Transient evolution of permeability and friction in a slowly slipping fault activated by fluid pressurization

The mechanisms of permeability and friction evolution in a natural fault are investigated in situ. During three fluid injection experiments at different places in a fault zone, we measured simultaneously the fluid pressure, fault displacements and seismic activity. Changes in fault permeability and friction are then estimated concurrently. Results show that fault permeability increases up to 1.58 order of magnitude as a result of reducing effective normal stress and cumulative dilatant slip, and 19-to-60.8% of the enhancement occurs without seismic emissions. When modeling the fault displacement, we found that a rate-and-state friction and a permeability dependent on both slip and slip velocity together reasonably fit the fault-parallel and fault-normal displacements. This leads to the conclusion that the transient evolution of fault permeability and friction caused by a pressure perturbation exerts a potentially dominant control on fault stability during fluid flow.

much to produce the observed order of magnitude enhancement in permeability, then why is there no obvious dilatant suction effect seen in the pressure profile?

REVIEWER COMMENTS
• Reviewer #1 (Remarks to the Author): This paper uses borehole fluid pressurization tests directly into a fault zone in an underground laboratory, in order to measure permeability (via the fluid pressure), dilatancy (aperture opening), and slip on the fault in response to fluid pressure steps. If I understand correctly, in addition to the direct measurements, permeability and slip functions are also calculated from the dilatancy measurements. Then, expressions are combined to relate the permeability to the slip. At the same time, slip measurements are combined with the rate-and-state friction law to produce a friction record during the pressure step. The outcome is, for a given pressure step, a calculated permeability function that can be compared to the measured permeability, a calculated slip function that can be compared to the measured slip, and a calculated friction function.
In general, I think the approach is sound and the work is clearly important for the topic of induced seismicity. The measurements seem well done and I don't see anything I would consider to be a serious methodological error. I did find the manuscript confusing at points, and I think the biggest area of improvement would be more precise explanations and language, which I list below. Some points may seem picky but I think clarity is important, because it may affect the interpretations. I don't think this will affect the story much, so the paper should be publishable after revision.
We are grateful to the reviewer for the positive comments on our manuscript, and the very interesting suggestions of improvement. We have tried to address all your questions and the details are below.
I think the role of effective normal stress should be emphasized more. Increasing the fluid pressure of course reduces the effective normal stress, here to very low values. This is really the cause of all subsequent observations, for example permeability, which is known to be sensitive to effective normal stress. I would like to see this in the text, and the effective normal stress can easily be added to Figure 3 as a double x-axis. Also, it is the effective normal stress that appears in the rate-andstate friction formulation. It is just called "normal stress" in the Hong and Marone and Linker and Dieterich papers because those experiments were conducted room dry with no pore fluid (so that the normal stress is the effective normal stress).
We agree with this point, and have added a new axis at the top of figures 3a and 3b to show the evolution of permeability and fault-parallel displacement as a function of the effective normal stress (i.e. total normal stress minus the fluid pressure). In the text, we have also added this point in lines 18, 150-152, 173, 184, 329 and 366. This is correct the normal stress is the effective normal stress in the rate-and-state formulation used here to analyze our fault activation experiment cause by increasing fluid pressure (line 218).
I think the fault zone itself needs to be more precisely described. It is introduced as "the fault zone" but is actually made of multiple fault strands (principal slip zones) and a damage zone, and within the damage zone there are "faults and fractures", so it is difficult sometimes to keep this all straight. What do the three boreholes actually intersect? It looks like Tests 1 and 2 are performed directly on one of the principal slip zones, whereas Test 3 is in the damage zone. Are both Tests 1 and 2 performed on a clay-bearing fault? This is of course important because clays have very different hydromechanical properties compared to fractured limestone. Is there a significant difference between the location of Tests 1 and 2? If so, this could explain some of the differences seen in Figure 4, for example the permeability fit in Test 3 may be related to the large overall permeability of the damage zone, whereas the less well-fit permeability model in Tests 1 and 2 could be the effect of clay gouge. But if the location of Tests 1 and 2 are the same, that does not explain the difference between these two.
We agree that more information about the fault zone architecture and the geology of the borehole intervals where injection tests are performed is needed. We have clarified this point by improving the Figure 1b, as well as in the text on lines 59-69 and 77-84 by adding details.
On lines 83-89, we now present details for each test interval: Inside the injection chamber, the pressurized fault plane is located at the middle of the interval between two inflatable packers. Tests 1 and 2 are situated along a principal slip zone, while Test 3 is in a fractured damage zone. In Test 1, the rock matrix around the pressurized fault plane contains three subparallel bedding planes in the sealed borehole interval, while in Test 2, the rock matrix contains micro-fractures without bedding planes. In Test 3, the pressurized fault plane is surrounded by a fractured matrix with a fracture density higher than in Tests 1 and 2. In the three tests, the selected planes are not filled with clay material. We think that some differences seen in the permeability and friction evolution in Figure 4 can be due to some differences in the borehole interval geology in and around the pressurized fault plane. Following the suggestion of the reviewer, we have now included additional text on lines 306-313: Although some differences in the fault response observed between the tests can be due to the different levels of fracturing of the rock matrix that surrounds the pressurized fault plane, the exact mechanical process responsible for permeability increase or decrease after the sudden acceleration remains elusive. Based on geological observations of the borehole intervals before injection, they could reflect geometrical changes of contact areas, gouge content and void space that comprise the fault during deformation at low effective stress for Tests 1 and 2, whereas the hydromechanical response observed in Test 3 may be related to the overall permeability of the fractured damage zone surrounding the tested fault segment.
I'd like a bit more information on the measured permeability values. What exactly is meant by the permeability of the "rock matrix"? Intact limestone, or the damage zone which includes fragments of intact limestone and a network of fractures? What is meant by the permeability of the fault zone? Across-fault permeability? Along-fault permeability? Is this a fault with clay gouge?
The permeability of the rock matrix corresponds to the intact limestone. We have clarified by adding "intact rock matrix" (lines 97 and 132).
With our in-situ protocol, the fluid pressure is increased step-by-step in a borehole interval intersecting the fault plane. Thus, the permeability of the fault zone is an apparent permeability, integrating both the across-and along-fault components. We have clarified by adding "apparent fault permeability" (line 134).
I found the calculations and relation of permeability to slip to be somewhat convoluted. Both the permeability increase and slip activation are the result of dilatancy (which is of course the result of reduced effective normal stress). So I am not sure if it is really correct to say that the permeability is a function of the slip (i.e., they are both effects of the same process but one does not necessarily cause the other) (e.g. Line 18). For the calculated permeability shown in Fig 4, why calculate it from the slip, which is calculated from the aperture opening, and not directly from the aperture opening itself? I think it also would help if the main goal/result of the study is clearly stated, "coevolution of friction and permeability is important" is not very clear. I guess the goal is to be able to calculate permeability and friction and/or frictional stability from a known pressure perturbation and measured dilatancy and/or slip? I suggest stating something like this directly.
We have clarified this point. The permeability change is due both to reducing effective normal stress and slip-induced dilation. We have added "reducing effective normal stress" (line 18), "during increasing fluid pressure" (lines 51-52). In the discussion (lines 326-328), we also added new sentences to directly state the main objective and result.
In Figure 3 (dots) and Figure 4 (orange line), the permeability change estimated from experimental data is directly calculated from the measured opening caused by increasing fluid pressure using equation 1. To clarify this point, we have added a sentence in the Methods (lines 390-392). Then, the modeled permeability (black line) is calculated from the opening associated with the slip induced by fluid pressure perturbation. In the model, slip is sensitive to the change in effective normal stress, and so slip increases upon an increase in the fluid pressure as observed experimentally (Fig. 3b, Fig. 4a,c,e). We now clarify this point on lines 173-174.
Care should be taken when referring to "seismic slip" vs "aseismic slip". All the seismicity is offfault (or at least remote from the test location in the borehole. So really, all the measured slip here is actually aseismic, and the "seismic slip" is triggered on a different fault somewhere else. On a related note, on Lines 288-290 it is stated that "small values of slip-weakening distance" (I guess here the critical slip distance Dc is meant?) are suggested to be responsible for remotely triggered seismicity, but the RSF parameters and critical nucleation lengths obtained here are only relevant for the fault for which the slip was modeled. For remote seismicity, the RSF and elastic properties for that fault have to be evaluated.
We agree with this comment. We have changed to "critical slip distance" (lines 342-343) and mentioned that the values are estimated at the injection points.
We have also added a new sentence (lines 413-416) in the Methods to clearly mention that "the frictional and elastic properties in the zones of seismicity observed at a distance of injection points are not evaluated in the present study. A future characterization of the frictional parameters within the whole fault zone may help for better defining the seismic potential of fault segments and fractures around the injection." Care also needs to be taken with the term "evolution of friction", I guess you mean here the friction time series as shown in Fig 4. But the friction parameters that determine fault stability (the rateand-state friction parameters) are fixed for a particular modeled pressure step, and do not evolve, or co-evolve with permeability (e.g. Line 22).
We agree, this is the transient evolution of friction and permeability. We have added "transient" to clarify this point (lines 22, 189, 365). Hence, we have modified the title to state "Transient evolution of permeability and friction in a slowly slipping fault activated by fluid pressurization".
Line 87: what samples were used in these experiments? Limestone? Clay gouge?
The laboratory experiments were performed on fault gouge collected from rock samples drilled from the fault zone, which we reactivated by fluid injection at a depth in the underground gallery (Cappa et al., Sci. Adv., 2019). We have clarified this point in the text on lines 102-103. Line 107: so the seismicity occurs only in the damage zone, and not on any of the clay-lined principal slip zones? this makes sense based on what is known about clay friction in general but is worth mentioning The seismicity indeed occurs in the fractured damage zone around the fault segment activated by the fluid pressurization. This point is mentioned in lines 121-124 with a reference to previous work on the seismicity analysis (see Duboeuf et al., JGR, 2017). However, this is not because of clay friction (as no clay is present in the tested fractures), but to the large nucleation lengths around the injection, as stated on lines 341-343. Lines 218-223: Δϕ is described as a "dilation parameter dependent on slip velocity" but ϕ is conventionally porosity, so is Δϕ just a porosity change? It seems simpler to describe it this way.
Indeed, in the initial equation proposed by Fang et al. (2017), Δϕ is described as a "dilation parameter dependent on slip velocity". To avoid confusion with the conventional porosity (ϕ), we have changed Δϕ by Δ in equations 6 and 7, and on line 249.
Lines 264-267: it would be helpful to report the rate-and-state friction values from the previous study, so the reader can directly compare.
Thanks for this suggestion. We now give on lines 316-317 the rate-and-state friction values estimated from the previous laboratory experiments on fault gouge (Cappa et al., Sci. Adv., 2019).
Line 311: as noted above, they are both linked to dilatancy (aperture opening) and reduced effective normal stress We have clarified by adding the following sentence "both linked to effective normal stress and slip" in lines 365-366.
• Reviewer #2 (Remarks to the Author): In their manuscript "Co-evolution of permeability and friction in a slowly slipping fault activated by fluid pressurization", Cappa et al. presented the results of three in-situ injection experiments where fluid pressure, fault displacement (normal and parallel) and slip velocity are measured. They then used a numerical model relating the hydraulic aperture (assumed to be equal to fault-normal displacement), permeability, slip, slip velocity, and rate-and-state friction to fit the observed permeability and fault slip data, finding a reasonably good fit. This study corroborates with some previous experimental studies they and others have done, showing the importance of permeability enhancement upon slip triggering. The results are very interesting to the seismology community, especially for those modeling injection-induced aseismic slip. I do have a few concerns regarding the data fit, and would appreciate if the authors could address the following comments.
We thank you for the helpful, constructive feedback, and your suggestions. We have tried to address all your questions.
Main comments 1. The fit to Test 1 vs. Tests 2 & 3 show some rather significant differences. The reason why Test 1 does not have as great fit is explained in the Discussion, but when it was first mentioned in Lines 242-246, the explanation was rather vague and general, perhaps adding some explanations there will make the reader more convinced, and then in the discussion, those points can be further developed. However, in concept, all tests involve similar set-ups, so whatever has not been taken into account in the model for one test also wasn't taken into account for the other tests. So why is there much less discrepancy for the other two tests?
We have added more explanations about the possible reason why Test 1 does not have as great fit in Lines 275-282, to help the reader before the Discussion on this specific point: The exact process responsible for such a difference remains subtle. It could be related to additional hydromechanical effects or geometrical complexities ignored in the model we use. In such welldeveloped fault zone, it could also reflect heterogeneous fluid flow (i.e. channeling) over the pressurized fault segment or a fluid leakage from the pressurized fault into the surrounding connected fractures or bedding planes. As the injected fluid volume in Test 1 is much larger than for the other tests, it is likely that an extended network of faults is pressurized, leading to more complex hydromechanical response.
2. I'm particularly interested in the iterative parameter search to produce the best fit. The values of dc and Ks, for example, span over an order of magnitude across the different tests, which are very close to each other in space. Is it realistic to have them be so different for such similar test locations?
Although the test locations are close in the fault zone, geological and geometrical differences exist (lines 77-84). Indeed, there is difference in fracture density and rock elasticity (Jeanne et al., 2012) around the pressurized fault that could explained the different value of Ks. The difference in dc could be due to different degree of roughness as observed in Jeanne et al., 2012. We now mention this in the caption of the Supplementary Table 1 3. Is there any consideration of using the mass balance equation to fit the fluid pressure evolution using the parameters found above? Maybe that will be a good check on whether they are not just (over)fitting the permeability profile, if they can also reasonably fit the pressure profile. This is an interesting point. With the precise hydromechanical measurements at injections points reported in this paper, the behavior of the fault zone is quite complex and fully coupled hydromechanical modeling is needed to reproduce the pressure profile. In future work, we intend to develop additional modeling with new experiments including more monitoring boreholes in the fault and distributed sensors to better track the three-dimensional fluid pressure evolution over time. With the current data and models, we feel that the new discovery presented here is quite important and relevant to our study.
4. My concern with the hydraulic-aperture and permeability relation is that, if the fault has opened so much to produce the observed order of magnitude enhancement in permeability, then why is there no obvious dilatant suction effect seen in the pressure profile?
In the experimental protocol used in the study, the injection corresponds to a pressure-control mode to maintain a quasi-constant pressure at each hydraulic loading. In short, we impose the fluid pressure in the injection chamber between inflatable packers. The fluid pressure is a boundary condition and was increased step-by-step. We now clarify this point on lines 72-73. Consequently, fluid pressure drop during fault opening are limited at the injection. We think that additional measuring points in the fault around the injection would have helped to see potential dilatant suction effect. Additionally, a constant flow rate boundary condition could be more appropriate to detect this effect.

Equation (1) the cubic law is written as square
To avoid confusion, we have removed "cubic law" in line 138.

Line 152: do the constants beta and gamma have meanings?
Beta represents how much dilatancy is involved when the fault slips. Gamma is geometric constant. We have clarified in lines 171-172.

Line 178: could you explain why this assumption is valid for high initial permeability fault?
This assumption is valid for faults with sufficiently high permeability, such that the characteristic timescale of fluid diffusion is smaller than the timescale of deformation. In other words, the pressure is assumed to be drained at all times. We have clarified on lines 199-200. Tests 1 and 2 show induced seismicity over the time window selected for the modeling. Figure 2D and 2E illustrates this seismicity which is located around the fault segment pressurized by fluid injection, which slips aseismically at slow velocity consistently with data presented in supplementary figure 2. We have added " (Fig. 2a and e)" on line 205. 5. Lines 262-263: could you expand on what is interesting about the permeability and friction evolving concurrently?
We have added the following sentence on lines 298-305:

Interestingly, the permeability and friction evolve concurrently under conditions of varying stress. This observation suggests a direct link between the transient evolution of permeability and friction presumably through rearrangement of fault surface asperities as a result of slip and opening or closure. The comparison between experiments shows two fault behaviors. In the first case, a rateweakening behavior is associated with a fault closure after the pressure increase (Test 2), and in the second case, a rate-strengthening behavior is observed together with a fault opening (Test 3)
. Figure 2: the green dots are labeled as distance of seismic events to injection, but where is the scale that shows how many far it is to injection?
The scale that shows how many far a seismic event is to injection is the right axis labelled "Seismic events". As indicated in the legend mentioned in Figure 2D, this axis is used both for the cumulative number of seismic events and the distance of seismic events to injection in meter. For clarity, we have added the significance of each axis in the figure caption (lines 572-574).

• Reviewer #3 (Remarks to the Author):
A review of "Co-Evolution of Permeability and Friction in a Slowly Slipping Fault activated by Fluid Pressurization by Cappa F., Giglielmi Y, De barros L.
This manuscript presents a large-scale in-situ experiment on permeability and friction evolution in a natural fault. The authors performed fluid injections in a km-scale fault zone in limestone in the LSBB lab (France). They measured fluid pressure, normal and shear displacements, and seismic activity. Permeability and friction are modelled from these data. This topic is highly relevant for unconventional reservoir geomechanics. The main result presented by the authors is that friction and permeability are dependent on both slip and slip velocity. The paper is well written and the main messages contained in it are clearly delivered and well supported by experimental and modelling data. It definitely deserves to be published. However, the work would better fit in a more specialized journal, where part of the interesting supp. mat. could be incorporated into the main text. I have only moderate comments.
We thank you for your constructive feedback and for recognizing the broad interest and applicability of this study and for placing the work into context. We have tried to address all your questions, and now included the suggested information in the main text and in additional supplementary figures.

Comments:
L14: in-situ (ita) Changed to italic was done for all "in situ". L90: Careful here! The lab experiments were performed on gouge material. The natural fault is rough at different scales and without gouge material (L 62-63). It is well known that the dependences of friction to slip, and slip rate are strongly related to fault structure (with (a-b) increasing with slip-velocity in gouge material, and decreasing on bare surfaces, Noel et al., (2019)). Moreover, the static friction coefficient of gouge material is different than the one for bare surfaces. Note also that gouge material has almost no cohesion.
Thanks for suggesting that. We have clarified by adding "on gouge material collected from rock samples drilled from the fault zone" on lines 102-103. The initial fault effective aperture was estimated in previous studies from the analysis of a series of hydraulic injection based on pulse and step-rate tests of different magnitudes and durations (Guglielmi et al, Science, 2015;Jeanne et al., 2012) (lines 147-148).
This point is mentioned in the Methods (please, see the section "Estimate of the fault permeability change from the temporal evolution of fault-normal displacement") (lines 379-392).

References :
Cappa F., Guglielmi Y., Rutqvist J., Tsang C-F., Thoraval A. Hydromechanical modelling of pulse tests that measure fluid pressure and fracture normal displacement at the Coaraze Laboratory site, France, Int J Rock Mech Min Sci, 43, 1062-1082, doi: 10.1016/j.ijrmms.2006.03.006, (2006 This is correct, equation 2 was originally derived from the CNS model (Niemeijer and Spiers, JGR, 2007) developed for granular material, and then successfully applied to reproduce both laboratory measurements (slip and dilation) on fault gouge and in situ measurements (slip and dilation) on natural faults (Van den Ende et al., Solid Earth, 2017). Interestingly, the model fits well the measured permeability into the three in situ experiments presented here. Although the model geometry simplifies the natural conditions of the experiment (roughness, geometry, segmentation, fluid flow, etc.), our numerical results are consistent with the observed fault hydromechanical response. Reproducing this permeability evolution is the main objective of the modelling presented here. We feel that this new discovery is quite important and relevant to our study. We also want to emphasize that such hydromechanical data collected in situ directly in fault zones are rare and L 217: Is it possible that mechanisms such as flux-driven unclogging of the fracture possibly link frictional evolution to permeability change in the presented experiment?
The mechanism of flux-driven unclogging with particle mobilization is a plausible scenario but difficult to study in the present in situ experiment. We mentioned this mechanism on line 359 as possible within the fault.
L232/figure 4: I would be curious to see more of those pressure steps fitted by the model.
In the model, the pressure step is imposed a loading condition. Thus, the pressure data are not fitted by the model, but correspond to an input parameter. The model is used to reproduce the fault displacements, and to infer evolution of permeability and friction.
L262: Please explain why some fault portions do experience dilation why others see compaction.
This is a good point. The exact mechanical process responsible for fault dilation or contraction remains elusive. They could reflect geometrical changes of contact areas and void space that comprise the fault during deformation at low effective stress. We have added new explanations on lines 299-309. Although some differences in the fault response observed between the tests can be due to the different levels of fracturing of the rock matrix that surrounds the pressurized fault plane, the exact mechanical process responsible for permeability increase or decrease after the sudden acceleration remains elusive. Based on geological observations of the borehole intervals before injection, they could reflect geometrical changes of contact areas, gouge content and void space that comprise the fault during deformation at low effective stress for Tests 1 and 2, whereas the hydromechanical response observed in Test 3 may be related to the overall permeability of the fractured damage zone surrounding the tested fault segment. Done as suggested. We have added "which showed that the seismicity is localized far from the injection point where the hydromechanical measurements are performed" on lines 338-339.
Frictional analysis of Test 3 indicates a rate-strengthening frictional behavior with a positive (a-b), which is a suitable condition for aseismic slip. Thus, we provide Lc only for the Tests 1 and 2 with a rate-weakening frictional behavior which favors potential seismic slip. Thanks for this suggestion. We added an additional Supplementary Figure 5 with close-up views of different pressure steps over the pressure range from 0 to 3 MPa, and from 3 MPa to the maximum injected pressure. This new figure better illustrates each pressure steps. Ideally, one would be able to clearly define the start and end of each pressure step. However, it is also important to mention that during fault activation experiments in the field, it is difficult to reach the ideal stability conditions generally obtained in laboratory experiments under a well-controlled environment. In nature, boundary conditions are not controlled, and it is possible to reach a near steady-state pressure. Thus, we have also added "near steady-state fluid pressure conditions" in the Methods (line 384).