The coupled poro-mechanical behaviour of geologic-fluid systems is fundamental to numerous processes in structural geology, seismology, and geotechnics, but is frequently overlooked in hydrogeology. Substantial poro-mechanical influences on groundwater head have recently been highlighted in the Bengal Aquifer System, however, driven by terrestrial water loading across the Ganges–Brahmaputra–Meghna floodplains. Groundwater management in this strategically important fluvio-deltaic aquifer, the largest in southern Asia, requires a coupled hydro-mechanical approach which acknowledges poroelasticity. We present a simple partially coupled, 1-D poroelastic model of the Bengal Aquifer System, and explore the poro-mechanical responses of the aquifer to surface boundary conditions representing hydraulic head and mechanical load under three modes of terrestrial water variation. The characteristic responses, shown as amplitude and phase of hydraulic head in depth profile and of ground surface deflection, demonstrate (i) the limits to using water levels in piezometers to indicate groundwater recharge, as conventionally applied in groundwater resources management; (ii) the conditions under which piezometer water levels respond primarily to changes in the mass of terrestrial water storage, as applied in geological weighing lysimetry; (iii) the relationship of ground surface vertical deflection with changes in groundwater storage; and (iv) errors of attribution that could result from ignoring the poroelastic behaviour of the aquifer. These concepts are illustrated through application of the partially coupled model to interpret multi-level piezometer data at two sites in southern Bangladesh. There is a need for further research into the coupled responses of the aquifer due to more complex forms of surface loading, particularly from rivers.
Throughout the Bengal Basin, the floodplains of the Ganges, Brahmaputra, and Meghna (GBM) rivers (Fig. 1) are underlain by the Bengal Aquifer System (BAS), the largest aquifer in southern Asia and the source of water to over 100 million people (Burgess et al., 2010). More than 10 million tubewells throughout the basin provide water from the BAS for domestic use and for irrigation of the rice crop (Ravenscroft et al., 2009); these include hand-pumped tubewells, normally between 15 and 30 m depth below ground level (b.g.l.), for domestic use, and tubewells installed with motor-driven pumps to abstract water from between 50 and 75 m depth b.g.l. for irrigation of the dry season rice crop (January to April). Municipal water supplies commonly abstract year-round from depths between 200 and 300 m b.g.l. (Shamsudduha et al., 2018). Management of the BAS groundwater resource relies on monitoring water levels in networks of observation boreholes, taking the conventional approach that changes in groundwater heads represent volumetric changes in groundwater storage through recharge and drainage (Shamsudduha et al., 2011). This approach presumes the hydraulic behaviour of the aquifer to be decoupled from its mechanical response to changes in stress. Recently, however, the distinctively poroelastic behaviour of the BAS has been recognized (Burgess et al., 2017), by which groundwater heads are subject to substantial mechanical perturbation driven by changes in the mass of terrestrial water storage (TWS) above the surface of the aquifer. A coupled hydro-mechanical approach is necessary for understanding groundwater conditions and managing resources in this environment, particularly in relation to recharge (Shamsudduha et al., 2012), sustainability of groundwater abstraction for irrigation (Shamsudduha et al., 2011) and municipal water supply (Ravenscroft et al., 2013), and the security of schemes for mitigation against groundwater arsenic (Michael and Voss, 2008) and salinity (Rahman et al., 2011; Sultana et al., 2015).
Location map showing the extent of the Bengal Aquifer System (BAS) and the Ganges–Brahmaputra–Meghna (GBM) floodplains.
The generally coupled poro-mechanical nature of geologic-fluid systems is well-established (Neuzil, 2003); porewater pressures affect the stress state and vice versa. These interactions are accepted as important where groundwater conditions are related to faulting (Roeloffs, 1988; Rojstaczer and Agnew, 1989; Sutherland et al., 2017), earthquakes (Manga et al., 2012), pumping-induced aquitard responses (Verruijt, 1969), ground subsidence (Burbey et al., 2006; Erban et al., 2014), glacial loading effects (Bense and Person, 2008; Black and Barker, 2016), and surface water interactions (Acworth et al., 2015; Boutt, 2010). Use of ground surface vertical displacements to infer aquifer or groundwater conditions (Chaussard et al., 2014; Reeves et al., 2014) is also predicated on coupling of the hydraulic and mechanical behaviour of aquifer sediments. For simulation of transient groundwater flow in aquifers, however, a decoupling simplification is frequently applied such that the elastic equation does not need to be solved simultaneously. Thus, the flow equation is solved without consideration of internal stresses and strains or mechanical boundary conditions. Despite this, the poro-mechanical nature of confined aquifers is embedded in the concept of specific storage which incorporates the elastic compressibility of the aquifer materials (Domenico and Schwartz, 1998; Green and Wang, 1990; Narasimhan, 2006). Furthermore, it is associated with the well-known concept of barometric efficiency (Spane, 2002), which describes the response of groundwater pressure to variations in atmospheric pressure, perhaps the example of surface loading effects most familiar to hydrogeologists. The decoupling assumption is reasonable where the effects of mechanical loading can be considered insignificant, either when the changes in load are small or when the applied load is mostly borne by the solid rather than the fluid (Black and Barker, 2016). Neither of these conditions apply to the BAS sediments, which are highly compressible (Steckler et al., 2010) and subject to substantial and extensive TWS mechanical loads due to heavy rainfall, deep flooding, and large river discharges as a consequence of the annual monsoon (Shamsudduha et al., 2012).
In the event of laterally extensive changes to mechanical loads and/or
hydraulic heads above the surface of an aquifer, and laterally homogeneous
aquifer properties, by symmetry it may be deduced that lateral strains are
zero. This condition gives rise to a
The purpose of this paper is to explore the behaviour of the BAS as a poroelastic aquifer subject to a variety of extensive TWS mechanical and hydraulic loads. Poro-elastic theory is very well-established, but has not previously been applied in the context of a thick and extensive aquifer such as the BAS to show the implications for groundwater pressures together with solid strains and ground surface displacements.
The Bengal Basin has a tropical climate dominated by the Indian monsoon, with
annual rainfall increasing from 1500 mm in the south and west to 5500 mm in
north-eastern Bangladesh, of which 85 % falls during the summer rainy
season (May to November) when individual storm events can contribute over
100 mm d
We firstly set out the partially coupled 1-D poro-mechanical approach that we use to examine the implications of specific surface (upper boundary) loading scenarios, with aquifer parameters set to represent the BAS underlying the GBM floodplains (Fig. 1). We consider an equivalent homogeneous uniform medium, as well as a layered structure based on lithological sections. The results provide a diagnostic framework which we apply to analysis of loading styles at Khulna and Laksmipur in southern Bangladesh.
We concentrate on the coupling between water flow and the mechanical behaviour of the BAS sediment, assuming isothermal conditions and that the aquifer material behaves in a linear-elastic way. This is likely to be reasonable under repeated mechanical load–unload cycles, provided there is no secular decline in groundwater level sufficient to cause effective stress to exceed the previous loading maximum.
The 3-D flow and mechanical equations are given in the Appendix. In the event
of uniform (1-D) areal mechanical loading, and where lateral strains are
negligible, the system simplifies to a flow equation coupled to a mechanical
equation for 1-D loading:
The sediment is assumed to sit on a rigid base, with the top surface free to
move, so strain can only be vertical. Thus from Eq. (A1), the vertical stress
and strains are related by
The 1-D model showing
The simplified system considered here is given in Fig. 2. On the upper boundary, the changing TWS is simulated by means of a changing head and a changing mechanical load, according to the nature of the contributing hydrological components. Under this simplification, vertical displacement at the surface will arise in only two ways: by contraction or expansion of the pore space where there is a net change in the volume of water in the column, and by contraction or expansion of the porewater. Being limited to 1-D movement, these volume changes are entirely taken up by vertical displacement.
The reference frame is the base of the model which is assumed fixed in space and set at 1 km depth, acknowledging the variation in aquifer thickness between south-eastern Bangladesh, 3000 m (Michael and Voss, 2009a), and West Bengal, 300 m (Mukherjee et al., 2007). Within this domain, Eqs. (1) and (2) are solved analytically for a homogeneous uniform material in the absence of pumping, and numerically where layers of individually homogeneous materials are simulated, with and without pumping. Where pumping is simulated, the water is assumed to be taken uniformly from the pumping interval. For simplicity, earth tides are neglected.
Taking Eq. (1) and assuming homogeneous
We apply the following sinusoidal hydraulic and mechanical loading boundary
conditions to Eq. (9), where we introduce a parameter,
Displacement and change in groundwater storage can be calculated as the time
integral of velocity at the surface. Applying Darcy's law at the surface
(
We used the COMSOL Multiphysics® software (COMSOL Multiphysics®, 2018), validated against the analytical solutions for uniform permeability, to solve the stress and flow Eqs. (1) and (2). The finite-element model is unrestricted in terms of spatial distribution of parameter properties and in terms of the boundary condition functions.
Selected parameter values for the BAS underlying the GBM floodplains are given in Fig. 2. The bulk values for the uniform representations are close to the harmonic average of the series components. We next discuss the context in which these parameter selections are made.
Textbook
Relationship between 1-D specific storage (
Specific storage
Estimates of (1-D) loading efficiency based (Jacob, 1940) on barometric
efficiency are rather lower: a range of 0.69–0.87 has been determined at
Laksmipur in the GBM sediment (Burgess et al., 2017). This is potentially
indicative of a considerable stiffening due to burial (
Basin-scale modelling suggests a horizontal–vertical anisotropy for
hydraulic conductivity in the BAS of
Specific yield is the drainable porosity of the material in which the water
table moves. Michael and Voss (2009b) cite a range from 0.02 to 0.19 in
Bangladesh, noting that much of the basin has a specific yield in the range
of 0.02–0.05. We take
Changes to the shallow water budget which have the potential to be laterally extensive and uniform include water arriving as rainfall at the surface and either ponding or moving to the shallow water table as recharge; and water departing the surface or the water table by evaporation, or as runoff to the extensive network of drainage channels. Pumping for domestic and irrigation supply may potentially be considered areally uniform, where sufficiently common and over a wide area (Michael and Voss, 2008). The changing shallow water budget causes a change in mechanical loading to the aquifer system, and if in direct hydraulic continuity with the saturated water column it also causes a change in head. If the shallow water is not hydraulically connected to the saturated aquifer system, the effects of the changing water budget are transmitted to depth by mechanical compression/extension of the sediment, but not by hydraulic diffusion. Changes to the barometric pressure also apply a laterally extensive changing force to the surface of the aquifer and to the water column, and earth tides are also laterally extensive. The daily perturbation on water heads by atmospheric pressure changes is of the order of 0.01 m (Burgess et al., 2017), which is small compared to the annual hydrograph amplitude of the order of 1 m. Barometric pressure and earth tides are both neglected for simplicity here.
To explore the consequences of these hydraulic and mechanical loading sources, the groundwater dynamics associated with three upper surface boundary conditions are modelled here (Fig. 2). Firstly, the effect of a changing level of free water is examined, such as would be seen in paddy fields, ponds, or during floodwater inundation. This condition is here termed “IN”. The change in free-water level is equal to both the change in head and the change in mechanical load at the upper surface (load is here parameterized in metres of water rather than as a stress). Secondly, the effect of changes to unconfined storage due to a moving water table is examined. This condition is here termed “WT”. The change in load is the specific yield times the head. For very small specific yields this condition approaches the hydraulic-only (“HO”) loading case, whereby there is insignificant mechanical load despite the change in head. Thirdly, we examine the effect of a changing surface water store (which could be either free water held above an impermeable barrier, or a perched phreatic aquifer) which is hydraulically isolated from the main aquifer system. A mechanical load only is applied; therefore, no head change is applied to the aquifer, and this condition is termed “LD”.
These three TWS loading scenarios are applied in turn to a uniform and
layered representation of the BAS underlying the GBM floodplains. The loading
is applied as sinusoidal functions with unit amplitude and a time period of
1 year to simulate the annual hydrological cycle. Additionally, the effects
of groundwater abstraction are simulated. Abstraction is taken evenly from
the depth interval 50–100 m at an average rate of 0.2 m a
The modelled responses of groundwater head to sinusoidal hydraulic and mechanical source terms, together with changes in groundwater storage and ground surface vertical displacements, are illustrated for the GBM environment with uniform properties in Figs. 4 and 5. Figure 4 shows the modelled responses over 10 years at depths of 30, 100, and 300 m, approximating typical BWDB multi-level piezometers (BWDB, 2013). The depth variations of amplitude and phase for groundwater head and the phase lag for surface displacement are summarized in Fig. 5. The effect of layering (Supplement) is to cause departure from the uniform cases, so interpretation of data in a real, heterogeneous aquifer should take into account local deviation from idealized uniform conditions. However, in general, the loading style (“IN”, “WT”, “LD”) and pumping regime are of more significance for the head responses and surface displacements than the detail of the BAS stratigraphy.
1-D model simulations for the GBM environment, showing results for
the scenarios
Profiles with depth for
Under free-surface water inundation, head changes are characteristically
equal in amplitude at all depths and in phase with the inundation signal.
Away from the top boundary, the instantaneous head due to loading in this
case is
By contrast with the “IN” scenario, head changes determined by a moving
water table are depth-variable in amplitude and phase. When
Heads in the case of a surface load hydraulically isolated from the aquifer
show a third characteristic behaviour. In this case the amplitude of head
change increases from zero at the top boundary (Fig. 5a), reaching a peak
which is greater than the load, 1.07 at 162 m (or
Introduction of pumping from the depth interval 50–100 m causes hydraulic disequilibrium which continues well beyond the 10 years of simulation, as the head drawdown propagates deep into the profile. As well as drawing water from storage at depth, pumping induces recharge from the surface, there being a downward hydraulic gradient from the surface to the pumped horizon, and upwards from the deeper levels to the pumped horizon. Variable perturbation due to the “IN” surface load is nevertheless clearly evident in the deep groundwater head measurements following correction for secular decline (Fig. 4e). Elastic displacement, manifested as ground surface decline, exceeds 40 cm after 10 years of pumping but, as in the un-pumped “IN” scenario, the annual fluctuation due to surface loading is vanishingly small (0.03 mm). Thus, in addition to the possibility of irreversible plastic deformation, elastic strain may gradually increase due to continuous pumping as stored water is drawn from increasing depths.
Intermittent pumping strongly increases the seasonal variation in heads at the depth of pumping, and this disturbance diffuses to adjacent levels. However, as in the case of continuous pumping, the surface load signal is largely preserved in the deep groundwater head response at 300 m. Also, intermittent pumping induces the same average long-term secular decline in stored water volume and ground surface displacement as continuous pumping, but with additional annual fluctuation caused by the pump switching on and off (decline/drawdown during the dry period when the pumps are used for irrigation and recovery during the rainy season when the pumps are off).
Taking into account a small correction for the compressibility of water,
surface displacement in the model is almost equal to the total change in
elastic storage in the permanently saturated aquifer. For the cases where
pumping dominates the removal of water, surface displacement is in phase with
the pumping (Fig. 4f). For the cases which set up a diffusion of the
hydraulic signal between the surface boundary and the aquifer, the phase of
surface displacement depends on the hydraulic (non-loading) head changes at
all depths (Fig. 4b, c, d). Therefore the lag for vertical displacements
under the “LD” surface condition is
Applying the 1-D partial-coupling analysis to field data, we examine poro-mechanical perturbations at two sites, Khulna and Laksmipur in southern Bangladesh (Fig. 1). Hourly measurements of groundwater pressure made between April 2013 and June 2014 in three closely spaced piezometers between 60 and 275 m depth at each site are illustrated as hydrographs of equivalent freshwater head in the Supplement. Data on changes of the actual water table at the field sites are unfortunately not available.
Khulna: comparison of observed heads (solid lines) and simulated
heads (dashed lines), starting 27 April 2013, for the WT upper boundary
condition (
The objective here is to apply the principles and assumptions of the partially coupled hydro-mechanical approach to reproduce the characteristic features of the multi-level groundwater hydrographs using broadly representative aquifer parameters, rather than to attempt an exact match by inverse modelling. Inspection of the hydrographs at both sites indicates, by reference to Figs. 4 and 5, that mechanical loading significantly influences the measured heads. Additionally, the presence of thick clay aquitards at both sites (Figs. 6, 7) suggests conditions under which heads may be determined solely by mechanical loads and piezometers might behave as geological weighing lysimeters, a possibility which we put to the test.
Laksmipur: comparison of observed heads (solid lines) and simulated
heads (dashed lines) starting 31 May 2013, for the “WT” upper boundary
condition (
The approach at each site is as follows.
A two-component sand–clay stratigraphy is based on site data, and
parameter values are selected from the ranges described in Sect. 2. The piezometric readings are compared to examine possible pumping
influences which need to be taken into account in the model by means of a
simple abstraction pattern. Based on what is known about nearby abstractions
an appropriate pumping depth interval is determined. The magnitude of the
extraction rate is manually adjusted as a fitting parameter. Where a piezometer is uninfluenced by pumping, we test its behaviour as
a geological weighing lysimeter. The heads in the chosen piezometer are
assumed to define the mechanical load at the surface, and this assumption is
tested for self-consistency by comparison of the simulations to the data
from all three piezometers. The nature of the upper head boundary is then examined by reference to
the implications for a variety of hydraulic loading conditions. For a “WT”
boundary, changing
At Khulna (Burgess et al., 2014), piezometers KhPZ60, KhPZ164, and KhP271
(the numbers indicate depth to the piezometer screen in metres) are located
700 m from the
The three Khulna hydrographs are characterized by periodic variations
containing tidal frequency components throughout the rising and falling limb
of the annual cycle, and a series of episodic increments superimposed on the
rising limb during the monsoon season; the annual amplitude of groundwater
head variation is
At a daily level the time series of groundwater heads in KhPZ164 and KhPZ271
include an additional frequency component which simple analysis of head
differences confirms as the hydraulic influence of the daily municipal
pumping schedule from which KhPZ60 is protected by an intermediate clay
layer. Therefore KhPZ60 alone is taken as recording a solely mechanical
loading response and the KhPZ60 head record is applied as the upper boundary
condition to represent the varying TWS load at the surface in a 1-D
hydro-mechanical model of the Khulna site (Fig. 6), assuming
Figure 6 compares the measured groundwater heads with the heads simulated by
the model under the assumption of a “WT” boundary with
At Laksmipur (Burgess et al., 2017) the piezometers LkPZ91, LkPZ152, and
LkPZ244 are situated in a rural region of rice-paddy and tree plantations on
the Lower Meghna floodplain (Supplement), 10 km distant from the River
Meghna and 8 km from municipal boreholes which pump from 270 to 300 m
depth. Seasonal pumping from depths up to 100 m for rice irrigation is
common in the vicinity. The lithological sequence indicates fine sand with
occasional silty clay layers. The hydrographs are characterized by a sequence
of episodic increments in groundwater head associated with periods of heavy
rainfall producing a rising limb of amplitude
Here, cyclical head differences between LkPZ244 and the shallower two
piezometers indicate hydraulic influences of dry-season pumping on the LkPZ91
and LkPZ152 hydrographs, whereas downward propagation of the hydraulic
signals to LkPZ244 is prevented by the clay layer at 170 m depth. Therefore
LkPZ244 is taken as recording a solely mechanical loading response and the
LkPZ244 head record is applied as the upper boundary condition to represent
the varying TWS load at the surface in a 1-D hydro-mechanical model of the
Laksmipur site (Fig. 7), with a small offset applied to the initial heads
above 170 m depth, consistent with the observed head perturbations being
shown as starting from a common zero value. The stratigraphy as modelled
draws from the detail of the drillers' log at Laksmipur (Burgess et al.,
2017) and the general form of the stratigraphy as seen across the GBM
floodplains (Fig. 2). All styles of upper boundary were applied (“IN”,
“LD”, and “WT” with a range of
For LkPZ244 the simulated heads are an excellent match with measurements over
the entire period. The simulated heads for the shallower two piezometers
LkPZ91 and LkPZ152 most closely match the measurements under a “WT”
boundary with
For the shallower piezometers, the best fit value for
Models based on the 1-D partially coupled hydro-mechanical analysis confirm
that substantial poroelastic influences should be expected in the Bengal
Aquifer System, and that groundwater heads respond characteristically to
changes in specific terrestrial water stores (Figs. 4 and 5). Only laterally
extensive flooding above an aquifer fully saturated to the ground surface
(the “IN” loading style) will drive instantaneous and synchronous head
variations at all depths determined by the loading efficiency, inducing
negligible flow of groundwater. In any situation involving a variable water
table (the “WT” loading style) and for any variable loads hydraulically
disconnected from the aquifer (the “LD” style), hydraulic gradients are
imposed due to the unequal magnitude of stress and head at the surface. These
gradients take time to dissipate, depending on the frequency of the signal
fluctuation and the aquifer hydraulic diffusivity, and so lead to differences
in amplitude and phase of the head response with depth. In these situations,
the relative importance of the hydraulic and mechanical influence is
controlled by the aquifer hydraulic diffusivity, the loading efficiency, and
the depth of interest. In the case of a fluctuating water table, the
difference between the head and stress signals is a function of the specific
yield,
The characteristic responses of the aquifer might therefore provide a key to
identifying the terrestrial water store dominating
In terms of the extent to which piezometer water levels indicate recharge and drainage, it is only where there is a rapid hydraulic connection between the piezometer and the water table that the piezometer will be sensitive to head change at the water table and therefore to changes in unconfined storage. If a piezometer is hydraulically isolated from surface water and/or the water table and is beyond other transient hydraulic influences, it can respond to changes in the weight of the TWS load, acting as a geological weighing lysimeter (van der Kamp and Maathuis, 1991; Smith et al., 2017). In this case, where the changing load is due to a moving water table, knowledge of the loading efficiency allows the load measurement to be converted into an estimate of recharge and discharge.
In all other situations, a wide range of coupled hydro-mechanical responses can be expected, as we have shown for the BAS (Figs. 4 and 5). Seasonally variable groundwater heads (Fig. 4) are therefore open to misinterpretation as seasonally variable groundwater storage, leading to error in determination of recharge if the poroelastic nature of the response is neglected. Consider heads at 30 m, a common depth for Bangladesh Water Development Board (BWDB) monitoring boreholes (Shamsudduha et al., 2011). For the case of a variable load hydraulically disconnected from the aquifer (Fig. 4d), the annual water level rise is equal to half the amplitude of the load, yet augmentation of elastic storage, by definition in this case, is nil. For the case of variable TWS inundation (Fig. 4a) the annual groundwater level rise is equivalent to the annual depth of inundation, yet augmentation of elastic and unconfined storage is insignificant. Conversely, relative to a variable water table (Fig. 4b, c), groundwater fluctuation at 30 m depth is attenuated. Failure to account for this would lead to an underestimate of recharge to unconfined storage by about 30 %. The error increases as hydraulic diffusivity decreases; therefore, errors could be expected to be greater in the coastal regions of the Bengal Basin, where the thickness of silty clays is greater (Mukherjee et al., 2007). Considerable caution is therefore necessary in the use of even relatively shallow piezometers as indicators of recharge to the water table. A true indication of recharge requires either a shallow tubewell screened over the depth interval of actual water table fluctuation or a deep piezometer responding as a geological weighing lysimeter to the varying mass provided by a fluctuating water table. In the latter case it is recharge to the shallow water table that is measured, not recharge at the depth of the piezometer.
The 1-D hydro-mechanical framework can be applied as a test for the special
cases where groundwater head responds solely to mechanical load, and hence to
validate the use of geological weighing lysimetry. The laterally extensive
loading criterion inherent to the 1-D analysis must apply, and the piezometer
screen must be isolated or distant from hydraulic transients originating at
the surface or from pumping. We have shown for the BAS that these
requirements most likely occur at depths beyond about 250 m, as in the case
of “WT” and “LD” loading styles in the absence of pumping (Fig. 5). The
inundation (“IN”) style of TWS variation leads to instantaneous
transmission of head without loss of amplitude at all depths; in this case
piezometers at all depths provide a mechanical record of
The models also demonstrate the amplitude and phase of ground surface displacement as a hydro-mechanical consequence of varying terrestrial water stores, and the significance of pumping (Fig. 4e and f). Under simplifications associated with the 1-D model, vertical surface displacements relative to a fixed model base at 1 km depth are approximately equal to the change in elastic storage, the small difference being due to compressibility of water. These changes are minor in the BAS under all TWS loading styles, of the order of millimetres, compared to the displacements in the case of seasonal groundwater pumping, which are of the order of centimetres. Seasonal surface displacements of the order of centimetres have also been attributed to strain acting over a depth scale of hundreds of kilometres due to the load applied by monsoonal inundation over the entire Bengal Basin (Steckler et al., 2010). Strains due to seasonal groundwater pumping at shallow depths may therefore be of the same order of magnitude but out of phase with crustal stain, making ground surface deflections a poor proxy for changing elastic storage in the aquifer. As a corollary, interpretation of seasonal ground surface fluctuations across the GBM floodplains solely in terms of deep crustal deformation (Steckler et al., 2010) potentially requires reassessment in the light of BAS aquifer poroelasticity.
In our analysis we have based values for the 1-D loading efficiency,
Data on changes in the water table would have greatly helped the analysis of loading effects at Khulna and Laksmipur. It is strongly recommended that in future hydro-mechanical analyses of the groundwater dynamics of large layered aquifers such as the BAS, both water table data and deeper head data should be obtained. For the water table, this requires a shallow piezometer to be screened across the full range of fluctuation of the true water table.
Under certain circumstances the extensive load assumption inherent in the 1-D analysis may break down. Rivers, as linear sources of head and load, can be accommodated within the 1-D framework where their contribution to the TWS load is minor as demonstrated at Khulna. In general, however, rivers should be expected to impose laterally variable heads and require a more generalized 2-D or 3-D fully coupled poro-mechanical treatment (Boutt, 2010; Pacheco and Fallico, 2015). An equivalent constraint applies to strains, an additional reason for surface displacement not to offer a secure proxy for groundwater storage in the BAS. The dense distribution of rivers, distributaries, and drainage channels in the Bengal Basin makes the BAS widely vulnerable to loading effects that may not adequately be reduced to a 1-D description; 13 % and 47 % of 1035 piezometers in the BWDB groundwater monitoring network lie within 1 and 5 km respectively of a river.
We argue that a 1-D
Groundwater levels, groundwater recharge, vertical groundwater
flow, and ground surface elevations
are all influenced by the poroelastic behaviour of the BAS. Our results
expose the error of the conventional assumption of decoupled hydraulic
behaviour which underlies previous assessments of recharge to the BAS. Also,
they demonstrate the complexities in applying ground surface displacements as
a proxy measure for variations in groundwater storage. We propose that the
1-D
The datasets analysed during the current study are available from the corresponding author on request.
The constitutive isotropic relation between elastic stress and strain,
coupled to the pore pressure by Terzaghi's effective stress law, is given by
(Neuzil, 2003)
Just as the elastic equations have a pore pressure term, the isothermal,
Darcian groundwater flow equation contains a coupled stress term
(Neuzil, 2003):
The 3-D specific storage is defined as
The (3-D) loading efficiency, or Skempton's coefficient,
The supplement related to this article is available online at:
WGB conceived the study; NDW led the modelling; all the authors contributed to the scenario descriptions and consideration of the modelling results; NDW and WGB drafted the manuscript; all the authors reviewed the manuscript.
The authors declare that they have no conflict of interest.
We acknowledge funding from the UK EPSRC Global Challenges Research Fund
(UCL/BEAMS EPSRC GCRF award 172313, EP/P510890/1) to William G. Burgess for
research on
This paper was edited by Monica Riva and reviewed by two anonymous referees.