05 — Critical Head & Preconsolidation Stress

Definition

The preconsolidation stress σ′_pc is the greatest effective stress the sediment skeleton has ever experienced. Because effective stress is set by head (page 02), there is an equivalent water level — the critical head h_c — at which σ′ = σ′_pc:

\[ h_c = \text{the head at which } \sigma' = \sigma'_{pc} \] \(\sigma'_{pc}\) corresponds to the lowest head ever reached (the historic low)

The behavioral switch is a simple comparison:

\[ \begin{cases} h \ge h_c & \Rightarrow\ \text{use } S_{ske}\ \text{(elastic, recoverable)} \\[4pt] h < h_c & \Rightarrow\ \text{use } S_{skv}\ \text{(inelastic, permanent)} \end{cases} \]

The ratchet

Critical head is not fixed. Whenever heads reach a new low, that becomes the new historic maximum stress — so h_c moves down to the new low and stays there.

Seasonal lows that don't beat the record → elastic, no net loss.
A new record low → a slice of permanent compaction, and a lower h_c going forward.

This is why drought years matter so much: each new low both causes permanent compaction and resets the threshold lower for next time.

Interactive: hydrograph, critical head, and the compaction it produces

Inputs

Pumping scenario

Preconsolidation margin 15 ft

Inelastic ratio S_skv/S_ske 40×

Total subsidence at end	— ft
Permanent (inelastic) portion	— ft
Recoverable (elastic) portion	— ft
Final critical head (vs. start)	— ft

The margin is how far heads can fall before crossing the initial critical head. Set it to 0 and every decline is permanent.

Figure 1. Top: a head hydrograph (blue) and the critical head h_c (orange dashed). h_c tracks the running historic low — note how it steps down and never rises. Red bands mark intervals when heads are below h_c. Bottom: cumulative compaction. During elastic intervals it wiggles reversibly around a flat line; whenever the hydrograph sets a new low, the curve drops a permanent step (red). Try the "Sustainable" scenario with a generous margin to see compaction stay nearly flat.

What managers should take from this

Safe operating space

Keep heads above h_c

The sustainable target is to hold seasonal lows above the critical head. Within that envelope, the basin can be pumped hard seasonally and still rebound with negligible permanent subsidence.

The danger of new lows

Records are expensive

A single new record low — often during drought — converts elastic storage into permanent compaction and lowers h_c. The damage is locked in even if the next year is wet.

Setting thresholds

h_c as a minimum threshold

Critical head gives SGMA a physically defensible basis for a groundwater-level minimum threshold tied directly to the subsidence indicator: protect the surface by protecting the head. DWR's Land Subsidence BMP (2026) builds its threshold guidance on exactly this logic.

How critical head is identified in practice

σ′_pc (and thus h_c) is estimated from: (1) the break in slope on a field stress–strain plot of compaction vs. effective stress (Riley's method, page 07); (2) the historic minimum water level in long records; and (3) lab consolidation tests on core (Casagrande construction on the e–log σ′ curve).

Where the modern historic low already exceeds anything before it, the aquifer is being loaded in the virgin range continuously, and h_c simply tracks the ongoing decline.

A subtlety: depth-dependent h_c

Different interbeds can have different preconsolidation stresses depending on their loading history (e.g., past erosion, desiccation, or earlier pumping). Critical head is therefore a property of a specific interval, not a single number for the whole column. Multiple-depth piezometer–extensometer installations (page 08) resolve this.

Helm's stress-dependent models (1976) and the Holly-site analysis (Sneed & Galloway 2000) formalize how σ′_pc varies and evolves.

Key references

Riley, F.S. (1969). Analysis of borehole extensometer data from central California. In Land Subsidence, IAHS Publication 89, Vol. 2, p. 423–431. (Field identification of preconsolidation stress.)
Helm, D.C. (1975, 1976). One-dimensional simulation of aquifer system compaction near Pixley, California (Parts 1 & 2). Water Resources Research 11(3): 465–478; 12(3): 375–391.
Sneed, M. & Galloway, D.L. (2000). Aquifer-system compaction and land subsidence: measurements, analyses, and simulations — the Holly site, Edwards Air Force Base, Antelope Valley, California. USGS Water-Resources Investigations Report 00-4015.
Sneed, M. (2001). Hydraulic and mechanical properties affecting ground-water flow and aquifer-system compaction, San Joaquin Valley, California. USGS Open-File Report 01-35.
Galloway, D.L. & Burbey, T.J. (2011). Review: Regional land subsidence accompanying groundwater extraction. Hydrogeology Journal 19(8): 1459–1486.
California Department of Water Resources (2026). Land Subsidence — Best Management Practice for the Sustainable Management of Groundwater. SGMA BMP series (lead author J.H. Ellis). (Basis for groundwater-level minimum thresholds tied to the subsidence indicator.)

Critical Head & Preconsolidation Stress