater table keeps constant. The main factors that affect water loads on the underwater tunnel linings due to water flow are: (1) relative ground-lining permeability; (2) relative ground-lining stiffness; and (3) geometric factors such as depth below the water body.

The water loads on the lining are greatly dependent on the relative permeability between the lining and surrounding ground. For a tunnel where the lining has a relatively low permeability when compared to the surrounding ground, the lining will behave almost as impermeable and almost no head will be lost in the surrounding ground resulting in hydrostatic water pressures applied directly on the lining.

A relatively permeable lining, on the other hand, will behave as a drain and almost no head will be lost when the water flows through the lining and no direct loads will act on the lining. The loads due to the groundwater will only act on the lining indirectly through the loads applied by the seepage force onto the surrounding ground.

The influence of the relative stiffness is well visualized for the tunnels in a stiff rock mass, where the linings are not designed for the full hydrostatic water pressures by using drained systems. For tunnels in soft ground, the linings are normally designed to withstand a full hydrostatic load. Empirical Groundwater Loads

The empirical groundwater loading conditions used for the design of tunnel linings in New York are shown in Figure 6-37 and are based on empirical data. As indicated in Figure 6-37 , the groundwater loading diagram follows hydrostatic pressure to a maximum near the tunnel springline (head of Hs), is held constant over a sidewall area of 1/3Hsw, then decreases to 10 percent of hydrostatic pressure at the invert (0.1Hw).

The empirical loads shown in Figure 6-37 are based on the assumptions that the drainage system is to be comprised of a wall drainage layer (filter fabric), invert drainage collector pipes placed behind the wall and below the cavern floor, and a drainage blanket developed by covering the entire invert with a gravel layer. The water load at the invert level is reduced to 10 percent of hydrostatic water pressure at the invert level with a well-sized and designed gravel drainage bed and drain pipe(s) in the invert (including appropriate provisions and follow up actions for long term maintenance). Under other circumstances, 25 percent of hydrostatic water pressure is recommended at the invert level. The empirical loads are probably conservative but address concerns that groundwater percolating through the wall rock over time could possibly clog the drainage layer (fabric) placed outside the concrete wall causing a buildup of groundwater pressure beyond that assumed under the assumption that the thick invert drainage blanket and collector drains should continue to function. Analytical Closed-Form Solution

An analysis of the interaction between a liner and the surrounding rock mass needs to be carried out to evaluate the rate of leakage and the hydraulic head drop across the liner. Fernandez (1994) presented a hydraulic model for the analysis of the hydraulic interaction between the lining and the surrounding ground.

When a tunnel is unlined, the hydrostatic water pressure is exerted directly on the tunnel boundary. When a liner is placed, the total head loss across the liner-rock system, Δhw, is composed of head losses across the liner, ΔhL, head losses across the grout zone if any, ΔhG, and head losses across the medium, Δhm. The head loss across the liner is systemically presented in Figure 6-38.

Empirical Groundwater Loads on the Underground Structures

Figure 6-37 Empirical Groundwater Loads on the Underground Structures

Head Loss across the Lining and Surrounding Ground

Figure 6-38 Head Loss across the Lining and Surrounding Ground

Fernandez (1994) indicated that the head loss across the liner normalized by the total head loss across the system is expressed by:

Change in h_L divided by change in h_w is equal to 1 over 1 plus C multiplied by k_L over k_m , where C is equal to the natural log of L over b divided by the natural log of b over a_1.

where kL and km are the permeability of the liner and surrounding ground, respectively, and b and a1 are outside and inside radii of the lining, respectively. L can be estimated as twice the depth of the tunnel below the groundwater level unless a drainage gallery is excavated parallel to the tunnel. If a drainage gallery is drilled parallel to the tunnel, the value of L can be adjusted and set equal to the center to center distance between the pressure tunnel and the gallery. In common engineering practice, the hydraulic head loss across the liner could be 80-90 % of the net hydraulic head for relatively impermeable liners, with kL/km approximately equal to 1/80 to 1/100. Numerical Methods

A finite element seepage analyses can be used to predict hydraulic response of the ground in the vicinity of the tunnel construction (Figure 6-39 ). In the finite element analysis, both the tunnel liner and surrounding ground are idealized as isotropic and homogeneous media. The actual flow regime through the jointed rock mass and cracked concrete may be a fluid flow through the fracture networks; therefore, the absolute value of the hydraulic and mechanical response of the rock mass and concrete liner may differ from the prediction based on the assumption of isotropic, homogeneous, porous media.

Two Dimensional Finite Element Groundwater Flow Model Analysis

Figure 6-39 Two Dimensional Finite Element Groundwater Flow Model Analysis

It should be noted that this Finite Element Method analysis was focused on the global behavior of the rockmass, treating the rockmass as a porous, continuum, isotropic rather than discrete (i.e., blocky) material. The finite element approach (i.e., rock mass rather than discrete rock blocks) considers the equivalent rockmass permeability, where the effects of hydraulic characteristics of fluid flow through rock joints are accounted for and approximated by the equivalent rockmass permeability. This approach has been used frequently for groundwater flow problems in the field of tunnel engineering. However, estimating the equivalent rock mass permeability closer than an order of magnitude is a great challenge and certainly requires special attention.

Use of discrete element analysis is sometimes very difficult because it requires detailed input parameters of the rock joints such as joint attitudes, joint spacing, joint connectivity, hydraulic apertures of the joints, normal and shear stiffness. Coupling effect of the mechanical and hydraulic behavior of rock joints also requires understanding of the relationship between mechanical closure and hydraulic aperture of the joints. Without proper input parameters, the results from the discrete element analysis would not be reliable.

6.8.4 Drained Versus Undrained System

Drained Waterproofing System Drained waterproofing systems reduce hydrostatic loads on structures, enabling thinner and more lightly reinforced liners to be designed. In a fractured rock mass, high groundwater inflows often enter drained systems (even after rock mass grouting) resulting in increased pumping costs. High inflows can also increase the deposition of calcium precipitate in pipes. Under these conditions, an undrained system may be more efficient.

In the drained waterproof systems, the pipes and drainage layers are required to remain open and flowing to prevent the build-up of hydrostatic pressures. Regular inspections and maintenance of the drainage system are required to prevent hydrostatic loads rising to a level that could exceed the capacity of the structure. Figure 6-40 presents the cross-sectional layout for typical drained waterproofing system.

Allowable water infiltration rate varies depending upon the purpose of tunnel, tunnel dimension and local environmental law requirements. The rate of allowable infiltration acceptable to the owner shall be as specified in the contract documents. Some owners have used a rate of 1 gallon/minute per 1000 ft of tunnel length. The local infiltration limit is 0.25 gallon per day for 10 square feet of area, and 1 drip per minute at any location.

Drained Waterproofing System

Figure 6-40 Drained Waterproofing System

Undrained Waterproofing System Undrained waterproofing systems incorporate a membrane that extends around the entire tunnel perimeter with the aim of excluding groundwater completely. Final linings are designed for full hydrostatic water pressures. Thus, flat-slab walls or inverts are generally thick, whereas curved liners generally require less strength enhancement. The increased volume of excavation to create a curved or thicker invert is offset by reduced excavation for a gravel invert and sidewall pipes. Figure 6-41 presents the cross-sectional layout for typical undrained waterproofing system.

Undrained Waterproofing System

Figure 6-41 Undrained Waterproofing System

No groundwater drainage system is provided in the undrained system, resulting in cost savings from eliminating perforated sidewall pipes, porous concrete, transverse pipes and the gravel layer. If initial construction is of a high quality, operations and maintenance costs are low, because there is reduced pumping and without groundwater entering the tunnel drainage system, calcite deposits accumulate much more slowly. Reducing the inflow and drawdown also minimizes the chance of having to deal with contaminated water.

6.8.5 Uplift Condition

The question of uplift forces on the tunnel lining must also be considered for tunnels in rock, especially if the tunnel is to be undrained. When squeezing or swelling conditions are encountered they act upwards on the invert just as they act anywhere else around the perimeter. When the tunnel is first driven, these forces may be at least partially relieved by the act of excavation and also somewhat reduced because gravity works in opposition to these upward forces. As time passes, however, the upward forces from swelling and/or squeezing come into full effect, that is, equal to those occurring anywhere else around the opening. Even if these rock loads should not be developed, the water head on an undrained tunnel will certainly be equal to the in-situ groundwater pressure.

Whether it is swelling, squeezing, water pressure or any combination thereof the invert of the tunnel will be subjected to upward forces. Typically, this means that the invert should be modified to a curved geometry to react to these upward forces - it is far easier to develop a stable curved structure than it is to permanently stabilize a flat invert. Even without squeezing or swelling the uplift water load can be quite expensive to resist with a flat invert as compared to a curved one. Thus, the most economical solution is usually to go directly to a curved configuration wherein the curved shape (when supported by steel ribs) will carry almost twice the load it will carry with a straight invert or straight sides (Proctor, 1968).

6.8.6 Waterproofing

For the most part tunnels in rock are waterproofed by a sandwich consisting of:

  • A geotechnical drainage fabric that is put in place directly against the rock either continuously or in strips. This may be held in place by pins or nails driven or shot into the rock.
  • Next a continuous waterproof membrane is installed. This membrane may be high density polyethylene (HDPE) or polyvinylchloride (PVC) or other similar material. To be continuous the membrane has to be cut and fit to all strange shapes and corners encountered and welded together (by heat) to make a continuous waterproofing membrane within the tunnel. Successful installation is quite dependent upon workmanship in three areas:
    • Avoiding puncturing, tearing and the like of the membrane.
    • Correctly making and testing all joints.
    • Connecting the waterproof membrane to the wall without introducing leaks.
  • Finally a cast in place lining of concrete is placed to hold the sandwich together and to provide the desired inner surface of the tunnel. Of course, the challenge is to get the concrete placed without damaging the membrane(s), this is especially challenging when the cast in place concrete must be reinforced.

Unlined and partial lined tunnels are common in many short mountainous tunnels in competent rock and stabilized with or without patterned rock bolts on the exposed rock (Figure 6-37). Groundwater inflows are tolerated and collected. See Chapter 16 for groundwater control measures.

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Updated: 06/19/2013
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