Riley's stress–strain method
Plot measured compaction (from a borehole extensometer) against effective stress (from a co-located water-level record, converted via page 02). The slope of that plot is the skeletal storage coefficient:
\[ \begin{aligned} S_{ske} &= \frac{\Delta(\text{compaction})}{\Delta\sigma'} \quad\text{(recompression loops)} \\[4pt] S_{skv} &= \frac{\Delta(\text{compaction})}{\Delta\sigma'} \quad\text{(virgin trend)} \end{aligned} \]
read the shallow loop slopes for elastic; the steep envelope for inelastic
- Seasonal head cycles trace narrow elastic loops → slope gives Sske.
- The overall down-and-to-the-right virgin trend → slope gives Sskv.
- The break between the two marks σ′pc (and thus hc).
Three lines of evidence
Field (Riley plot): in-situ, full-thickness, real stress path — the gold standard where extensometers exist.
Lab consolidation: oedometer tests on core give Cc, Cr, cv, and σ′pc by Casagrande construction — independent, but sample-scale and disturbance-prone.
Compaction/head ratio: a quick first diagnostic of effective storage from the bulk record.
Interactive: read parameters off a stress–strain plot
"True" parameters of the synthetic record
| Recovered Sske (loop slope) | — ft⁻¹·b |
| Recovered Sskv (virgin slope) | — ft⁻¹·b |
| Recovered σ′pc (slope break) | — psi |
| \(S_{skv} / S_{ske}\) | — |
Slopes are shown as compaction per unit stress for the lumped interbed (storativity-like). The point: the same plot a hydrogeologist makes from real data yields all three parameters at once.
Figure 1. A synthetic stress–strain (Riley) plot. Time runs along the path: seasonal cycles before σ′pc trace tight, reversible elastic loops (shallow slope). Once effective stress passes σ′pc (gray line), the path steepens onto the virgin compression trend, and seasonal unload–reload now traces narrow elastic loops riding down the steep envelope. The change in slope locates σ′pc; the two slopes give Sske and Sskv. After Riley (1969).
Doing it with real records
Convert heads to stress
Use the deepest relevant head record. Each foot of head decline adds γw ≈ 0.433 psi of effective stress to the interval below (page 02). Multiple piezometers resolve stress at different depths.
Account for the time lag
Thick interbeds compact with delay (page 06), so instantaneous compaction lags instantaneous stress. The Riley plot loops "fatten" with lag; matching that fattening also yields cv. Helm's model fits stress, strain, and lag jointly.
Check against the lab
Convert field Sskv to a virgin compressibility and compare with oedometer Cc on core from the same interval. Agreement builds confidence; large mismatch flags sample disturbance or scale effects.
Common pitfalls
- Wrong head for the stress. Compaction of a deep interbed responds to the deep aquifer head, not the water-table well next door.
- Ignoring residual compaction. Attributing delayed compaction to current stress overestimates Sskv.
- Too short a record. Without a virgin-range excursion, you can't see σ′pc or Sskv at all.
- Multiple interbeds. An extensometer integrates all beds in its depth range; deconvolving them needs nested instruments.
Why this page underpins the rest
Every projection on page 09 — and every regulatory threshold built on critical head — is only as good as these parameters. The Riley plot is the bridge from monitoring data (page 08) to predictive models. Poland's San Joaquin program and Riley's central-California analyses established the method that USGS still uses today (Ireland, Poland & Riley 1984; Sneed 2001).
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. (The stress–strain method.)
- Riley, F.S. (1998). Mechanics of aquifer systems — the scientific legacy of Joseph F. Poland. In Borchers, J. (ed.), Land Subsidence Case Studies and Current Research, Assoc. Eng. Geologists Spec. Pub. 8, p. 13–27.
- Helm, D.C. (1976). One-dimensional simulation of aquifer system compaction near Pixley, California: 2. Stress-dependent parameters. Water Resources Research 12(3): 375–391.
- Ireland, R.L., Poland, J.F. & Riley, F.S. (1984). Land subsidence in the San Joaquin Valley, California, as of 1980. USGS Professional Paper 437-I.
- 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.
- Terzaghi, K., Peck, R.B. & Mesri, G. (1996). Soil Mechanics in Engineering Practice (3rd ed.). Wiley (Casagrande construction; oedometer testing).