Groundwater hydraulics

In short

Groundwater hydraulics is the study of how water stored in soil and rock moves under a hydraulic gradient, and how much of it a well can safely yield. It rests on Darcy's law and on a small family of well equations (Thiem, Dupuit, Theis, Cooper–Jacob) that convert pumping-test drawdowns into aquifer constants. It matters because about 60–65% of India's irrigation and most of its rural drinking water come from groundwater, and a large number of assessment units are already semi-critical to over-exploited. The topic is examined in GATE Civil (Water Resources / Environmental), in state PSC and ESE papers, and is interviewed at CGWB, state ground water departments, irrigation and minor-irrigation departments, WAPCOS, NABARD-funded well projects, and consultancies doing dewatering, tube-well design and EIA hydrogeology.

Explained

Occurrence of groundwater and types of aquifers

• Aquifer: a saturated formation that both stores and transmits water in usable quantity (sand, gravel, weathered/fractured rock).
• Aquifuge – neither stores nor transmits (massive unfractured granite); aquiclude – stores but does not transmit (clay); aquitard – transmits slowly, leaks to adjacent aquifers (sandy clay).
• Unconfined (water-table / phreatic) aquifer: upper surface is the water table at atmospheric pressure; pumping dewaters pores, so the saturated thickness itself falls.
• Confined (artesian) aquifer: sandwiched between impervious layers; water is under pressure, rises in a well to the piezometric surface. If that surface is above ground level, the well flows freely (flowing artesian well).
• Leaky (semi-confined) aquifer: bounded by an aquitard that leaks when head drops — common in the Indo-Gangetic alluvium.
• Perched aquifer: small saturated body held above the main water table by a local impervious lens.
• Zones: zone of aeration (soil water, intermediate/vadose, capillary fringe) above the water table; zone of saturation below.
• Indian settings: thick alluvial multi-aquifer systems (Punjab, Haryana, UP, Bihar, Bengal); hard-rock weathered-and-fractured aquifers with low storage (Deccan basalt, Peninsular granite/gneiss); coastal sands prone to salinity.

Aquifer properties

• Porosity n = volume of voids / total volume. Effective porosity = interconnected voids only.
• Specific yield Sy = drainable water per unit volume (gravity drainage); specific retention Sr = water held by capillarity and adsorption; n = Sy + Sr. Sand Sy ≈ 0.20–0.30; clay has high n (0.45) but Sy ≈ 0.02–0.05.
• Coefficient of permeability (hydraulic conductivity) K – Darcy velocity per unit gradient, units m/day or m/s; depends on the medium (grain size, shape, packing) *and* on the fluid (viscosity, density).
• Intrinsic permeability k₀ = K μ /(ρg), units m² or darcy — a property of the medium alone.
• Transmissivity T = K b (m²/day), b = saturated thickness. For an unconfined aquifer b changes with pumping, so T is not constant.
• Storage coefficient (storativity) S = volume released per unit plan area per unit head drop (dimensionless). Confined: 10⁻⁵–10⁻³ (compression of the matrix and expansion of water). Unconfined: S ≈ Sy ≈ 0.05–0.30, i.e. 100–1,000 times larger.
• Specific storage Ss = S/b; diffusivity = T/S governs how fast a cone of depression spreads.
• Measurement of K: laboratory constant-head (coarse soils) and falling-head (fine soils) permeameters; field pumping tests (most reliable, gives bulk K and S), tracer tests, and empirical Hazen's formula K (cm/s) ≈ C d₁₀² for clean sands.

Darcy's law, its validity and layered ground

• Darcy (1856): Q = K i A, with i = dh/dL. The Darcy (discharge) velocity v = Q/A is a flux over the gross area; the actual seepage velocity vs = v/n is larger.
• Valid only for laminar flow, Re = ρvd/μ ≲ 1 (d = representative grain size, usually d₁₀). It breaks down in coarse gravel, in karst and in the turbulent zone immediately around a pumped well, and at very low gradients in clay.
• Anisotropy: Kh > Kv in nearly all sedimentary deposits because of bedding; ratio 2–10 typical, up to 100 in varved clay.
• Layered aquifer: flow parallel to layers → thickness-weighted arithmetic mean; flow across layers → harmonic mean, so the least permeable layer controls vertical flow.
• Two-dimensional problems (seepage to drains, flow under a dam, flow nets of equipotentials and stream lines) use the Laplace equation ∂²h/∂x² + ∂²h/∂z² = 0, obtained by combining Darcy's law with continuity.

Steady radial flow to a well (equilibrium / Thiem theory)

Assumptions (the "Dupuit–Thiem" assumptions): homogeneous, isotropic aquifer of infinite areal extent; fully penetrating well; steady state reached; laminar radial flow; horizontal flow with the gradient equal to the slope of the free surface (small slope); constant discharge.

1. Confined aquifer: area of flow at radius r is 2πrb; integrate Q = 2πrb K (dh/dr) between two observation wells → Thiem equation. Drawdown varies with log r, so a semi-log plot of s against r is a straight line.
2. Unconfined aquifer: area is 2πrh (h measured from the impervious base) → Q = πK(h₂² − h₁²)/ln(r₂/r₁). The free surface actually curves above the Dupuit parabola near the well (seepage face), so computed drawdown near the well is in error, but Q is nearly right.
3. Radius of influence R: distance at which drawdown becomes negligible; it grows with time and is estimated empirically (Sichardt, Kusakin) or by extrapolating the semi-log drawdown line. Typically 100–300 m in fine sand, 300–3,000 m in gravel.
4. Specific capacity = Q/sw (m³/day per m) — the practical yardstick of a well; it falls as the well ages and screens clog.
5. Well losses: total drawdown in the well sw = BQ (aquifer/formation loss, laminar) + CQ² (well loss through screen, gravel pack and turbulent entry). Well efficiency = BQ/(BQ + CQ²), found from a step-drawdown test; good wells exceed 70%.
6. Partial penetration concentrates flow and increases drawdown for the same Q; corrections (Kozeny) or a reduced effective screen length are applied.
7. Interference: drawdowns of nearby wells superpose (linear for confined aquifers), so the yield per well in a well field is less than for an isolated well — hence minimum spacing norms (commonly 150–300 m for alluvial irrigation tube wells; follow state/CGWB norms).
8. Boundaries by image wells: an impermeable boundary is simulated by an identical pumping image (drawdown doubles at the boundary); a recharge boundary (river, lake) by a recharging image well (drawdown is cancelled).

Unsteady (non-equilibrium) flow and pumping tests

• Theis (1935) solved transient radial flow to a well in a confined aquifer: s = (Q/4πT) W(u), u = r²S/4Tt, where W(u) is the well function (exponential integral). Analysis is by curve matching of field s–t data on the Theis type curve.
• Cooper–Jacob approximation: for u < 0.01 (large t, small r) W(u) ≈ −0.5772 − ln u, giving a straight line of s against log t. Then T = 2.303Q/(4πΔs) per log cycle and S = 2.25Tt₀/r², t₀ being the intercept where s = 0.
• Chow's method: uses one point and the slope of the semi-log plot — avoids curve fitting.
• Recovery (residual drawdown) test: after the pump stops, s′ = (2.303Q/4πT) log₁₀(t/t′); a plot of s′ against log(t/t′) gives T, and it is free of pump-discharge fluctuations. It does not give S reliably.
• Leaky aquifers: Hantush–Jacob solution adds a leakage factor; drawdown stabilises earlier than Theis predicts. Unconfined aquifers show delayed yield (Boulton/Neuman) — an S-shaped three-segment curve.
• Test procedure: measure static water level; pump at constant Q (measured by V-notch, orifice plate or flow meter) for 24–72 h; read drawdown in at least one, preferably two, observation wells at a geometric time sequence (0.5, 1, 2, 3, 5, 10, 20, 40 min …); then monitor recovery for a similar period. Report T, S, K, b, specific capacity and well efficiency.

Wells in Indian practice, management and codes

• Open (dug) wells: 2–10 m diameter, shallow, large storage, low inflow — suited to low-permeability weathered rock; yield assessed by the recuperation (constant-level or variable-head) test.
• Tube wells: shallow (strainer/cavity type, 30–70 m) and deep (60–300 m) in alluvium; bore wells with submersible pumps in hard rock. Components: housing pipe, blind pipe, well screen/strainer (slot size from the sieve analysis of the aquifer sand, usually retaining 40–50% of the formation), gravel pack/shrouding (pack-to-aquifer D₅₀ ratio commonly 4–6), bottom plug, cement sanitary seal at the top.
• Well development (surging, jetting, over-pumping, air development, sometimes acidisation) removes fines, increases specific capacity and must be done before the yield test.
• Drilling methods: hand boring, direct and reverse rotary (alluvium), down-the-hole hammer (hard rock), percussion/cable tool.
• Safe yield of an aquifer = withdrawal that can continue without undesirable effect (declining levels, salinity, subsidence). Over-draft symptoms: falling water tables, dried springs, land subsidence, arsenic/fluoride mobilisation, and sea-water intrusion in coastal aquifers, governed by the Ghyben–Herzberg relation.
• Indian framework (verify the current version, these are revised periodically): groundwater is a State subject. CGWB carries out exploration and the Dynamic Ground Water Resource Assessment (annual since 2022, periodic before that) using the GEC-2015 methodology; assessment units are categorised by stage of extraction — Safe ≤70%, Semi-critical >70–90%, Critical >90–100%, Over-exploited >100%. The Central Ground Water Authority, constituted under the Environment (Protection) Act, 1986, regulates abstraction and issues NOCs under guidelines notified in 2020 (amended since). The Model Bill for Conservation, Protection and Regulation of Groundwater, 2017 offers states a legal template; Atal Bhujal Yojana funds community-led management in seven states.
• Standards: IS 2800 (construction and testing of tube wells), CGWB manuals on exploratory drilling and aquifer testing, IS 11624 (irrigation water quality), IS 10500:2012 (drinking water) for the quality of the pumped water.

Key points

• Aquifer - formation that both stores and yields water usefully; aquiclude stores but will not yield.
• Confined vs unconfined - pressure release versus actual dewatering; S differs by 2–3 orders of magnitude.
• Darcy's law - Q = KiA, valid for laminar flow, Re < 1; fails near the well face and in karst.
• Darcy velocity vs seepage velocity - vs = v/n; seepage velocity is always larger and is the one that moves a pollutant.
• Transmissivity T = Kb - the aquifer's ability to transmit through its full thickness, m²/day.
• Storativity S - 10⁻⁵–10⁻³ confined, 0.05–0.30 (≈ Sy) unconfined.
• Specific yield + specific retention = porosity - clay has high porosity but almost no specific yield.
• Thiem (confined) - drawdown is linear with log r; two observation wells give T without knowing R.
• Dupuit (unconfined) - Q depends on the difference of squares of depths; free surface lies above the Dupuit parabola.
• Theis - unsteady drawdown via W(u) and u = r²S/4Tt; matched by type curves.
• Cooper–Jacob - semi-log straight line valid for u < 0.01; T from slope per log cycle, S from the zero-drawdown intercept.
• Recovery test - uses residual drawdown versus log(t/t′); independent of discharge fluctuation.
• Specific capacity Q/sw - well performance index; declines with clogging and ageing.
• Well loss CQ² - turbulent entry loss; step-drawdown test separates B and C and gives well efficiency.
• Interference and image wells - superposition handles well fields, impermeable boundaries and recharge boundaries.
• Recuperation test - standard Indian method for open wells; yields the specific yield constant C = K/A.
• Ghyben–Herzberg - 1 m of freshwater head above sea level supports about 40 m of freshwater below it.
• Stage of extraction - extraction ÷ annual extractable resource; >100% means over-exploited (CGWB/GEC-2015).

Formulas and examples

Example 1 – Darcy's law, transmissivity and seepage velocity. A confined sand aquifer is 25 m thick, K = 30 m/day, porosity 0.25, and the piezometric surface falls 1 m in 200 m.

• i = 1/200 = 0.005; T = 30 × 25 = 750 m²/day.
• Darcy velocity v = K i = 30 × 0.005 = 0.15 m/day; seepage velocity = 0.15/0.25 = 0.6 m/day.
• Flow through a 1 km wide strip: Q = T i W = 750 × 0.005 × 1000 = 3,750 m³/day (43.4 L/s).
• A tracer would travel 0.6 m/day → about 219 m in a year, not 55 m as the Darcy velocity suggests.

Example 2 – Thiem test on a confined aquifer (T, K, specific capacity). A fully penetrating well in a 20 m thick confined aquifer is pumped at a steady 1,800 m³/day. Drawdown is 3.0 m at r = 10 m and 1.2 m at r = 100 m.

• T = Q ln(r₂/r₁)/[2π(s₁ − s₂)] = 1800 × 2.3026 /(2π × 1.8) = 4144.7/11.310 = 366 m²/day.
• K = T/b = 366/20 = 18.3 m/day (medium-to-coarse sand).
• Extrapolating the semi-log line: s = 0 when log r increases by 1.2/(1.8/1) log-cycle beyond r = 100 m → R ≈ 100 × 10^1.2/1.8 ≈ 464 m.
• If the well (rw = 0.15 m) shows sw = 6.5 m, specific capacity = 1800/6.5 = 277 m³/day per m.

Example 3 – Dupuit equation for an unconfined aquifer. Unconfined aquifer, K = 25 m/day, initial saturated depth H = 30 m above the impervious base. A 30 cm diameter well is pumped until the water depth in it is 24 m, with R = 300 m.

• Q = πK(H² − hw²)/ln(R/rw) = π × 25 × (900 − 576)/ln(300/0.15).
• Numerator = 78.54 × 324 = 25,447; ln(2000) = 7.601.
• Q = 25,447/7.601 = 3,348 m³/day = 38.8 L/s.
• Note the drawdown in the well (6 m) is 20% of the original thickness; beyond about 30% the Dupuit result becomes unreliable.

Example 4 – Cooper–Jacob prediction of drawdown. Confined aquifer, T = 500 m²/day, S = 2 × 10⁻⁴. A well pumps 1,500 m³/day. Find the drawdown at r = 50 m after 1 day.

• u = r²S/(4Tt) = (2500 × 2×10⁻⁴)/(4 × 500 × 1) = 0.5/2000 = 2.5 × 10⁻⁴ < 0.01 → Jacob is valid.
• 2.303Q/(4πT) = 3454.5/6283.2 = 0.550 m per log cycle.
• 2.25Tt/(r²S) = (2.25 × 500 × 1)/0.5 = 2250; log₁₀ 2250 = 3.352.
• s = 0.550 × 3.352 = 1.84 m (the full Theis solution with W(u) = 7.717 gives 1.84 m — identical, as expected).
• Drawdown after 10 days would be 1.84 + 0.550 = 2.39 m: each tenfold increase in time adds just one slope value.

Example 5 – Open well recuperation test (Indian practice). A 2 m diameter open well is depressed 2.5 m below the static level by pumping; in 90 minutes the level recuperates by 1.8 m.

• A = π/4 × 2² = 3.142 m²; h₁ = 2.5 m, h₂ = 2.5 − 1.8 = 0.7 m; t = 1.5 h.
• C = (2.303/1.5) log₁₀(2.5/0.7) = (1/1.5) × ln(3.5714) = 1.2730/1.5 = 0.849 per hour.
• Safe yield for a working depression head H = 1.0 m: Q = C A H = 0.849 × 3.142 × 1.0 = 2.67 m³/h ≈ 64 m³/day.
• Over a 10-hour pumping day the well delivers about 26.7 m³ — enough for roughly 0.5 ha of a light irrigation turn, not for a tube-well-scale command.

Where it is used

• Irrigation and minor irrigation departments, CGWB and state ground water boards: aquifer mapping (NAQUIM), resource estimation, tube-well siting and spacing, NOC assessments for industrial abstraction.
• Urban water supply: well-field design and yield certification for towns on alluvium (for example the Ranney/radial collector wells along the Yamuna, Ganga and Krishna), plus monitoring of declining levels in Bengaluru, Chennai and NCR.
• Geotechnical and construction dewatering: well points and deep wells for metro stations, basements and dry docks; the same equations predict the pumping rate and the settlement risk for neighbouring structures (DMRC, L&T, Afcons projects).
• Groundwater quality and contaminant transport: seepage velocity and flow direction for landfill siting, fly-ash pond leachate, arsenic in Bengal/Bihar, fluoride in Rajasthan and Telangana, and the hydrogeology chapter of an EIA report.
• Artificial recharge and managed aquifer recharge: percolation tanks, check dams, recharge shafts and injection wells, where infiltration rate and aquifer storage decide the structure's size.
• Job roles: hydrogeologist, junior/assistant engineer (ground water), drilling supervisor, water resources consultant, pump and submersible manufacturers' application engineers, NABARD/World Bank project appraisal.

Interview questions

• Q: What is the difference between transmissivity and permeability? A: Permeability K is the discharge per unit area per unit hydraulic gradient (m/day); transmissivity T = Kb is the discharge through the entire saturated thickness per unit width per unit gradient (m²/day).
• Q: Why is the storage coefficient of a confined aquifer so small? A: No pores are dewatered — water comes only from the elastic compression of the aquifer skeleton and expansion of the water, which releases a very small volume per unit head drop.
• Q: When does Darcy's law cease to be valid? A: When flow is no longer laminar, roughly Re > 1 — in coarse gravels, karst channels and in the turbulent zone next to a pumped well screen.
• Q: A clay has 45% porosity but a poor well yield. Why? A: Almost all of its water is held by capillary and surface forces (high specific retention, specific yield of 2–5%) and the pores are too fine to transmit water, so it is an aquiclude.
• Q: What are the Dupuit assumptions and where do they fail? A: Horizontal flow with the gradient equal to the water-table slope, small slope, fully penetrating well, steady state; they fail close to the well where the free surface is steep and a seepage face forms, so the Dupuit parabola lies below the true free surface and the drawdown it predicts there is too large, though Q is nearly right.
• Q: How do you get T and S from a pumping test by the Cooper–Jacob method? A: Plot drawdown against log time for one observation well; T = 2.303Q/4πΔs using the drawdown change per log cycle, and S = 2.25Tt₀/r² from the time intercept at zero drawdown — valid only for u < 0.01.
• Q: Why is a recovery test often preferred? A: The pump is off, so there is no discharge fluctuation; residual drawdown versus log(t/t′) gives a clean straight line and a reliable T.
• Q: What is well loss and how do you measure it? A: The extra drawdown inside the well from turbulent entry through screen and gravel pack, CQ²; it is separated from the aquifer loss BQ by a step-drawdown test, and gives the well efficiency.
• Q: How is an impermeable boundary handled in well hydraulics? A: By superposing an imaginary pumping well of equal discharge at the mirror position, which makes the drawdown pattern symmetric and the flow across the boundary zero.
• Q: Two tube wells are 50 m apart in the same aquifer. What happens to their yields? A: Their cones of depression overlap, drawdowns add, so each well yields less for the same drawdown — hence minimum spacing norms in notified areas.
• Q: What does the Ghyben–Herzberg relation tell a coastal designer? A: Each metre of freshwater head above mean sea level supports about 40 m of fresh water below it, so a small drawdown causes a large upward movement of the interface — pump shallow, at low rates, well back from the shore.
• Q: When is an assessment unit "over-exploited" in India? A: When the stage of ground water extraction, as assessed by CGWB using the GEC-2015 methodology, exceeds 100% of the annual extractable resource; the thresholds for safe, semi-critical and critical are 70% and 90%.

Common mistakes

• Using the Darcy velocity as the actual travel speed of water or of a pollutant instead of dividing by porosity.
• Applying the confined (linear-drawdown) Thiem equation to an unconfined aquifer, where the discharge depends on h₂² − h₁².
• Measuring h from the water table instead of from the impervious base in the Dupuit equation.
• Forgetting to check u < 0.01 before using Cooper–Jacob, or taking Δs over a part of the curve rather than a full log cycle.
• Mixing units — K in m/s with Q in m³/day, or r in cm with T in m²/day; and forgetting the factor 2.303 between ln and log₁₀.
• In the open well recuperation test, using the total depth of water instead of the depression head below the static level, or forgetting that the yield formula needs the working depression head, not the test depression.
• Treating specific yield, specific capacity and specific storage as the same thing, and quoting the yield of a well that has not been properly developed as the aquifer's capability.

Related topics

Hydrology · Irrigation engineering · Water supply engineering · Rainwater harvesting and water conservation · Fluid properties and statics · Seepage and permeability in soil mechanics