Brittle Deformation of Damaged Mafic and Ultramafic Rocks and Their Implications on Plate Bending

The effect of damage on the brittle deformation of mafic and ultramafic rocks has been investigated by performing triaxial deformation experiments on thermally cracked and intact rock samples. The investigation was performed by recording the axial and lateral strains during deformation while simultaneously capturing the ultrasonic velocity, and electrical resistivity. While the peak strength is presumably controlled by the stiff intrinsic fractures, the crack opening mode also showed critical effects on the attained peak strength. The pore pressure distribution showed an apparent control over the dynamic Young's modulus as the ratio between the dynamic and static modulus of thermally cracked rocks is significantly higher than that of intact rocks. The compliant nature and the higher inelastic volumetric strain of the thermally cracked samples further indicated a possible explanation to the steep dipping plates and the taller topographic heights at the trench outer rise systems of old subduction zones.


Introduction
Various geophysical investigations have illuminated the structural alterations suffered by the incoming plate due to the vast number of extensional faulting and rupturing generated with the bending of the subducting plate (Fujie et al., 2013(Fujie et al., , 2018;;Grevemeyer et al., 2018;Key et al., 2012;Naif et al., 2015).Such alterations primarily include the breaking of the lithosphere (Abe, 1972;Lay et al., 2009) creating conduits for fluid migration, through extensive damage, into the previously intact rocks.This ultimately leads to serpentinization of the mantle, that has been well identified by V P /V S anomalies (e.g., Grevemeyer et al., 2018) and electrical resistivity anomalies (e.g., Naif et al., 2015).A critical aspect of serpentinization is the effect that it has on the brittle deformation of the oceanic lithosphere.First, serpentinization is a process that is associated with volume increase which result in brittle fracture of the deforming peridotite (O'Hanley, 1992).Second, presence of serpentinite reduces the strength of peridotite in several factors and demonstrate a non-dilatant deformation as the deformation is primarily accompanied by the serpentine (Escartín et al., 1997(Escartín et al., , 2001)).Third, as serpentinite bodies cross their stability field with increasing pressure and temperature the resulting body is subjected to dehydration embrittlement with reduction in effective pressure as pore pressure increase (Raleigh & Paterson, 1965).These are critical phenomena related to the brittle deformation of subduction zone that are well discussed.However, we believe the fractures, which stage the setting for fluid influx for serpentinization by cutting across the mafic and ultramafic rocks of the oceanic lithosphere, have been overlooked on their contribution to the brittle deformation, especially since it has been recognized that damage has a pronounced effect on the brittle deformation (Wang et al., 2013).

RESEARCH LETTER 10.1029/2023GL106576
Key Points: • The effect of damage on brittle deformation of mafic and ultramafic rocks has been addressed via experiments • The ultrasonic velocity, electrical resistivity, and strain are measured simultaneously during deformation of rocks • Presence of cracks strongly influence deformation and physical properties which are comparable to outer rise geophysical observations

Supporting Information:
Supporting Information may be found in the online version of this article.
Indeed, several investigations have been conducted on mafic and ultramafic rocks (Christensen, 1984;Rao & Raman, 1974;Shimada et al., 1983).Due to the partial serpentinization of dunite used by Rao and Raman (1974), which leads to a stress-strain response incomparable with an unaltered specimen, and the large uncertainty of the volumetric strains of Shimada et al. (1983), which is essential in identifying the deformation accurately, Akamatsu et al. ( 2019) also performed triaxial experiments on mafic and ultramafic rocks.Akamatsu et al. (2019) reported contrasting dilatant behaviors as diabase reached nearly three times the inelastic volumetric strain of peridotite.Their microstructural observations revealed that diabase deformed by axial crack opening while peridotite deformation was dominated by shear cracking along the olivine grain boundaries.However, neither of the above investigations addressed the effect of damage on brittle deformation nor performed investigations under fluid saturated conditions.Christensen (1984) on the other hand, did perform hydrostatic experiments under various confining pressures and pore pressures to show that seismic velocity varies as a function of effective pressure.However, they also did not look into the effect of damage.Followed by the lack of investigations on damaged mafic and ultramafic rocks, Jayawickrama and Katayama (2023), performed hydrostatic experiments on thermally cracked (in analogy to damage) diabase and peridotite, under both dry and wet conditions.Even though they showed that the damage has the potential to reduce the elastic properties of rocks, hydrostatic experiments alone cannot illuminate the effect that damage poses on brittle deformation.Therefore, in this study, we investigate the effect of damage on brittle deformation by performing laboratory triaxial experiments on saturated mafic and ultramafic rocks while simultaneously recording the ultrasonic velocity, electrical resistivity, and strain.Subsequently we show how our results could be utilized to implicate the subduction zone deformation.Particularly how those could be related to plate bending.The merit of our work thus lies in the addressing of the effect of damage on the brittle deformation of saturated mafic and ultramafic rocks for the first time and their implications on the subduction zone brittle deformation.

Methods
The deformation experiments were conducted in the triaxial apparatus at the Department of Earth and Planetary Systems Science of Hiroshima University.For the current investigation, we employed a new multi-channel feedthrough system that accommodates 16 channels.Oppose to the previous 8 channel system which allowed either only the seismic velocity measurements (Akamatsu et al., 2019;Jayawickrama & Katayama, 2023) or seismic velocity and electrical resistivity measurements simultaneously (Katayama et al., 2023), the new design allows the measurement of higher number of rock properties simultaneously (i.e., seismic velocity, electrical resistivity, and strain).This increases the possibility of detailed analysis of rock deformation.Since cracks have different effects on various geophysical properties, such simultaneous measurements are critical.
The experiments were performed on cylindrical core samples with a diameter of 20 mm and a height of 40 mm, each cored from the respective peridotite (Horoman, Japan) and diabase (Rydaholm, Sweden) blocks.A detailed description of the sample properties is given in Jayawickrama and Katayama (2023).To induce damage, the peridotite and diabase samples were thermally cracked under 600°C, and 800°C, respectively.With thermal cracking, both samples generated a porosity of 1.2% and this was significantly higher compared to their intact porosity (Diabase: 0.17%, Peridotite: 0.16%).Subsequently, the strain gauges were glued parallel to each other on the polished cylindrical surface, and the transducers for measuring velocity were glued in the direction normal to the strain gauges.In the current investigation, to ensure full saturation, we pre-saturated the prepared samples for 10 days, by dipping them in a 0.5 mol/l NaCl solution, as it is proven sufficient by Nagase et al. (2020).The deformation experiments were conducted under a confining pressure of 30 MPa and an effective pressure of 20 MPa to ensure brittle deformation.Despite the applied pore pressure (10 MPa), to minimize dilatancy hardening, we axially compressed the sample at a strain rate of 2 × 10 6 s 1 and recorded the ultrasonic waveforms, and impedance and phase angle (at 1 kHz), at every 0.06 mm displacement.The data were recorded within 5-10 s to compute simultaneous ultrasonic velocities, and resistivity of the deforming sample, until the sample failed by fracture.

Mechanical Response
With increasing differential stress both thermally cracked diabase and peridotite showed a highly nonlinear response in strain compared to their intact counterpart (Figure 1).This nonlinearity is generated due to the compliance introduced to the rock by the high population of compliant thermal cracks.While the axial (ε a ) and radial (ε r ) strains were computed by averaging the directly recorded strains from the two strain gauges, the volumetric strain (ε v ) was calculated as ε a + 2ε r .Subsequent to the initial compaction, the thermally cracked samples dilated as indicated by the deviation in volumetric strain from linearity, which is typical of brittle deformation (Brace et al., 1966).Since it is challenging to identify a linear section in the stress-strain response of the thermally cracked samples, we have estimated the onset of dilatancy (C′) (the stress at which volumetric strain deviates from the linearity) from a linear trace between 20% and 30% of the peak stress (C), as C′/C is generally close to 0.35 for slow loading rates (Brace et al., 1966).The same procedure was followed to obtain C′ of intact samples.As estimated, C′ of the thermally cracked rocks appear much earlier than their respective intact rocks, and C′ of the damaged diabase appears earlier than the C′ of the damaged peridotite.While the onset of full transition to dilatancy (D′) can be clearly marked in the thermally cracked samples, that of intact samples cannot be clearly identified due to the undulations in the volumetric strain.The deviation of volumetric strain from the linear trace at C is termed, D, and that of the thermally cracked and intact diabase shows nearly similar values.However, D of thermally cracked peridotite is significantly enhanced with respect to the intact specimen.
The peak strength of diabase shows no significant difference despite the existence of thermal cracks in one sample.That of peridotite on the other hand shows a marked difference as the intact specimen fails at a much lower peak stress.The Young's modulus estimated from the slope between 20% and 30% of C are always higher for the intact rocks, indicating that those are stiffer than the thermally cracked rocks.These results agree with previous investigations performed on thermally cracked granite (Wang et al., 2013).In their investigation, Wang et al. (2013) suggest that the thermally cracked rocks behave as a homogeneous elastic solid with reduced stiffness, and the onset of dilatancy is initiated at a lower stress state due to lower Young's modulus.Both these explanations agree with our result, as the thermally cracked rocks show a homogeneous deformation with a smaller Young's moduli, while the respective intact rocks show significant undulation in the later part of the deformation and yield higher Young's moduli.

Velocity and Electrical Resistivity
The ultrasonic velocity of the axially compressed samples increases until dilation and subsequently drops (Figure 2).While both damaged diabase and peridotites have low ultrasonic velocities with respect to their intact samples, in all samples, V P and V S begins to drop simultaneously with dilation.Among the thermally cracked samples, peridotite agrees well with the C′ identified from the mechanical data (Figure 2b).Diabase however shows a substantial difference to the C′ since velocity drop initiates approximately around 250 MPa.This suggests that despite the onset of dilation, the cracks inclined to the increasing axial stress continue to close.
The electrical resistivities of the thermally cracked rocks are approximately two orders of magnitude lower than the intact rock.Given that electrical resistivity is a measure of crack connectivity and permeability, such difference strongly suggests that the thermal cracks generate an interconnected fracture network, in comparison to the poorly connected preexisting cracks in the intact samples (deMartin et al., 2004;Evans & Clarke, 1980;Fredrich & Wong, 1986).However, close to the peak stress the cracks interconnect and the resistivity drops.As witnessed via thermally cracked samples, the full transition to dilation is subsequent to the onset of this resistivity drop, suggesting that dilation of the samples is dominant only after crack coalescence.
Similar to the measured ultrasonic velocities, the electrical resistivity also increases with initial crack closure and begins to drop mid-way of the stress history.However, there is a slight delay with the onset of the drop with respect to the stress at which the velocity drops.Since velocity is sensitive to crack opening (Fortin et al., 2011;Hadley, 1975;Jayawickrama et al., 2019;Schubnel et al., 2003), and the electrical resistivity is sensitive to crack connectivity (Brace & Orange, 1968;Glover et al., 2000), such delays are hardly a surprise as crack coalescence is obviously subsequent to crack opening.While this is the case for both diabase and the thermally cracked peridotite samples, the velocity drop, and the electrical resistivity drop of intact peridotite initiate around the same differential stress (Figure 2d).

Failure Modes and Peak Strength Dilemma
During brittle deformation, as the rock begins to dilate with crack nucleation and opening (Mode I), pore water gradually penetrates into the new open spaces.In this process, if the crack development is faster than the water inflow, the pore pressure is subjected to drop locally.Consequently, the effective pressure increases, and the sample which initially dilated may compress.The radial contractions of intact diabase around 400 MPa in Figure 1c facilitate crucial evidence for such behavior (Figure S1 in Supporting Information S1).This phenomenon is dilatancy hardening.Despite our efforts to minimize this effect with long saturation times and slow strain rates, the intact samples still tend to be susceptible to this effect.Since we believe that saturation is sufficient, further slower strain rates might negate dilatancy hardening (However, the time scale of the deformation Geophysical Research Letters 10.1029/2023GL106576 might generate difficulties in performing series of experiments).Subsequent to initial dilatancy hardening, with crack coalescence, the pore pressure begins to distribute homogeneously, and the sample produces a significant amount of dilation prior to failure.The discussed behavior in stress can also be noticed in the resistivity profile (Figure 2c) where a local increase is registered around 400 MPa during the global drop in the resistivity profile.This sudden increment well aligns with the contraction in Figure 1c.
Noticeably, despite such undulations and difference in the existence of damage, the peak strengths of the two diabase samples are nearly similar (545 ± 20 MPa).This result cannot be explained by the existing wing models, which generally approximate the brittle deformation of rocks (Ashby & Hallam, 1986;Ashby & Sammis, 1990).This is because the wing crack model has a dependence on the number of flaws embedded, as a body with more flaws essentially should fail earlier due to crack interaction, than a body with a single flaw (Ashby & Sammis, 1990).

10.1029/2023GL106576
The contradicting result of diabase to this general acceptance suggests that peak stress may be controlled by other means such as intrinsic cracks and stress shielding as previously proposed by Wang et al. (2013).Stress shielding is the effect which is caused on other cracks' propagation by the stress field induced by the propagation of a neighboring crack tip.The effect which is caused by the intrinsic fractures is generated by their stiff nature in comparison to the compliant nature of thermal cracks that close upon a small increase in differential stress.The relative difference in velocity increment in the thermally treated diabase and the intact diabase until the onset of dilation clearly show this effect caused by the difference in stiffness of the fractures.The rapid increment in velocity of damaged sample (Figure 2a) is due to the rapid closure of thermal cracks which are more compliant, and slow increment in velocity of intact sample (Figure 2c) is due to the slow closure of stiff intrinsic cracks.Therefore, once the thermal cracks are rapidly closed, the subsequent deformation is essentially dominated by the intrinsic fractures while shielding the propagation of thermal cracks that open later.Therefore, the stiff nature of intrinsic fractures (Figure S2 in Supporting Information S1) essentially dominates the deformation of the sample, hence the peak stress.This however is not the outcome of intact peridotite as the sample failed at a significantly low peak strength with a noticeable minor dilation.Note that peridotites are rich in olivine, and grain boundary sliding is commonly identified in olivine (Marquardt & Faul, 2018).Therefore, we postulate that the non-dilatant deformation is due to the shear cracking (Mode II) along the olivine grain boundaries.Dominated by Mode II crack propagations, the intact peridotite also exhibits radial contractions indicating the effect of pore pressure heterogeneity which ultimately leads to an earlier failure compared to the thermally cracked sample.However, the deformation of the thermally cracked sample is dominated by Mode I opening of thermal cracks that produce a higher inelastic volumetric strain and distribute pore pressure homogeneously leading to a higher peak stress.As such, we propose that, in addition to stress shielding and preexisting cracks, the pore pressure distribution and mode of crack opening also affects the attained peak strength of the rocks.

Static Versus Dynamic Elastic Moduli
The apparent difference between the static modulus, estimated from the slope of the stress-strain response, and the dynamic modulus estimated from the ultrasonic velocities has been explained by the poroelastic theory (Zimmer, 2003;Zoback, 2007).In accordance with the exact effective stress law proposed by Nur and Byerlee (1971), the pore pressure has a maximum influence on the rock behavior when the cracks and pores are interconnected.Upon quasi static loading fluid within such interconnected networks drains gradually.However, when an ultrasonic wave propagates, the fluid within the cracks is unable to dissipate the stress which builds up due to insufficient time.Thus, behaves as an undrained system.This transition from a drained to an undrained system depends on the viscosity of the fluid and the interconnectivity of the pore and fracture network (Dvorkin et al., 1995).Hence, rocks with fluid filled cracks momentarily acts stiffer as the fluid pressure contributes to the rock stiffness.As a result, the dynamic Young's modulus of thermally cracked rocks is higher than their static estimations (Figure 3a).In the studied rocks, the dynamic modulus is about 1.4 times the static modulus.The intact rocks, however, where the pore pressure effect is nearly negligible (Nur & Byerlee, 1971), the effect caused by the fluid vibration is weak, mainly due to the poor fracture connectivity.Therefore, their static modulus is relatively similar to the dynamic estimation (±10 GPa).A similar relationship can be found for most of the rocks investigated by Davarpanah et al. (2020), who empirically derived relationships between dynamic and static moduli for various rock types.These relationships are very valuable in various geomechanical and geophysical aspects.However, our investigation has shown that when significant damage is present, there is a clear difference between the ratio of dynamic and static Young's modulus of damaged and undamaged rocks.Hence it is possible that such empirical derivations might not always be able to capture the relationship between the moduli accurately.Therefore, one must handle such relationships with care when applying their outcome in geomechanical and geophysical modeling.Walsh (1965) on the other hand suggested that this difference between the dynamic and static Young's moduli could be approximated by a stress oscillation that is superimposed on the applied stress.In that investigation, Walsh (1965) schematically showed that at a point along the stress history, the sonic wave vibration generates a small stress oscillation and the average slope estimated from the oscillating stress path is larger than the slope generated by the static stress-strain response.Hence, the Young's modulus's dynamic estimation is larger than its static estimation.Therefore, it is apparent that the stress state of the rock is strongly affected by the sonic vibration, that is, by the frequency of the passing wave.As such, depending on the frequency of the wave, the effect that is caused on the dynamic modulus is critical.For example, under seismic (10-50 Hz) or well logging (∼10 kHz), since the frequencies are lower, the pressure build up within the fluids are relatively lower hence the added stiffness is lower.Thus, the in situ velocities are bound to be lower than the laboratory derived sonic wave velocities.Therefore, one should always be cautious about the effect of wave frequency when comparing the laboratory data with geophysical data and implementing laboratory data on geophysical model constructions.

Implications on Plate Bending
As the relatively intact oceanic lithosphere approaches the subduction zone and begins its descent into the mantle, the plate suffers enormous amounts of damage as implicated by anomalies in geophysical observations such as, V P / V S ratios and electrical resistivities.Previous investigations have shown that the number of bending related faults increase toward the trench (Grevemeyer et al., 2018;Naif et al., 2015;Ranero et al., 2003) and such faulting significantly increases damage creating conduits for fluid infiltration.This ultimately increase the crustal and mantle V P /V S ratios due to fluid filled fractures and enhanced serpentinization, respectively.A classic example for crustal V P / V S anomalies can be found in Fujie et al. (2013), where they showed the lateral variation of V P /V S ratio in the upper crust systematically increases toward the Kuril trench.This evolution is consistent with our laboratory V P /V S evolution against the crack density (Akamatsu et al., 2021;Fortin et al., 2011;Sayers & Kachanov, 1995) as both, damaged peridotite and diabase show an increase in the V P /V S ratio with increasing damage (Figure 3b).In addition, the resistivity profiles captured from the Nicaragua trench indicate a reduction in orders of magnitude close to the trench and the outer rise (Key et al., 2012;Naif et al., 2015).These anomalies are strong indications of the fluid filled pervasive damage suffered by the incoming plate.
The current study has shown that the presence of fluid filled damage in mafic and ultramafic rocks reduce their Young's moduli in comparison to intact rocks and deforms as a homogeneous elastic body due to the introduced compliance by damage (Figure 1).According to previous investigations (e.g., Caldwell et al., 1976), the Young's modulus is directly related to the flexural rigidity of rocks.Therefore, as evident by our results, presence of damage in the trench outer rise leads to low flexural rigidity despite the unaffected ultimate strength.Hence bending of the plate is escalated with extensive damage accumulation at the trench outer rise.Such escalated bending has in fact been reported by Protti et al. (1995) where seismic events beneath Nicaragua and Costa Rica have been mapped and identified steep dipping plate segments in regions where a large number of seismic events are reported.Therefore, we presume that fluid filled damage contributes to the formation of a steep dipping angle via a positive feedback loop.That is, the damage created by faulting at the trench outer rise assists the bending by reducing the stiffness while the bending itself further strains the trench outer rise leading to more breaking in the plate.Yet it is unknown which triggered the other.That is whether bending created damage or whether damage led to bending.Despite this chicken and egg situation where both phenomena are important, as enlightened by our results, fluid filled damage is a sole necessity for the elastic deformation of a rigid rock body.
Moreover, the results show that cracked fluid saturated rocks promote homogeneous elastic deformation due to the introduced compliance by damage.The nonlinear deformation and the attained inelastic volumetric strain (D in Figure 1) of the two damaged samples provides comprehensive evidence for this.Note that the relative The symbols indicate the dynamic values estimated from the ultrasonic velocities and the values given indicate their static estimations from the stress-strain response.In the thermally cracked samples, the dynamic Young's modulus is always higher than the static estimation while the intact samples have nearly similar values.(b) The V P /V S evolution against crack density until the failure of thermally cracked samples.With initial crack closure and the dehydration of the samples, V P /V S decrease and begins to increase with increasing differential stress as cracks open and samples dilate.

Geophysical Research Letters
10.1029/2023GL106576 difference of D in the two damaged specimens (Figures 1a and 1b) is merely a reflection of the strains recorded by the gauge.Postmortem investigation (e.g., Jayawickrama et al., 2021Jayawickrama et al., , 2022) ) of the thermally cracked samples by X-ray computed tomography (Figure S3 in Supporting Information S1) has revealed that the peridotite has failed dominantly along a single shear plane that lies approximately 30°to the axial stress (typical of brittle failure) while multiple fracture planes are observed in the diabase.Regardless, the contrasting compliant nature and the low Young's modulus of the damaged rocks can be related to the difference in bathymetric profiles studied by Caldwell and Turcotte (1979) that demonstrated an increase in the topographic heights attained by the trench outer rise with the aging of the plate.That is, with more damage accumulated in the old plates at the trench outer rise, they possess the capacity to deform with more elasticity in comparison to the young plates with less damage.Such deformation in damaged rocks leads to larger volumetric expansion than that of which the young plates with less damage could achieve.As a result, the old plates reach greater heights at the trench outer rise, than the young plates.

Summary
In this study, we investigated the brittle deformation of damaged mafic and ultramafic rocks while measuring the strains, ultrasonic velocities, and electrical resistivities.The damaged rocks showed a significant amount of dilation which is directly comparable to the deformation mode.We also suggest that the pore pressure distribution within the rock has a significant effect on the stress state of the rock influencing the peak strength and the dynamic properties of the rock.The ultrasonic velocity, and electrical resistivity evolutions were strongly influenced by the presence of damage.Their evolution and the inelastic volumetric strain attained by damaged rocks could clearly be correlated to the geophysical observations of an incoming plate that undergoes strong structural alterations and deformation in the trench outer rise system.

Figure 1 .
Figure 1.The stress-strain response of deformed samples.The thermally cracked (a) diabase and (b) peridotite show a significant nonlinear response in axial strain with initial crack closure and subsequent crack opening.The zoom in box shows the nonlinear response in volumetric strain.The stress-strain response of intact (c) diabase with a zoom in box on the undulation and (d) peridotite show clear undulations which occur due to the pore pressure heterogeneity rising through the deformation.The dashed line is the trace of the elastic response taken as the reference for inelastic strain.The positive strains indicate compressions, and the negative strains indicate the extensions.Note that the open symbols indicate the assumed C′ and D′.C′: Onset of dilatancy; D′: Full transition to dilatancy; C: Peak stress; and D: Deviation of volumetric strain from the linear trace at C.

Figure 2 .
Figure2.The velocity and electrical resistivity evolution of deformed rocks.Thermally cracked (a) diabase and (b) peridotite have relatively low velocities and electrical resistivities with respect to the intact (c) diabase and (d) peridotite samples.Because of the presence of fluid filled cracks, a systematic evolution of the velocity and electrical resistivity is present in the damaged rocks.Subsequent to the initial crack closure, the velocity begins to drop with crack opening and the electrical resistivity begins to drop with crack coalescence.Please note that only the confident estimations of C′ and D′ have been marked.

Figure 3 .
Figure 3. (a) Static and dynamic Young's modulus of the deformed samples.The symbols indicate the dynamic values estimated from the ultrasonic velocities and the values given indicate their static estimations from the stress-strain response.In the thermally cracked samples, the dynamic Young's modulus is always higher than the static estimation while the intact samples have nearly similar values.(b) The V P /V S evolution against crack density until the failure of thermally cracked samples.With initial crack closure and the dehydration of the samples, V P /V S decrease and begins to increase with increasing differential stress as cracks open and samples dilate.