Pore pressure embrittlement in a volcanic edifice

Abstract

The failure mode of porous rock in compression—dilatant or compactant—is largely governed by the overlying lithostatic pressure and the pressure of pore fluids within the rock (Wong, Solid Earth 102:3009–3025, 1997), both of which are subject to change in space and time within a volcanic edifice. While lithostatic pressure will tend to increase monotonously with depth due to the progressive accumulation of erupted products, pore pressures are prone to fluctuations (during periods of volcanic unrest, for example). An increase in pore fluid pressure can result in rock fracture, even at depths where the lithostatic pressure would otherwise preclude such dilatant behaviour—a process termed pore fluid-induced embrittlement. We explore this phenomenon through a series of targeted triaxial experiments on typical edifice-forming andesites (from Volcán de Colima, Mexico). We first show that increasing pore pressure over a range of timescales (on the order of 1 min to 1 day) can culminate in brittle failure of otherwise intact rock. Irrespective of the pore pressure increase rate, we record comparable accelerations in acoustic emission and strain prior to macroscopic failure. We further show that oscillating pore fluid pressures can cause iterative and cumulative damage, ultimately resulting in brittle failure under relatively low effective mean stress conditions. We find that macroscopic failure occurs once a critical threshold of damage is surpassed, suggesting that only small increases in pore pressure may be necessary to trigger failure in previously damaged rocks. Finally, we observe that inelastic compaction of volcanic rock (as we may expect in much of the deep edifice) can be overprinted by shear fractures due to this mechanism of embrittlement. Pore fluid-induced embrittlement of edifice rock during volcanic unrest is anticipated to be highest closer to the conduit and, as a result, may assist in the development of a fractured halo zone surrounding the conduit, potentially explaining commonly observed near-conduit outgassing at many active volcanoes. Further, rock embrittlement at depth may create transient outgassing pathways by linking fracture networks near the edifice to larger-scale regional fault systems. Our experimental results affirm that pore pressure fluctuations associated with volcanic unrest may play a crucial role in dictating the evolution of a volcanic system.

Appendices

Appendix A: Effective pressure law for andesite

Any loading of a saturated porous medium is defined by the stress components σ _ij and the pore fluid pressure P _p . Moreover, if the poromechanical response of said medium to an applied stress coincides with that of the stress difference σ _ij  − αP _p δ _ij , then the latter quantity is referred to as the effective stress σ _ij . In particular, if the coefficient α is unity, then the quantity σ _ij  − P _p δ _ij corresponds to Terzaghi’s formulation, often called “Terzaghi’s effective stress” or “Terzaghi’s principle” (Terzaghi 1923; Baud et al. 2015). For elastic deformation, the effective stress law can be derived from the linear theory of poroelasticity (Berryman 1992; Wang 2000) with the effective stress coefficient given by the Biot-Willis coefficient α, whereby 0 ≤ α ≤ 1 (Biot 1941; Paterson and Wong 2005). For inelastic deformation and failure, α can be determined experimentally.

In conventional triaxial deformation experiments, this simple effective stress law is defined in terms of an effective pressure, whereby P _eff  = P _c  − αP _p ; P _eff and P _c being the effective and confining pressures, respectively. Simply put, in the case where α = 1, the stress regime on a sample deformed at respective confining and pore pressures of 10 and 15 MPa would be identical to that imposed with confining and pore pressures of 100 and 105 MPa, respectively (the effective pressure would be 5 MPa in both cases). In contrast, if the volumetric response of the fluid and solid constituents are unequal and α < 1, then the stress regimes in the two scenarios will differ. In essence, this means that the measured failure stress of a sample would be different in each scenario, all other parameters being equal. There exists a paucity of data on this coefficient for the failure of porous rocks, largely due to the natural variability between samples, which makes its determination often challenging and sometimes quite impossible.

Since we present triaxial experiments at different pressures in this study, it is important to verify that the effective pressure coefficient does not differ significantly from unity in porous andesites. We therefore performed a series of constant strain rate triaxial tests at the same nominal effective pressure according to Terzaghi’s principle (i.e. P _eff if α = 1), but imposing different confining and pore pressures. In an attempt to minimise sample variability, we selected samples that contained the same connected porosity. The experimental conditions and differential stress at failure are given in Table 2.

Table 2 Porosity, pressure conditions, and differential stress at failure for porous A5 andesite. P _p , P _c , and P _eff correspond respectively to the pore, confining, and effective pressures and are all given in MPa

Herein, we calculate α as the value that equalises the ratio of minimum and maximum peak stresses (σ _Pa and σ _Pb) and the ratio of the corresponding effective pressures (P _effa and P _effb):

$$ \frac{\sigma_{\mathrm{Pa}}}{\sigma_{\mathrm{Pb}}}=\frac{P_{eff\mathtt{a}}}{P_{eff\mathtt{b}}} \approx 0.73 $$

(A1)

which occurs when α ≈ 0.98, a value comparable to that determined recently by Baud et al. (2015) for Bleurswiller sandstone. However, we note that the natural variability in strength of these andesites is high: samples A5-09 and A5-11 were deformed under identical experimental conditions, yet there is a discrepancy of 18.68 MPa between their differential stresses at failure. Given the level of natural heterogeneity in these andesites (a result of their complex and variable microstructure)—and indeed, in other intrusive and extrusive igneous rocks—we highlight that our data are not sufficient to state conclusively that the effective pressure coefficient differs significantly from unity in these materials. Nevertheless, although we cannot constrain the exact value of the Biot-Willis coefficient in these andesites, this pilot study does confirm that the true value is not likely to differ significantly from unity. As such, the use of Terzhagi’s principle of effective pressure in our tests is a valid assumption.

Appendix B: Sample drainage

If the deformation of a sample proceeds at a rate faster than the response time of the pore pressure intensifier/volumometer, the experiment is considered “undrained”. In such a scenario, the tips of fast growing dilatant microcracks would not be fluid-saturated; this not only provides an underestimate of the porosity change during deformation but also influences the mechanical behaviour of the rock. Sample drainage was an important consideration in the experiments presented herein because we are interested in the mechanical response of a rock as pore pressure is increased. If our experiments were undrained, there would be a discrepancy between the pore pressure we expect in the rock, and the pore pressure within the rock. This would further complicate matters by creating a heterogeneous pore pressure distribution within the sample. In order to assess whether our samples were drained (i.e. fully saturated) during all the experiments, the setup shown in Fig. 10 was used. This experimental setup allows the increase or decrease of pore pressure using an intensifier whilst monitoring both up- and downstream pressure. When the downstream valve (8 in Figure 10) is closed, any pressure deviation measured by the downstream transducer (6 in Figure 10) must first have flowed through the sample. By servo-controlling the upstream pore fluid pressure and monitoring the downstream pressure, we can thus determine whether the sample is drained at different pressure increase rates. Pore pressure was oscillated between 10 and 20 MPa, whilst confining pressure was maintained at 40 MPa. Pressure was cycled at incrementally faster rates, from an initial value of 5.0 × 10⁻² MPa s⁻¹, to a final rate of 5.0 × 10⁻¹ MPa s⁻¹. If the sample were undrained, we would expect to see a delay in the response of the downstream pressure relative to the upstream pressure. However, as shown in Figure 11, no delay can be seen. This indicates that the permeability of these porous andesites is sufficiently high to preclude sample desaturation, even at significantly high rates of pore pressure increase.

Fig. 10

Schematic of the setup used to test sample drainage. When the upstream valve is open, pore pressure within the sample can be increased or decreased by the intensifier (10). If the downstream valve is open, then the pore pressure circuit is fully connected. However, when (9) is open and (8) closed, the pressure response measured at (6) depends on whether or not the sample is fully saturated

Fig. 11

Mechanical data from a triaxial experiment designed to examine sample drainage in porous andesitic rock (sample C8). a Graph of pore pressure against time showing the monitored upstream (red dotted curve) pressure as a function of changing downstream (black dotted curve) pressure. b Graph of pore pressure rate against time showing the (absolute) rate of pore pressure change during the experiment