This research improves field based estimates of aquitard compressibility and permeability. A semianalytical model of partially penetrating, overdamped slug tests achieves this objective. The short term solution is an existing fully penetrating model, the long term solution is the polar residue of an inverse Laplace transform, and an exponential spline function patches the solutions together. Large amplitude slug test data from ten pairs of partially penetrating monitoring wells installed in an unweathered till at Scituate Hill in eastern Massachusetts calibrate the model. The deposit is bound by weathered till and the Dedham Granite fracture zone, and both are far more permeable than the unweathered till. The calibrated till permeability of 8.4 × 10–16 m2 is about 25% less than existing model calibrations that include boundary recharge in permeability values. The calibrated till compressibility of 5.1 × 10–10 Pa–1 reflects the proper inclusion of recharge as a long term source of groundwater, rather than the unrealistically large compressibility calibrations required by fully penetrating models.
NOMENCLATURE
- AJ
Jth Fourier sine series coefficient (m-s)
- a0
simple pole (1/s)
- BJ
integrating factor of Jth sine series coefficient
- b
unweathered till thickness (m)
- cJ
Jth integration constant (m-s)
- D
hydraulic diffusivity (m2/s)
- FShort
transform of short term solution (m-s)
- f(t):F(p)
Laplace transform pair
- g
gravitational acceleration (m/s2)
- HO
amplitude of slug test (m)
- h
disturbed hydraulic head (m)
- hLong
long term solution for disturbed water level in well (m)
- hRes
residue of simple pole (m)
- hS
disturbed water level in well (m)
- hShort
short term solution for disturbed water level in well (m)
- h*
transformed hydraulic head (m-s)
transformed hydraulic head in well (m-s)
- JN
Bessel function of the first kind, of order N
- KN
modified Bessel function of the second kind, of order N
- k
permeability of unweathered till (m2)
- kBR
Bouwer & Rice (1976) estimate of unweathered till permeability (m2)
- L
length of sandpack (m)
- LMatch
matching length (m)
- mJ
Jth radial eigenfunction (m-s)
- p
Laplace transform variable (1/s)
- pGage
gage pressure (kg/m-s2)
- qJ
Jth vertical eigenfunction
- R
distance along negative real axis of Bromwich contour (1/s)
- RJ
Jth branch point (1/s)
- r
radial distance from center of well (m)
- rC
radius of casing (m)
- re
effective radius in Bouwer & Rice (1976) model (m)
- rS
radius of sandpack (m)
- S
unweathered till storativity
- T
unweathered till transmissivity (m2/s)
- t
time from start of slug test (s)
- u
changed variable of integration in Cooper et al. (1967) model
- YN
Bessel function of the second kind, of order N
- z
elevation above lower recharge boundary (m)
- zS
elevation of the base of the sandpack (m)
- zT
elevation of transducer (m)
- α
unweathered till compressibility (m-s2/kg)
- β
sum of integrating factors
- ρ
density of groundwater (kg/m3)
- ν
kinematic viscosity of groundwater (m2/s)
INTRODUCTION
We derive and calibrate a closed form model of partially penetrating slug tests to improve field based estimates of aquitard compressibility and permeability. Aquitards are important because they protect underlying aquifers from surface contamination (van der Kamp 2001), an attribute of particular significance in stratified drift deposits (Klinger 1996) and till mantled bedrock (Lukas et al. 2015) of New England. Aquitard leakage affects confined aquifer hydraulics (Wang et al. 2015), and an improved understanding of the confining layer properties distinguishes recharge from aquifer compressibility in the calibration of transient pump test data (Neuman & Witherspoon 1969).
Slug tests estimate hydraulic properties of soil near monitoring wells, as documented by an established (Butler 1997) and continuing (Sakata et al. 2015) literature. Impermeable soil responds monotonically to an abrupt change of head in the well, and Cooper et al. (1967) use Laplace transforms to derive an analytical model for a fully penetrating sandpack in a confined aquifer. The overdamped slug test theory balances radial flow and storage in the soil with an integrated conservation of mass for the monitoring well imposed as a boundary condition at the interface of the sandpack and soil. Water level observations in the well calibrate the aquifer transmissivity and storativity, hence the radial permeability and compressibility of the soil. Partially penetrating wells, packers, or unconfined aquifers add a vertical component to the hydraulics of overdamped slug tests (Zlotnik 1994). Bouwer & Rice (1976) neglect soil storage, and compare cylindrical finite difference solutions with a radial closed form solution for overdamped slug tests in an unconfined aquifer to determine an equivalent radius in the soil. The latter determines the exponential decay constant for the water level in the monitoring well, along with the calibrated soil permeability. Hvorslev (1951) adopts a similar approach, but uses a steady cylindrical solution and shape factors to infer soil permeability from an exponential decay constant. Hyder et al. (1994) include soil storage in their cylindrical model of overdamped slug test hydraulics and derive a closed form Laplace transform solution for partially penetrating wells in a confined aquifer. Their transformed solution is inverted numerically, and features in many recent investigations. Paradis & Lefebvre (2013) use it to interpret slug test data in observation and slugged intervals in a single monitoring well equipped with multiple packers. Brauchler et al. (2010) use the Hyder et al. (1994) model to interpret slug test data in separate observation wells. Yeh et al. (2008) add a skin zone to the cylindrical model of a partially penetrating slug test in a confined aquifer and, like Hyder et al. (1994), invert the analytical Laplace transform solution numerically. Multiple wells and more complicated groundwater settings require numerical models, and Yang et al. (2015) summarize a recent MODFLOW application in aquitards. The challenge of heterogeneous property estimation from an array of observation and partially penetrating slugged wells is considered as an inverse tomographic exercise by Paradis et al. (2015).
Our study was motivated by the documented response of unweathered till monitoring wells to the introduction of seasonal pumping from underlying fractured bedrock more than a decade after the initial site characterization experiments. The latter followed van der Kamp's (2001) strategy of aquitard analysis across steady, seasonal, and diurnal scales; and included Hvorslev (1951) permeability calibration of slug tests and downward attenuation of storm scale transience for compressibility estimation (Ostendorf et al. 2004). Bedrock pumping introduces seasonal transience from below, and reveals the fracture zone as a leaky aquifer (Hantush 1960). Discrete (Ostendorf et al. 2015a) and continuous (Lukas et al. 2015) records of drawdown and recovery in the monitoring wells calibrate site averaged values for permeability and compressibility of the till. Ostendorf et al. (2015b) confirm the corresponding bedrock properties with a novel theory of slug tests and geophysical logs in uncased boreholes through the fracture zone. The present study completes the cycle in the till, with an improved model of partially penetrating slug tests that includes compressibility and recharge boundaries.
SITE DESCRIPTION
Scituate Hill
Parameter . | Value . | Source . |
---|---|---|
Unweathered till thickness (b) | 30 m | Soil borings |
Groundwater kinematic viscosity (ν) | 1.3 × 10–6 m2/s | White (2011) |
Groundwater density (ρ) | 1.0 × 103 m3/s | White (2011) |
Weathered till permeability | 10–13 m2 | Ostendorf et al. (2004) |
Leaky bedrock aquifer transmissivity | 4 × 10–5 m2/s | Ostendorf et al. (2015a) |
Casing radius (rC) | 2.5 cm | Ostendorf et al. (2004) |
Unweathered till permeability (k) | 8.4 × 10–16 m2 | Geometric calibration average |
Unweathered till compressibility (α) | 5.1 × 10–10 Pa–1 | Arithmetic calibration average |
Matching length (LMatch) | 6.3 m | Arithmetic calibration average |
Parameter . | Value . | Source . |
---|---|---|
Unweathered till thickness (b) | 30 m | Soil borings |
Groundwater kinematic viscosity (ν) | 1.3 × 10–6 m2/s | White (2011) |
Groundwater density (ρ) | 1.0 × 103 m3/s | White (2011) |
Weathered till permeability | 10–13 m2 | Ostendorf et al. (2004) |
Leaky bedrock aquifer transmissivity | 4 × 10–5 m2/s | Ostendorf et al. (2015a) |
Casing radius (rC) | 2.5 cm | Ostendorf et al. (2004) |
Unweathered till permeability (k) | 8.4 × 10–16 m2 | Geometric calibration average |
Unweathered till compressibility (α) | 5.1 × 10–10 Pa–1 | Arithmetic calibration average |
Matching length (LMatch) | 6.3 m | Arithmetic calibration average |
Prior testing, modeling, and analysis have established that the weathered till and bedrock fracture zones are more than an order of magnitude more permeable than the unweathered till between them. Infiltration and unconfined aquifer hydraulics at steady and seasonal scales have established weathered till permeability of 10–13 m2 in radial (Ostendorf et al. 2004) and horizontal (Ostendorf et al. 2015a) flow fields along the toe and flank of the drumlin. Irrigation pumping from the Dedham Granite at an adjacent apartment complex completed in 2011 has revealed the fracture zone hydraulics to function as a confined aquifer of 4 × 10–5 m2/s transmissivity that receives leakage from the unweathered till.
Monitoring well details and slug test protocol
Twenty-two monitoring well clusters were constructed by the University of Massachusetts Amherst in the late 1990s and early 2000s to investigate the fate, transport, and remediation of deicing agent chloride contamination of the groundwater (Ostendorf et al. 2006). Ten of the clusters include pairs of 0.025 m radius (rC) PVC monitoring wells, with 1.52 m screen sections with uniform sandpacks in closely spaced (<5 m) boreholes. One well was drilled to the contact surface with the Dedham Granite and a second was drilled 15–25 m higher up in the unweathered till. Table 2 lists attributes of the pairs, which feature sandpack radii rS varying from 0.049 to 0.108 m and sandpack lengths L from 2.13 to 2.74 m in extent, and, in one instance, 5.34 m. The sandpacks were sealed with bentonite grout or chips, and each monitoring well was finished with a locked steel cover and concrete collar at the ground surface.
Well (date) . | rS, m . | L, m . | zS, m . | β . | zT, m . | HO, m . |
---|---|---|---|---|---|---|
AB (1/29/13) | 0.108 | 2.59 | 0.0 | 0.086 | 1.1 | –21.0 |
AD (7/28/15) | 0.049 | 2.13 | 18.5 | 0.070 | 18.8 | –8.88 |
BB (7/28/15) | 0.108 | 1.89 | 16.9 | 0.062 | 17.5 | –7.17 |
BC (1/29/13) | 0.108 | 2.59 | 0.0 | 0.086 | 6.4 | –22.3 |
CB (1/29/13) | 0.108 | 2.44 | 0.0 | 0.082 | 1.8 | –23.0 |
CD (7/28/15) | 0.108 | 2.13 | 20.2 | 0.070 | 20.5 | –7.19 |
DB (1/29/13) | 0.108 | 2.13 | 0.0 | 0.070 | 3.7 | –25.3 |
DC (7/28/15) | 0.108 | 2.13 | 21.8 | 0.070 | 21.9 | –7.66 |
EB (8/4/15) | 0.108 | 2.21 | 0.0 | 0.072 | 0.3 | –15.6 |
ED (7/28/15) | 0.108 | 2.44 | 16.7 | 0.082 | 17.4 | –10.4 |
GB (1/29/13) | 0.049 | 5.34 | 0.0 | 0.18 | 1.0 | –18.6 |
GC (7/28/15) | 0.049 | 2.13 | 18.0 | 0.070 | 18.9 | –7.46 |
HB (1/29/13) | 0.049 | 2.44 | 0.0 | 0.082 | 0.7 | –19.6 |
HC (7/28/15) | 0.049 | 2.59 | 18.9 | 0.086 | 20.7 | –7.08 |
IB (1/29/13) | 0.108 | 2.13 | 0.0 | 0.070 | 0.1 | –24.0 |
ID (7/28/15) | 0.108 | 2.44 | 25.9 | 0.081 | 26.2 | –6.41 |
LA (1/29/13) | 0.108 | 2.13 | 0.0 | 0.070 | 14.5 | –26.5 |
LD (7/28/15) | 0.108 | 2.44 | 21.7 | 0.070 | 23.0 | –8.78 |
TA (8/4/15) | 0.049 | 2.74 | 0.0 | 0.090 | 1.0 | –19.3 |
TD (7/28/15) | 0.049 | 2.44 | 16.1 | 0.081 | 16.6 | –10.0 |
Well (date) . | rS, m . | L, m . | zS, m . | β . | zT, m . | HO, m . |
---|---|---|---|---|---|---|
AB (1/29/13) | 0.108 | 2.59 | 0.0 | 0.086 | 1.1 | –21.0 |
AD (7/28/15) | 0.049 | 2.13 | 18.5 | 0.070 | 18.8 | –8.88 |
BB (7/28/15) | 0.108 | 1.89 | 16.9 | 0.062 | 17.5 | –7.17 |
BC (1/29/13) | 0.108 | 2.59 | 0.0 | 0.086 | 6.4 | –22.3 |
CB (1/29/13) | 0.108 | 2.44 | 0.0 | 0.082 | 1.8 | –23.0 |
CD (7/28/15) | 0.108 | 2.13 | 20.2 | 0.070 | 20.5 | –7.19 |
DB (1/29/13) | 0.108 | 2.13 | 0.0 | 0.070 | 3.7 | –25.3 |
DC (7/28/15) | 0.108 | 2.13 | 21.8 | 0.070 | 21.9 | –7.66 |
EB (8/4/15) | 0.108 | 2.21 | 0.0 | 0.072 | 0.3 | –15.6 |
ED (7/28/15) | 0.108 | 2.44 | 16.7 | 0.082 | 17.4 | –10.4 |
GB (1/29/13) | 0.049 | 5.34 | 0.0 | 0.18 | 1.0 | –18.6 |
GC (7/28/15) | 0.049 | 2.13 | 18.0 | 0.070 | 18.9 | –7.46 |
HB (1/29/13) | 0.049 | 2.44 | 0.0 | 0.082 | 0.7 | –19.6 |
HC (7/28/15) | 0.049 | 2.59 | 18.9 | 0.086 | 20.7 | –7.08 |
IB (1/29/13) | 0.108 | 2.13 | 0.0 | 0.070 | 0.1 | –24.0 |
ID (7/28/15) | 0.108 | 2.44 | 25.9 | 0.081 | 26.2 | –6.41 |
LA (1/29/13) | 0.108 | 2.13 | 0.0 | 0.070 | 14.5 | –26.5 |
LD (7/28/15) | 0.108 | 2.44 | 21.7 | 0.070 | 23.0 | –8.78 |
TA (8/4/15) | 0.049 | 2.74 | 0.0 | 0.090 | 1.0 | –19.3 |
TD (7/28/15) | 0.049 | 2.44 | 16.1 | 0.081 | 16.6 | –10.0 |
The groundwater density is ρ and gravitational acceleration is g.
Modifications for the study site
The exact integration of the Bromwich contour needed to invert transformed cylindrical hydraulics is complicated, as demonstrated by Neuman & Witherspoon (1969) for pump tests in leaky aquifers. We follow Hantush (1960) instead, who interpolates between simple short and long term solutions in his analysis of pump tests in leaky aquifers. Our long term solution is exponential, with a pole and a residue that permit a semilogarithmic regression whose slope and intercept calibrate the compressibility and permeability of the unweathered till. The short term solution is similar to that of Cooper et al. (1967), with the inclusion of a factor dependent on partial well geometry. Our closed form model, though new, does rest on its predecessors.
MATHEMATICAL MODEL
Governing equation and assumed transformed solution for cylindrical flow
Short term solution
If the sandpack extends over the entire till, zS is zero, L is b, β is one (Spiegel & Liu 1999), and Equation (15a) becomes identical to the Cooper et al. (1967) model for a fully penetrating, overdamped slug test in a confined aquifer. The coincidence suggests that most of the initial recovery of the head in the well is due to radial flow of stored groundwater released by soil near the sandpack. Leakage and cylindrical flow happen later.
A simple pole as the long term solution
Spline function between the short and long term solutions
Calibration
Well . | a0, s–1 . | hRes, m . | LMatch, m . | D, m2/s . | S . | T, m2/s . | k, m2 . | α, Pa–1 . |
---|---|---|---|---|---|---|---|---|
AB | –1.0 × 10–5 | –13 | 6.4 | 0.00092 | 0.00012 | 1.1 × 10–7 | 4.8 × 10–16 | 4.0 × 10–10 |
AD | –2.1 × 10–5 | –4.0 | 7.0 | 0.0019 | 0.00021 | 3.9 × 10–7 | 1.7 × 10–15 | 7.0 × 10–10 |
BB | –1.3 × 10–4 | –3.4 | 7.0 | 0.012 | 0.00018 | 2.1 × 10–6 | 9.3 × 10–15 | 6.1 × 10–10 |
BC | –1.1 × 10–5 | –3.6 | 4.1 | 0.00098 | 0.00012 | 1.2 × 10–7 | 5.2 × 10–16 | 4.0 × 10–10 |
CB | –8.3 × 10–6 | –3.5 | 4.1 | 0.00076 | 0.00012 | 9.4 × 10–8 | 4.1 × 10–16 | 4.2 × 10–10 |
CD | –3.2 × 10–6 | –4.4 | 6.1 | 0.00029 | 0.00016 | 4.6 × 10–8 | 2.0 × 10–16 | 5.3 × 10–10 |
DB | –3.1 × 10–5 | –3.8 | 3.7 | 0.0028 | 0.00014 | 3.8 × 10–7 | 1.7 × 10–15 | 4.6 × 10–10 |
DC | –2.1 × 10–5 | –2.3 | 4.1 | 0.0019 | 0.00016 | 3.0 × 10–7 | 1.3 × 10–15 | 5.3 × 10–10 |
EB | –1.9 × 10–6 | –14.0 | 5.3 | 0.00017 | 0.00013 | 2.3 × 10–8 | 1.0 × 10–16 | 4.5 × 10–10 |
ED | –7.1 × 10–6 | –6.0 | 7.8 | 0.00065 | 0.00014 | 9.3 × 10–8 | 4.1 × 10–16 | 4.8 × 10–10 |
GB | –3.8 × 10–5 | –0.90 | 2.4 | 0.0034 | 8.3 × 10−5 | 2.8 × 10–7 | 1.2 × 10–15 | 2.8 × 10–10 |
GC | –6.4 × 10–6 | –3.0 | 16 | 0.00059 | 0.00021 | 1.2 × 10–7 | 5.4 × 10–16 | 7.1 × 10–10 |
HB | –5.0 × 10–5 | –2.0 | 3.4 | 0.0045 | 0.00016 | 7.3 × 10–7 | 3.2 × 10–15 | 5.5 × 10–10 |
HC | –6.5 × 10–5 | –4.0 | 5.7 | 0.0060 | 0.00017 | 1.0 × 10–6 | 4.6 × 10–15 | 5.9 × 10–10 |
IB | –9.7 × 10–6 | –3.5 | 3.0 | 0.00086 | 0.00014 | 1.2 × 10–7 | 5.3 × 10–16 | 4.6 × 10–10 |
ID | –2.6 × 10–5 | –3.5 | 4.7 | 0.0024 | 0.00013 | 3.2 × 10–7 | 1.4 × 10–15 | 4.5 × 10–10 |
LA | –7.6 × 10–6 | –15 | 5.7 | 0.00069 | 0.00014 | 9.4 × 10–8 | 4.2 × 10–16 | 4.6 × 10–10 |
LD | –5.9 × 10–6 | –5.0 | 6.4 | 0.00054 | 0.00016 | 8.4 × 10–8 | 3.7 × 10–16 | 5.3 × 10–10 |
TA | –1.4 × 10–5 | –5.0 | 19.9 | 0.0013 | 0.00015 | 2.0 × 10–7 | 8.7 × 10–16 | 5.1 × 10–10 |
TD | –1.6 × 10–5 | –1.8 | 3.7 | 0.0015 | 0.00018 | 2.7 × 10–7 | 1.2 × 10–15 | 6.3 × 10–10 |
Well . | a0, s–1 . | hRes, m . | LMatch, m . | D, m2/s . | S . | T, m2/s . | k, m2 . | α, Pa–1 . |
---|---|---|---|---|---|---|---|---|
AB | –1.0 × 10–5 | –13 | 6.4 | 0.00092 | 0.00012 | 1.1 × 10–7 | 4.8 × 10–16 | 4.0 × 10–10 |
AD | –2.1 × 10–5 | –4.0 | 7.0 | 0.0019 | 0.00021 | 3.9 × 10–7 | 1.7 × 10–15 | 7.0 × 10–10 |
BB | –1.3 × 10–4 | –3.4 | 7.0 | 0.012 | 0.00018 | 2.1 × 10–6 | 9.3 × 10–15 | 6.1 × 10–10 |
BC | –1.1 × 10–5 | –3.6 | 4.1 | 0.00098 | 0.00012 | 1.2 × 10–7 | 5.2 × 10–16 | 4.0 × 10–10 |
CB | –8.3 × 10–6 | –3.5 | 4.1 | 0.00076 | 0.00012 | 9.4 × 10–8 | 4.1 × 10–16 | 4.2 × 10–10 |
CD | –3.2 × 10–6 | –4.4 | 6.1 | 0.00029 | 0.00016 | 4.6 × 10–8 | 2.0 × 10–16 | 5.3 × 10–10 |
DB | –3.1 × 10–5 | –3.8 | 3.7 | 0.0028 | 0.00014 | 3.8 × 10–7 | 1.7 × 10–15 | 4.6 × 10–10 |
DC | –2.1 × 10–5 | –2.3 | 4.1 | 0.0019 | 0.00016 | 3.0 × 10–7 | 1.3 × 10–15 | 5.3 × 10–10 |
EB | –1.9 × 10–6 | –14.0 | 5.3 | 0.00017 | 0.00013 | 2.3 × 10–8 | 1.0 × 10–16 | 4.5 × 10–10 |
ED | –7.1 × 10–6 | –6.0 | 7.8 | 0.00065 | 0.00014 | 9.3 × 10–8 | 4.1 × 10–16 | 4.8 × 10–10 |
GB | –3.8 × 10–5 | –0.90 | 2.4 | 0.0034 | 8.3 × 10−5 | 2.8 × 10–7 | 1.2 × 10–15 | 2.8 × 10–10 |
GC | –6.4 × 10–6 | –3.0 | 16 | 0.00059 | 0.00021 | 1.2 × 10–7 | 5.4 × 10–16 | 7.1 × 10–10 |
HB | –5.0 × 10–5 | –2.0 | 3.4 | 0.0045 | 0.00016 | 7.3 × 10–7 | 3.2 × 10–15 | 5.5 × 10–10 |
HC | –6.5 × 10–5 | –4.0 | 5.7 | 0.0060 | 0.00017 | 1.0 × 10–6 | 4.6 × 10–15 | 5.9 × 10–10 |
IB | –9.7 × 10–6 | –3.5 | 3.0 | 0.00086 | 0.00014 | 1.2 × 10–7 | 5.3 × 10–16 | 4.6 × 10–10 |
ID | –2.6 × 10–5 | –3.5 | 4.7 | 0.0024 | 0.00013 | 3.2 × 10–7 | 1.4 × 10–15 | 4.5 × 10–10 |
LA | –7.6 × 10–6 | –15 | 5.7 | 0.00069 | 0.00014 | 9.4 × 10–8 | 4.2 × 10–16 | 4.6 × 10–10 |
LD | –5.9 × 10–6 | –5.0 | 6.4 | 0.00054 | 0.00016 | 8.4 × 10–8 | 3.7 × 10–16 | 5.3 × 10–10 |
TA | –1.4 × 10–5 | –5.0 | 19.9 | 0.0013 | 0.00015 | 2.0 × 10–7 | 8.7 × 10–16 | 5.1 × 10–10 |
TD | –1.6 × 10–5 | –1.8 | 3.7 | 0.0015 | 0.00018 | 2.7 × 10–7 | 1.2 × 10–15 | 6.3 × 10–10 |
The storativity (0.00012) follows from Equation (19b), then the permeability (4.8 × 10–16 m2) and compressibility (4.0 × 10–10 Pa–1) from Equations (11b) and (15b), respectively. The long term behavior alone estimates intrinsic properties of the till, by graphical calibration.
The splined approximation Equation (21) of the complete solution then drives a Fibonacci search (Knuth 1973) for the matching length that minimizes the root mean square of the error defined by Equations (1) and (21). A value of 6.4 m yields an rms error of 2.7 cm, and the calibration plots as the line in Figure 6(b). The AB calibration is also plotted in Figure 5.
RESULTS
Calibrated parameter values
The long term behavior generates polar decay constants that range from –1.9 × 10–6 to –1.3 × 10–4 s–1, so that wells regain their ambient water levels within a few hours or a few days (Figure 2). The permeabilities vary from 1.0 × 10–16 m2 in monitoring well EB to 9.3 × 10–15 m2 in well BB with a (geometric) average value of 8.4 × 10–16 m2. Table 1 confirms that the weathered till is over an order of magnitude more permeable than the unweathered till beneath it. The transmissivities of Table 3 range from 2.3 × 10–8 to 2.1 × 10–6 m2/s, with a (geometric) average (1.9 × 10–7 m2/s) that is two orders of magnitude less than the fractured bedrock zone transmissivity cited in Table 1. The unweathered till is far less permeable than the underlying Dedham Granite, and the recharge boundary assumptions of the closed form analysis are justified at the site.
The calibrated compressibilities range from 2.8 × 10–10 to 7.1 × 10–10 Pa–1, with an arithmetic average of 5.1 × 10–10 Pa–1. The values are an order of magnitude larger than the product of the 22% till porosity and the 4.4 × 10–10 Pa–1 compressibility of water (White 2011) and the 2 × 10–11 Pa–1 compressibility of unfractured Dedham Granite (Leet & Ewing 1932). Storage comes from the rearrangement of incompressible grains of the till in incompressible groundwater.
Bouwer & Rice (1976) and Cooper et al. (1967) comparisons
The effective radius re depends on the well geometry and distance of the sandpack from the water table, and the impermeable lower boundary of the aquifer.
DISCUSSION
As a practical matter, the use of quasi-steady, radial slug test models to estimate permeability is confirmed by the cylindrical, closed form approach of the present analysis. Figure 8 establishes that Bouwer & Rice (1976) calibrations are well within an order of magnitude of the Table 3 permeabilities. Ostendorf et al. (2004) summarize Hvorslev (1951) calibrations of small amplitude slug tests at the site with an average permeability (1.4 × 10–15 m2) that is close to the Table 1 value. Hyder et al. (1994) arrive at a similar conclusion through an extensive set of simulations. Our method does yield a tighter compressibility estimate than the radial models when the boundary conditions are met, however. The parameter is absent altogether from the Bouwer & Rice (1976) and Hvorslev (1951) models, while the Cooper et al. (1967) application precludes vertical flow and leakage. The radial models offer little insight into storage properties for partially penetrating slug tests in till.
Although the –20 m scale amplitude of the deep and –10 m scale amplitude of the shallow slug tests eliminate complicating effects of ambient transience on till property estimation, centimeter scale fluctuations can be used to advantage in simpler analyses. Ostendorf & DeGroot (2010) incorporate a linearly varying ambient head into a Bouwer & Rice (1976) analysis of a small amplitude slug test at a deep monitoring well (MA) at the Cohasset site; the 6.0 × 10–16 m2 permeability compares favorably with the Table 3 values. The downward attenuation of storm scale disturbances observed at the G cluster implies a hydraulic diffusivity of 0.00043 m2/s in the unweathered till (Ostendorf et al. 2004). This is less than the 0.0013 m2/s site-wide value implied by Table 1, though it is the same order of magnitude. A site average compressibility of 3 × 10–9 Pa–1 and a site average permeability of 5.9 × 10–16 m2 calibrate the response of the unweathered till to seasonal irrigation pumping of the Dedham Granite at an adjacent apartment complex (Ostendorf et al. 2015a).
CONCLUSIONS
A new semianalytical cylindrical model of a slug test in a partially penetrating monitoring well calibrates hydraulic properties of till bound by zero head recharge layers. A heuristic spline function patches initial and long term solutions together. Ten pairs of large amplitude slug tests in deep and shallow monitoring wells calibrate permeability and compressibility values at a till drumlin in eastern Massachusetts. The 8.4 × 10–16 m2 permeability estimate is close to the value established by simpler radial slug test models at the site. The calibrated compressibilities of the 20 tests do not vary much from the site average value of 5.1 × 10–10 Pa–1 because the present analysis models vertical flow and recharge as a progressively more important groundwater source later in the experiment. Thus the low compressibility calibration accurately reflects the short term response to the test, when soil immediately near the sandpack flows radially into the well. Radial models rely on storage release for the groundwater throughout the test duration, and calibrate late term response with unrealistically high compressibilities as a consequence.
ACKNOWLEDGEMENTS
The Massachusetts Department of Transportation Highway Division funded this research under Interagency Service Agreement No. 73140 with the University of Massachusetts Amherst. The views, opinions, and findings contained in this paper are those of the authors and do not reflect MassDOT official views or policies. This paper does not constitute a standard, specification, or regulation.