Impact of injection rate ramp-up on nucleation and arrest of dynamic fault slip

Fluid injection into underground formations reactivates preexisting geological discontinuities such as faults or fractures. In this work, we investigate the impact of injection rate ramp-up present in many standard injection protocols on the nucleation and potential arrest of dynamic slip along a planar pressurized fault. We assume a linear increasing function of injection rate with time, up to a given time $$t_c$$ t c after which a maximum value $$Q_m$$ Q m is achieved. Under the assumption of negligible shear-induced dilatancy and impermeable host medium, we solve numerically the coupled hydro-mechanical model and explore the different slip regimes identified via scaling analysis. We show that in the limit when fluid diffusion time scale $$t_w$$ t w is much larger than the ramp-up time scale $$t_c$$ t c , slip on an ultimately stable fault is essentially driven by pressurization at constant rate. Vice versa, in the limit when $$t_c/t_w \gg 1$$ t c / t w ≫ 1 , the pressurization rate, quantified by the dimensionless ratio $$\dfrac{Q_m t_w}{t_c Q^*}$$ Q m t w t c Q ∗ with $$Q^*$$ Q ∗ being a characteristic injection rate scale, does impact both nucleation time and arrest distance of dynamic slip. Indeed, for a given initial fault loading condition and frictional weakening property, lower pressurization rates delay the nucleation of a finite-sized dynamic event and increase the corresponding run-out distance approximately proportional to $$\propto \left( \dfrac{Q_m t_w}{t_c Q^*}\right) ^{-0.472}$$ ∝ Q m t w t c Q ∗ - 0.472 . On critically stressed faults, instead, the ramp-up of injection rate activates quasi-static slip which quickly turn into a run-away dynamic rupture. Its nucleation time decreases non-linearly with increasing value of $$\dfrac{Q_m t_w}{t_c Q^*}$$ Q m t w t c Q ∗ and it may precede (or not) the one associated with fault pressurization at constant rate only.

On the dynamic slip boundary condition for Navier–Stokes-like problems

The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting.

Pain Control Affects the Radiographic Diagnosis of Segmental Instability in Patients with Degenerative Lumbar Spondylolisthesis

Background: Diagnosing intervertebral instability is crucial for the treatment of degenerative lumbar spondylolisthesis (DLS). Disabling back pain will reduce spinal mobility which leads to an underestimate of the incidence of intervertebral instability. We hypothesized that adequate analgesia could alter the flexion/extension exam performance, and thus increase the diagnostic accuracy of segmental instability. Materials and methods: One hundred patients with low-grade DLS were prospectively enrolled in the before–after cohort study. Standing lateral flexion/extension radiographs of lumbar spines were examined and analyzed before and after intramuscular injections of 30 mg ketorolac. Results: Pain score decreased significantly after analgesic injections (p < 0.001). Dynamic slip (DS), dynamic segmental angle (DA), dynamic lumbar lordosis, and slip percentage (SP) were significantly increased after pain reduction (all p < 0.001). According to the diagnostic criteria for segmental instability (DS > 4.5mm, DA>15°, or SP >15%), there were 4%, 4%, and 0.7% of total motion segments fulfilling the criteria which markedly increased to 42%, 32%, and 16.7% after analgesia was administered. The incidence of instability also increased from 6% to 38% after analgesia. Conclusions: The diagnosis rate of intervertebral instability is commonly underestimated in the presence of low back pain. This short-term pain relief facilitates reliable functional imaging adding to the diagnosis of intervertebral instability.

Impact of injection rate ramp-up on nucleation and arrest of dynamic fault slip

Fluid injection into underground formations reactivates preexisting geological discontinuities such as faults or fractures. In this work, we investigate the impact of injection rate ramp-up present in many standard injection protocols on the nucleation and potential arrest of dynamic slip along a planar pressurized fault. We assume a linear increasing function of injection rate with time, up to a given time tc after which a maximum value Qm is achieved. Under the assumption of negligible shear-induced dilatancy and impermeable host medium, we solve numerically the coupled hydro-mechanical model and explore the different slip regimes identified via scaling analysis. We show that in the limit when fluid diffusion time scale tw is much larger than the ramp-up time scale tc, slip on an ultimately stable fault is essentially driven by pressurization at constant rate. Vice versa, in the limit when tc/tw ≫ 1, the pressurization rate, quantified by the dimensionless ratio (Qm tw / tc Q∗), does impact both nucleation time and arrest distance of dynamic slip. Indeed, for a given initial fault loading condition and frictional weakening property, lower pressurization rates delay the nucleation of a finite-sized dynamic event and increase the corresponding run-out distance approximately proportional to (Qm tw / tc Q∗)^(-0.472). On critically stressed faults, instead, the ramp-up of injection rate activates quasi-static slip which quickly turn into a run-away dynamic rupture. Its nucleation time decreases non-linearly with increasing value of (Qm tw / tc Q∗) and it may precede (or not) the one associated with fault pressurization at constant rate only.

Effects of varying injection rate on dynamic slip nucleation along a frictional weakening fault

&lt;div&gt; &lt;p&gt;&lt;span&gt;Anthropogenic injection of fluid into tight fractured reservoirs is known to alter the stress state of the Earth`s crust, &amp;#160;inducing micro-seismicity and eventually significant earthquakes. The injection scenario, in terms of injection pressure or injection rate, is one of the key controlling parameters for injection-induced seismicity. Although a number of studies have been carried out on understanding the effects of injection strategy on seismicity rates, less is known about its effect on the nucleation of dynamic slip on a pressurized fault, especially for non-stationary injection protocols.&lt;/span&gt;&lt;/p&gt; &lt;/div&gt;&lt;div&gt; &lt;p&gt;&lt;span&gt;In this contribution we study the effects of injection rate variation on the transition between aseismic and seismic slip along a frictional weakenig fault. Notably, we parametrize the injection strategy by assuming an initial linear increase of injection rate in time, up to a value after which it remains constant. We perform a scalying analysis and identify the governing parameters that control the fault response. We solve numerically the coupled hydro-mechanical problem using a fast boundary element solver for localized inelastic deformations [1]. Upon benchmarking the numerical results with the semi-analytical ones of Garagash and Germanovich [2] for the specific case of constant injection rate, we investigate the effect of injection rate variation on critically stressed and marginally pressurized faults. We derive analytical expressions for nucleation time and we confirm them via numerical results. Furthermore, we present a small scale yielding solution for marginallly pressurized faults and investigate the influence of injection scenario on shear crack run-out distances (when occuring).&lt;/span&gt;&lt;/p&gt; &lt;/div&gt;&lt;div&gt; &lt;p&gt;&lt;span&gt;&amp;#160;&lt;/span&gt;&lt;/p&gt; &lt;/div&gt;&lt;div&gt; &lt;p&gt;&lt;strong&gt;&lt;span&gt;References &amp;#160;&amp;#160;&lt;/span&gt;&lt;/strong&gt;&lt;/p&gt; &lt;/div&gt;&lt;div&gt; &lt;p&gt;&lt;span&gt;[1] Ciardo, F., Lecampion, B., Fayard, F., and Chaillat, S. (2020), A fast boundary element based solver for localized inelastic deformations, &lt;/span&gt;&lt;em&gt;Int J Numer Methods Eng&lt;/em&gt;. 2020; 1&amp;#8211;23.&lt;/p&gt; &lt;/div&gt;&lt;div&gt; &lt;p&gt;&lt;span&gt;[2] Garagash, D., and L. N. Germanovich (2012), Nucleation and arrest of dynamic slip on a pressurized fault, &lt;em&gt;J. Geophys. Res&lt;/em&gt;., 117, &lt;/span&gt;B10310&lt;span&gt;.&lt;/span&gt;&lt;/p&gt; &lt;/div&gt;

A Crosslink Constraint Method for Modeling Episodic Dynamic Rupture on Intersecting Faults

We present a crosslink constraint method for numerically modeling dynamic slip on intersecting faults, without prescribing slip (dis-)continuation directions. The fault intersections are constrained by crosslinked split nodes, such that the slip can only be continuous on one of the two intersecting faults at a time and location. The method resolves the episodic intersection offset by examining the dynamic fault traction resulting from two sets of constraint equations, one for each slip direction. To verify this method, we modify two benchmark problems, hosted at Southern California Earthquake Center (SCEC), by allowing a branching fault to step across a main fault. The modified SCEC problem results agree with our expectations that the intersection offset scenarios are dictated by the nucleation patch location and initial fault traction. This new method comes with an open-source finite-element code Defmod.