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Groundwater Inflow to Tunnels Breakthroughs in Tunneling Boulder, Colorado
September 2016
Agenda
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1. Nature of Inflows
2. Groundwater basics โ Conservation of Mass and Darcyโs Law
3. Practical formulas for calculating inflows โ Different formulas depending on the geology
4. The problem of permeability โ Estimating the permeability of a fractured rock mass
Rule of Uneven Inflow
1. Most of the inflow occurs in a few places (from a few, well-connected, open fractures)
2. Some of the inflow occurs in many places (from many smaller interconnected fractures)
3. Much of the tunnel is dry (long reaches have no water-bearing fractures)
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Total inflows accumulate at the large scale. Individual inflows occur at medium scale.
Field tests occur at the small scale.
Key Question
How much water is my tunnel going to make?
1. What capacity for managing inflows? โข pumps, treatment plant, discharge options
2. Will inflows cause third party impacts? โข ground settlements, dry wells, dry streams
3. Do I need pre-excavation grouting? โข how big a program? what are its goals?
4. Is open-face tunneling even an option?
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Groundwater Basics Inflow: 400 gpm (25 L/s) Depth: 300 feet (90 m)
Resulting Problem: Dry streams half a mile away(800 m)
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Two Controlling Laws
1. Conservation of Mass (Continuity) 2. Darcyโs Law
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Any valid approach to predicting inflows must address both explicitly!
Three Key Issues
1. Source of the Water (Conservation of Mass) โ indicates which equation to use
2. Potential Energy Difference (Darcyโs Law) โ easy to estimate; average values work
3. Transmissivity of the Ground (Darcyโs Law) โ permeability integrated over a large thickness of ground
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Control Volume
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๐๐
๐ฟ๐ฟ ๐ฅ๐ฅ
โข Conservation of Mass: inflows and outflows must balance.
โข Darcyโs Law: flow rate is limited by the permeability of the ground
๐ฟ๐ฟ = distance along the tunnel
๐ฅ๐ฅ = distance away from the tunnel
๐๐ = height of the flow zone
Darcyโs Law
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โข ๐๐ is the flow rate
โข โโ is the head difference over the distance ๐ฅ๐ฅ
โข ๐พ๐พ is the average permeability over the control volume
โข ๐พ๐พ๐๐ is the transmissivity
๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐ ๐๐
๐ฟ๐ฟ ๐ฅ๐ฅ
โโ ๐๐ = ๐พ๐พ๐๐๐ฟ๐ฟ โโ๐ฅ๐ฅ
Direction of flow
K is an average value over the whole control volume.
Conservation of Mass
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โข Flow going out must balance the sum of the flows coming in plus the change in storage
๐๐๐๐๐๐๐๐ = ๐๐1 + ๐๐2 + โฏ+โ๐๐๐ก๐ก
๐๐๐๐๐๐๐๐ ๐๐1
๐๐2
โ๐๐
โโ
โข The change in storage is the change in volume over time โ๐๐ ๐ก๐กโ
โข Water table decline is the most important way to change the storage.
Upstream Downstream
Recharge, Leakage
Formulas for Calculating Inflow
1. Based on Conservation of Mass and Darcyโs Law
2. Some assume a declining water table
3. Some assume steady-state conditions
4. The formula depends on the hydrogeology
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Concept of Inflow to a Tunnel
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โข Tunnel is large relative to thickness of flow zone (๐๐). โข Flow is lateral toward the tunnel, not radial around it. โข Thickness (๐๐) of flow zone is important. โข Tunnel width is not important
2๐๐
Actual Modeled
๐๐
Inflow Sketches
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PROFILE
โ0 ๐๐
โ0 Initial head (depth of tunnel below water table) ๐๐ Thickness of the flow zone prior to start of inflow
Tunnel
Unsaturated Ground
Static Water Table
Base of flow system
Saturated Ground
Flow is to one side of the tunnel only! Double the result to get flow to both sides
1: Declining Water Table
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PROFILE
โ0 ๐๐
๐๐ =๐ฟ๐ฟ๐๐๐ก๐ก
โ0 โโ02
2๐๐ ๐๐๐พ๐พ๐๐
โข Isotropic (non-stratified) flow system
โข Water table draws down toward tunnel
โข Water comes from existing storage
โข Flow declines over time
โข Flow can come from both sides (๐๐ ร 2)
โข Flow (๐๐) is proportional to ๐พ๐พ
๐๐ Inflow to one side of the tunnel ๐ฟ๐ฟ Length of tunnel (or reach) ๐พ๐พ Average horizontal permeablity ๐๐ Specific yield (free-draining porosity) ๐ก๐ก Elapsed time since start of inflow
Adapted from Lohman, 1972
2: Upland Recharge
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โข Flow through random fractures or soil
โข Water table draws down toward tunnel
โข Recharge is captured over large area
โข Recharge is independent of drawdown
โข Flow can come from both sides (๐๐ ร 2)
โข Flow (๐๐) is proportional to ๐พ๐พ
PROFILE
โ0 ๐๐
Precipitation
๐๐ Inflow to one side of the tunnel ๐ฟ๐ฟ Length of tunnel (or reach) ๐พ๐พ Average horizontal permeablity ๐ ๐ Average groundwater recharge rate
๐๐ = ๐ฟ๐ฟ 2๐พ๐พ๐๐๐ ๐ โ0 โโ02
2๐๐
Derived by Raymer from differential equations for continuity and Darcyโs Law
3: Downward Leakage in Stratified Ground
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โข Horizontally stratified flow system
โข Lateral flow through permeable layer
โข Steady water source above tunnel
โข Rate of leakage depends on drawdown in main flow zone
โข Flow can come from both sides (๐๐ ร 2)
โข Flow (๐๐) is proportional to ๐พ๐พ
Water
Leaky Layer โ0 ๐๐๐
๐๐
๐๐ = ๐ฟ๐ฟ โ0๐พ๐พ๐๐๐พ๐พ๐๐๐๐
๐๐ Inflow to one side of the tunnel ๐ฟ๐ฟ Length of tunnel (or reach) ๐พ๐พ Average horizontal permeablity of flow zone ๐พ๐พ๐ Vertical permeability of leaky layer
PROFILE
Lateral Flow
Derived by Raymer from differential equations for continuity and Darcyโs Law
๐ฅ๐ฅ
โ0 ๐๐ Water Body
4: Flow along Dipping Strata or Joints
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โข Dipping strata or joint set leads from constant water source down to tunnel
โข Flow only comes from the updip side
โข Distance ๐ฅ๐ฅ is along dip of strata or joints; thickness (๐๐) is perpendicular
โข Flow (๐๐) is proportional to ๐พ๐พ PROFILE
๐๐ Inflow to one side of the tunnel ๐ฟ๐ฟ Length of tunnel (or reach) ๐พ๐พ Average horizontal permeablity
๐๐ = ๐พ๐พ๐๐๐ฟ๐ฟโ๐๐๐ฅ๐ฅ
Darcyโs Law
Numerical Modeling
1. Does the same thing as these equations, but with more detail
2. Highly advanced; requires much expertise
3. No better than the your understanding of the ground or the data you collect.
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The geologic and permeability models are still the hard parts!
Problem of Permeability
1. Range of test results is enormous โข six orders of magnitude: typically 10-7 to 10-1 cm/sec โข 100,000 times greater than the other parameters
2. Formulas require the average for the rock mass
3. Problem of Scale Scale of the flow system
Scale of the tunnel Scale of the tests
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Packer Tests
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โข Seal off an section of borehole โข Inject water, record flow rate ๐๐
and applied pressure โ๐๐ ๐พ๐พ =
๐๐โ๐๐
ln ๐ฟ๐ฟ ๐๐๏ฟฝ2๐๐๐ฟ๐ฟ
๐ฟ๐ฟ = length of interval ๐๐ = radius of borehole
Packer Tests โ Scale
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โข Length โ distance between the packers
โข Time (Radius of Influence) โ porosity and permeability โ borehole and pipe volume
Recommendations: Standard length of about 20 ft (6 m) Standard duration of about 10 minutes
Scale Effects
The estimated average can change greatly depending on the number and scale of the tests.
1. Estimated average permeability tends to increase as the number of tests increases
2. Estimated average permeability tends to increase as the test zones become shorter
3. Estimated average permeability tends to increase if tests are not run long enough
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Testing High Permeability Zones
Transient solutions that require much expertise 1. High-rate packer tests
โข Perform in existing core holes โข 4 to 6 hours, including injection and recovery
2. Pumping tests โข Requires specially designed well network โข Typically 24 to 72 hours continuous duration
Value: โข Permeability of highest yielding zones โข Insight into which formula to use
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Testing Rules for Standard Packer Tests
1. Perform hundreds of tests โข many statistical problems are solved with quantity
2. Perform all tests identically
3. Longer vertical intervals produce better results โข 20 ft or 6 m is a good length.
4. Donโt skip any intervals
5. Use more sophisticated methods if necessary โข High-rate packer tests (for takes >10 to 30 gpm) โข Pumping tests in the most extreme circumstances
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Conclusions
1. Put a groundwater expert on your team โข from the beginning to plan the right investigation โข teach your expert about tunnels and fractured rock
2. Inflow formulas depend on the hydrogeology โข one formula does not fit all situations โข square-root of permeability usually controls inflow โข require a lot of geological judgement
3. Permeability is a problem โข average of the tests is not the average for the ground โข saving graces: lots of tests and the square root
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Three Requirements for Inflow
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1. Source โข what is the source of the water?
2. Potential Energy โข how much energy is available to drive the flow?
3. Pathway โข how much resistance will the rock mass create? โข will the pathway be circuitous?
Five Hydrogeologic Conditions
1. Massive Rock 2. Blocky Rock 3. Horizontal Fractures 4. Dipping Fractures 5. Karstic Systems
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Only the open, water-bearing fractures matter!
Blocky Rock
โข Multiple Open Fractures = flow in any direction
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Water Table
River
Tunnel
Soil
Fractured Rock
Horizontal Fractures
โข Poor Vertical Connection to the Source
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Soil
Water Table
River
Fractured Rock
Dipping Rock
โข Direct Connection between Source and Tunnel
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Soil
Water Table
River
Fractured Rock
Relevant Publications Jack Raymer, P.G., P.E. (Georgia and others)
jack.raymer@jacobs.com ; jack.raymer@gmail.com
Raymer, J., and Maerz, N. H., 2014, โEffect of Variability on Average Rock-Mass Permeability,โ Procedings of the the 48th Meeting of the American Rock Mechanics Association, ARMA 14-149, (2nd edition available by email from the author includes post-publication corrections.)
Raymer, J., 2010, โGeotechnical Variability and Uncertainty in Long Tunnels,โ in North American Tunneling 2010, in Eckert and others, [eds.], Society of Mining Metallurgy and Exploration, Inc., Englewood, Colorado, pp. 316-322.
Raymer, J., 2005, โGroundwater Inflow into Hard Rock Tunnels: a New Look at Inflow Equations,โ in Proceedings of the Rapid Excavation and Tunneling Conference, Society of Mining Metallurgy and Exploration, Inc., Englewood, Colorado (2nd edition available by email from the author includes post-publication corrections.
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