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1. 1
Transient Modelling of
Groundwater Flow
Application to Tunnel Dewatering
E.J. Wexler, P.Eng.
Earthfx Incorporated
February 13, 2013

2. 2
Outline
 Introduce the SEC Case Study
 Review general concepts of numerical
modelling
 Show how basic principles and models can
be extended to more complex settings
 Discuss results of SEC model and insights
gained

3. 3
SE Collector Sewer
Environmental Assessment
 Done for Conestoga-Rovers & Associates, Earth Tech
(Canada) Inc. and Regional Municipality of York
 Study to look at impact of construction dewatering
on groundwater and baseflow in nearby streams
 Previous construction (16th Ave) needed large-scale
dewatering after boring into Thorncliffe aquifer
 SEC alignment designed to pass mostly through
Newmarket Till
 Design used sealed shafts and EPBM when in
aquifers (now EPBM for entire run)
 Study used MODFLOW to investigate baseline
impacts and contingencies (e.g., TBM rescue and
delays).

4. 4
Southeast Collector Trunk Sewer
Links to York-Durham Sewer System to Duffins Creek WPCP
Hydrogeologic investigation by CRA

5. 5
Alignment is 15 km long
Four tunnel boring machines
3.6 m sealed concrete liner
Shafts for access and turning TBM
Shaft 13 for connection to existing sewer
Construction currently underway

6. 6
Dewatering applications for groundwater models:
 How long will we have to pump to reach target
levels?
 How much will we have to pump to maintain levels?
 What are the impacts on:
 nearby wells
 nearby streams (baseflow) and wetlands
 Can we optimize pumping rates and minimize
impacts?

7. 7
What is a groundwater model?
 A model is a simplified representation of a real
physical system
 We want to analyze response in simple system and
extrapolate
 Need to simplify because we often have limited
knowledge of subsurface geology
 Limited data on hydraulic properties
 Inputs (e.g. recharge) are highly variable in time
and space.

8. 8
Mathematical groundwater model:
 Based on two simple principals
 Darcy’s Law: Flow is proportional to
change in head (gradient)
 q = - K dh/dx (K is hydraulic conductivity)
 Conservation of mass:
 Flow out – Flow in = Decrease in storage
 Flow in/out can be related to heads through
Darcy’s Law
 Change in storage can also be related to change
in head through the storage coefficient
 Two basic types of models: analytical and
numerical

9. 9
Analytical solutions for predicting drawdown:
 Integrate the GW flow equation directly. Get
“closed form” solution
 Steady-State:
 Single and multiple wells (e.g., Theim equation)
 Line sources (e.g., DF drain discharge)
 Transient
 Single well – constant discharge (Theis)
 Single well – constant drawdown (Lohman)
 Late time (straight-line) solutions (Jacob)
 Multiple wells (super-position) and boundaries
 Leaky aquifers and partial penetration (Hantush)
 Multiple aquifers (Neuman-Witherspoon)
 Recharge and regional flow
 Change in streamflow
 Hunt (1999) and others

10. 10
Analytical solutions example:
 What pumping rate do I need to get a 2 m
drawdown at 30 days at the edge of a 100 m wide
site. T is 650 m2/d, S is 0.0015
 If there was a stream 500 m from the well with a
bed thickness of 1 m and a K’ of 0.086 m/d, how
much flow would be coming from the stream?

11. 11
Limitations of analytical solutions:
 Need to assume infinite extent or that h=Ho at
some radius of influence
 Simple geometry
 Uniform properties
 Theis eqn assumes single, infinite aquifer with no recharge
and fully penetrating well
 Simple stream geometry and properties.
 Note: More complex solutions can address specific
limitations.
 Image wells and superposition can help deal with boundary
issues

12. 12
Numerical Models:
 Finite Difference Methods:
 Break area into a rectangular grid
 Approximate derivatives in GW flow equation with
expressions relating to heads in neighbouring cells
 Flows must satisfy mass balance criteria
 Solve for heads at centre of cell
 Finite Element Method
 Break area into triangular or rectangular mesh
 Approximate head in element as
simple function of heads at nodes
and take derivatives
 Combine with weighted residual
method to minimize error
 Solve for heads at each node

13. 13
Groundwater Modelling Programs:
 Many codes available
 MODFLOW-2005 is a finite difference code
 developed by U.S. Geological Survey
 open source and free (www.usgs.gov/software)
 Many user-interfaces (e.g. Visual MODFLOW or GW-
Vistas) available for purchase
 FEFLOW 6.0 is a Finite-Element Code
 developed by DHI-WASY
 closed source
 built in GUI
 Which method is better?
FD Guy FE Guy

14. 14
Numerical models have many important features:
 Multiple aquifers and aquitards
 Irregular geometry and discontinities
 Irregular boundaries
 Spatial variability in hydraulic properties
 Variation in recharge rates
 Multiple pumping sources
 Confined/unconfined transition
 Interaction with streams
Warning: All models are simplifications. Not all features can be
represented and are often unknown. Simplifying assumptions,
and extrapolations should be identified.

15. 15
Model information requirements (Conceptual Model):
 Model geometry
 Model extent should be determined by natural hydrologic
boundaries
 Layer thickness (B) and continuity
 Aquifer and aquitard properties (K, T, S, Sy)
 Boundary conditions (heads and inflows at physical
limits of model)
 Initial Conditions (heads at t=0)
Simple conceptual
model for a well in
a confined aquifer
Assumes infinite
areal extent

16. 16
SEC Model extents:
Included all of Duffins Creek and Rouge River watersheds
All overburden layers and weathered bedrock
Large model but better able to analyze affects on streams

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Question: Local versus sub-regional models:
 Dewatering analysis may only need a local-scale
model
 Impact assessment needs to consider effects
beyond site boundary
 Detailed information may exist only on site
 Process and extrapolate from other information:
 Surficial geology and bedrock maps
 Aquifer maps
 MOE WWIS and UGAIS geotechnical data
 Larger scale model should not sacrifice detail at
local scale

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Model grid design:
 Model grid should be refined (i.e., small cells or
elements) around area of interest
 Often use expanding grid to reach model boundaries
 Uniform grids are better for regional models
because all features (e.g., streams) are of interest

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Portion of SEC Model grid:
Uniform 100-m cell size outside of SEC study area.
Down to 2.5 x 2.5 m near Shaft 13

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SEC Model layer geometry defined by analyzing borehole data
Many monitoring wells and geotechnical boreholes installed for SEC
Other data obtained from YPDT database

21. 21
SEC Model Geology:
Good geologic control along the alignment
Less detail at depth (e.g., to locate bedrock valleys)
Information about Newmarket Till extent used in design
Tunnel passes through TAC and ORAC at some locations

22. 22
Geology section outside SEC area inferred primarily from MOE
WWIS geologic logs
Location errors, ft-m conversion errors, and other data quality
issues add to difficulty in interpretation process
Potentiometric surfaces from MOE WWIS static water levels

23. 23
Three main types of Boundary Conditions:
 Known head at boundary
 Constant or time-dependent
 Lakes and large rivers
 Known flow at boundary
 No-flow at stream divides
 Impermeable boundaries (aquifer base)
 Head-dependent flow
 Leakage across confining units
 Leakage across stream beds
H=H0
No Flow
No
Flow
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
No Flow
Model for a well in a
confined aquifer with
simple boundaries

24. 24
SEC Model uses natural hydrologic boundaries
No-flow boundaries at regional groundwater divide
Lateral boundaries defined by Rouge/Duffins watersheds
Constant head (72.5 masl) at Lake Ontario

25. 25
Boundary Conditions for Dewatering:
 Specifying flow at a well or multiple well points:
 Useful if you need to know the time to achieve target
drawdown
 Can provide detailed pumping schedule (e.g., if using
multiple wells on different benches)
 Specified Head
 Once target is achieved, head can be maintained with
decreased rate of pumping
 Can set head and determine
inflows from mass balance
 MODFLOW CHD package
allows you to turn on
constant head boundaries.
We modified to turn them
off again.
 Dewatering ahead of TBW
was simulated with moving
CH boundary
Click for Animation

26. 26
Aquifer properties:
 Aquifer tests conducted by CRA:
 Provide local information on T and S
 Regional aquifer and aquitard properties
 K’s inferred from previous studies and lithologic log data
 Aquitard properties inferred previous work (e.g., Gerber
and Howard) and regional ORM model calibration
 Local data incorporated and K’s refined

27. 27
Aquifer Inflows:
 For simple models, recharge can be estimated and
refined through calibration
 For SEC, groundwater recharge determined through
separate water budget analysis
 Used USGS Precipitation-Runoff model (PRMS)
 Daily water balance calculated for each model cell
 Daily climate data inputs
(P, Temp, Solar Radiation)
 Soil Properties and land use
(e.g., % impervious and
vegetative cover density)
from available mapping
 Simulated 7 years and
averaged results

28. 28
SEC Model recharge:
High values on Oak Ridges Moraine and Iroquois Beach
Lower recharge on Halton and Newmarket Till and urban areas

29. 29
Aquifer Outflows:
 For dewatering with wells or wellpoints, discharge
rates are specified.
 For drains, a control elevation is specified.
 For SEC Model, all permitted groundwater takings
were represented
 Streams represented by MODFLOW rivers or drains
 Discharge calculated internally based on difference
between stage and aquifer head
 Stage is assumed constant (other MODFLOW packages
adjust stage based on upstream inflows and leakage)

30. 30
Model calibration:
 After we define geometry, boundary conditions,
aquifer properties, and inflows, we still need to
calibrate to observations.
 For SEC, calibration targets were observed
potentials and average baseflow in stream
 K’s and recharge primary calibration factors
 MOE WWIS water levels
 Data quality problems, large number makes them useful
 Baseflow estimated for HYDAT gauges
 Automated base-
flow separation
methods not exact

31. 31
Match of simulated (blue) to observed (red) is reasonable
White areas are “dry”, heads are below base of ORAC

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Match aquifer test results to calibrate storage properties
Also tried to match simulated and observed 16th Ave dewatering

33. 33
Modelling dewatering and streamflow depletion:
 Pumping near a stream can induce surface water
infiltration.
 More likely, pumping can reduce amount of water
that would naturally discharge to the steam.
 Impacts depend on pumping rate, proximity to
stream, and aquifer properties (transmissivity and
storage), and streambed properties

34. 34
Modelling dewatering and streamflow depletion:
 Lag between start of
pumping and change in flow
 Due to high storage (Sy)
 May not see in short-term test
 Recovery is also lagged

35. 35
SEC Dewatering analysis – Baseline Scenario:
 Four Tunnel Drives:
 TBM run in regular mode through Newmarket Till
 Run in EPBM mode through aquifers
 Shafts:
 Sealed shafts in aquifers; open shafts in till.
 Shaft 13 needs dewatering for 5 months at end for
connection to old sewer
 Water takings:
 300 L/m at Shaft 11 for construction
 All other water from municipal supply
 (now permitted for 220 L/min for construction and 300
L/min for seepage and dewatering).
 Change in baseflow determined by subtracting
simulated baseflow from simulated discharge under
baseline conditions

36. 36
Schedule for Tunnel Drives and Shaft construction (not current schedule)
Green indicates no expected impact (sealed shafts and EPBM mode)

37. 37
Click for Animation
Simulated Drawdowns and Change in GW Discharge to Streams

38. 38
Simulated change in baseflow (GW discharge to stream)
Largest changes occur as TBM approaches channel

39. 39
Click for Animation
Contingency Simulations: Stuck TBM on Drive A

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Conclusions:
 Numerical models can account for complex geology,
multiple aquifers and aquitards, and regional flow
conditions
 Transient flow modelling is needed to represent behavior
of groundwater system under short-term and longer-term
dewatering
 Models can account for decreasing inflows over time
 Can account for change in aquifer storage and seasonal
changes in recharge
 Can be used to assess time-dependent changes to
groundwater discharge to streams
 Models results and understanding of geology helped in
route selection and dewatering design to minimize
impacts.