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Transient Modelling of Groundwater Flow

Application to Tunnel Dewatering

E.J. Wexler, P.Eng.

Earthfx Incorporated

February 13, 2013

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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

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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).

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

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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

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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?

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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.

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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

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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

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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?

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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

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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

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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

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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

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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)

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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

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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

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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

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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

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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

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

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

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

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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.