Laboratory Acousto‐Mechanical Study Into Moisture‐Induced Reduction of Fracture Stiffness in Granite

Water infiltration into fractures is ubiquitous in crustal rocks. However, little is known about how such a progressive wetting process affects fracture stiffness and seismic wave propagation, which are highly relevant for characterizing fracture systems in situ. We study the acousto‐mechanical behavior of a free‐standing fractured granite subjected to gradual water infiltration with a downward‐moving wetting front over 12 days. We observe significant differences (i.e., by an order of magnitude) in wave amplitudes across the fractured granite compared to an intact granite, with both cases showing a strong correlation between wave amplitudes and wetting front movement. Effects of water infiltration into the fracture and surrounding matrix on seismic attenuation are captured by a numerical model with parameters constrained by experimental data. Back‐calculated fracture stiffness decreases exponentially with the wetting front migration along the fracture. We propose that moisture‐induced matrix expansion around the fracture increases asperity mismatch, leading to reduced fracture stiffness.

relationship among water imbibition, seismic attenuation, and stiffness evolution in a wetted fracture • Wave amplitudes across a fracture correlate strongly with the wetting front movement of infiltrated water within the fracture • Fracture stiffness exponentially decreases with the advance of the wetting front along the fracture Supporting Information: Supporting Information may be found in the online version of this article.Schoenberg, 1980;Scuderi et al., 2016;Shokouhi et al., 2020;Shreedharan et al., 2020Shreedharan et al., , 2021;;Tinti et al., 2016).Among these studies, fractures are modeled as non-welded interfaces consisting of contact patches and adjacent voids (Archard, 1957;Bowden & Tabor, 2001;Greenwood & Williamson, 1966;Johnson, 1985;Tsang & Witherspoon, 1981).Along interfaces, real contact area via distributed patches is small, for example, less than 10%, compared to the nominal contact area (Dieterich & Kilgore, 1994;Persson, 2006).As elastic waves travel through the real contact area, the displacement field is discontinuous, whereas the stress field remains continuous (Kendall & Tabor, 1971;Pyrak-Nolte et al., 1990;Schoenberg, 1980).The ratio of stress to displacement discontinuity defines fracture stiffness that controls the amount of transmitted wave energy.When the fracture is subjected to increased normal stress, the separation distance between the fracture walls decreases and the real contact area increases, leading to increased fracture stiffness.The real contact area, which is approximately proportional to the fracture stiffness, behaves akin to a "filter," allowing high-frequency wave contents to pass through the fracture (Pyrak-Nolte et al., 1990).
Laboratory investigations have focused on the mechanical response of fractured rocks, either dry or saturated, subjected to compression or shear, as examined through ultrasonic waves (Choi et al., 2014;Kame et al., 2014;Nagata et al., 2008;Pyrak-Nolte et al., 1990;Shreedharan et al., 2020).Little attention has been paid to fractured rocks undergoing progressive wetting due to spontaneous water imbibition which is important in nature.Previous studies (David, Barnes, et al., 2017;David, Sarout, et al., 2017;Wu, Selvadurai, Li, Sun, et al., 2023) revealed substantial variations in wave amplitudes as the wetting front progressively infiltrated an intact specimen.These elastic changes could be explained by the elastic wave refraction at the wetting front, which delineates the transition between the dry and wet regions (Knott, 1899;Kovalyshen, 2018;Zoeppritz, 1919).In this research, we further investigate water imbibition in a fractured specimen, aiming to understand the relationship between progressive wetting, wave transmission, and stiffness evolution.

Specimen Preparation and Experimental Setup
In Figure 1a, we generate a semi-planar fracture in a notched beam subjected to a three-point bending test via a constant displacement rate of 1 μm/s.As the load approaches the peak strength (14.4 ± 0.5 kN) and subsequently exhibits a reduction greater than 5% of its peak strength, a servo-controlled failure detection will promptly relieve the load.This prevents the beam from being fully broken such that it is supported by rock bridges across the fracture.The fracture produced has an opening of about 0.05 mm near the notch, measured with a crack gauge, and is barely visible at its tip, about 16 mm from the bottom of the beam.A prismatic specimen (dimension: 65 × 35 × 90 mm), containing part of the fracture, is extracted from the central part of the beam (Figure 1a).
We perform water imbibition tests on this extracted specimen placed in a free-standing state.The specimen is oven-dried at 80°C and then acclimated to ambient laboratory conditions for 16 hr.Subsequently, distilled water is introduced to the top surface of the specimen via a filter paper that is immersed in a water reservoir where the water table is maintained for 270 hr.Bond number, a dimensionless parameter comparing the gravitational to capillary forces (Su et al., 1999), is calculated to be below 2 × 10 −3 for matrix (estimated from average pore size of below 100 nm) and above 0.2 for fracture (estimated from average opening of above 0.01 mm).Thus, as the specimen is gradually wetted from top to bottom, the wetting process in the matrix is dominated by the capillary force.In contrast, the wetting process in the fracture is governed by both capillary and gravitational effects.

Time-Lapse Acousto-Mechanical Monitoring
We utilize time-lapse digital image correlation (DIC) and ultrasound techniques to investigate the acousto-mechanical response of the fracture under gradual wetting.Monitoring methods are detailed in Text S2 in Supporting Information S1.Acoustic changes are measured using ultrasonic pulse transmission (Birch, 1960).
In Figure 1b, a transmitter and a receiver (T-R) are installed on two sides of the specimen.This pair arrangement determines a Fresnel zone-a confocal prolate ellipsoidal region (dashed ellipse in Figure 1b) where direct waves mostly reveal elastic properties of this zone (Spetzler & Snieder, 2004).P-wave first (n = 1) Fresnel zone (P-FFZ) is adopted following the nomenclature in Wu, Selvadurai, Li, Sun, et al. (2023) with its minor axis R 1 given as: where λ is the wavelength and L is the T-R distance (65 mm).Ultrasonic pulses are emitted from the transmitter using a 200 V excitation voltage (P. A. Selvadurai et al., 2022;Wu et al., 2020Wu et al., , 2021)).A survey is conducted every 15 min with 1,144 measurements obtained over 286 hr.In Figure 1c, waveforms acquired at 20 MHz are aligned at the trigger time (before: 4.7 μs, after: 97.7 μs).Direct waves are windowed within 20 μs (gray box) centered around the P-wave arrival in Figure 1d.The first peak amplitude is stable at around 1 mV before moisture uptake (gray), reduces significantly after 72 hr of the introduction of water (black to yellow), and eventually fades to the noise level (below 0.15 mV).The high-frequency content is dissipated during the moisture uptake as the waveform is observed to "broaden" (green inset).The ultrasonic data acquisition and processing, including P-wave arrival picking, frequency bandwidth selection (500-700 kHz), and amplitude calculation, is detailed in Texts S2 and S3 in Supporting Information S1.
Besides ultrasonic monitoring, the frontal surface of the specimen is simultaneously imaged with a digital camera at 30-min intervals over 286 hr (Figure 1b).The acquired images are processed to calculate the strain field (Text S4 in Supporting Information S1) and track the wetting front movement (Text S5 in Supporting Information S1).

Results
Amplitude changes (ΔT f ) of the direct waves (Figure 1d) are analyzed over the entire experimental period, focusing on the gradual wetting phase.In Figure 2a, ΔT f (red) is isolated over 150 hr (140 hr under progressive wetting).The beginning of the wetting phase (0 hr) is associated with introduction of the water to the top of the specimen.Times corresponding to transitions in ΔT f are marked as times i (2.5 hr), ii (10.5 hr), iii (29.3 hr), and iv (72 hr).The amplitude changes from inverse modeling (blue crosses) will be described later in Section 4.2.
To relate seismic attenuation (ΔT f ) to the wetting process and surface deformation of the specimen, vertical (ϵ yy ) and horizontal (ϵ xx ) strains are shown in Figures 2b and 2c, respectively.The full strain field on the frontal surface is shown for the times of interest in Figure 2a.The Prior to wetting, the specimen is equilibrated under ambient laboratory conditions with less than 0.15 dB variation of ΔT f .After the water is introduced, the wetting front moves downward and enters into the P-FFZ of 500 kHz, and the fracture begins to open at time i with an observed increase in ΔT f of 3 dB.A wetting channel, nearly symmetric around the fracture, is formed and migrates downward, for example, reaching a depth of about 55 mm and a width of about 8 mm at time ii.This channel is much ahead (by around 30 mm) of the wetting front in the matrix which reaches a depth of approximately 22.5 mm at time ii.The channel serves as a source for the surrounding matrix to imbibe due to the greater capillary forces in the microcracks which have a much smaller aperture than the macroscopic fracture.Consequently, a significant amount of horizontal strain is observed within the wetting channel with an average magnitude of 300-400 μϵ.There is a monotonic decrease in ΔT f from 3 dB at time i to −26 dB at time ii.
After time ii, the wetting front migrates to the lower part of P-FFZ and leaves P-FFZ completely at time iii.ΔT f remains stable at −26 ± 0.6 dB.As the wetting front continues to migrate downward and reaches the middle part (about y = 48 mm) at time iv, the wetting channel appears to stagnate at a depth of 65 mm.This may be because the fracture aperture decreases significantly, hindering moisture transportation.ϵ xx within P-FFZ evolves significantly while ΔT f decreases from −26 to −48 dB.After time iv, the direct waves are difficult to distinguish from the noise (see Figure 1d) until the end of the test.The ΔT f evolution over the whole experimental period is provided in Figure S5 in Supporting Information S1.

Effect of Progressive Wetting on Elastic Wave Transmission Across a Fracture
We analyze the influence of progressive wetting on the amplitude variations of the elastic waves transmitted across the fracture.We plot the amplitude variations (ΔT f , originally in Figure 2a) in response to the vertical movement of the wetting front (detailed in Text S5 in Supporting Information S1) in Figure 3a.The vertical position of the T-R raypath is taken as the baseline.We also show the amplitude changes (ΔT i , blue) of an intact specimen for comparison (Figure 1a).The purple area shows the differential region of the P-FFZ between 500 and 700 kHz.
Both ΔT f and ΔT i show some similarities in their responses.Amplitude changes are simultaneously amplified to a peak as the wetting front crosses the upper boundary of the P-FFZ at 500-700 kHz (time i).The similarity could be interpreted by the elastic wave reflection/refraction surrounding the P-FFZ in the bi-layered medium, where an interface between two layers is defined by the wetting front (Knott, 1899;Kovalyshen, 2018;Wu, Selvadurai, Li, Sun, et al., 2023;Zoeppritz, 1919).In Figure 3b, the incident P waves arrive at the wetting front at time i, and are converted into refracted P (denoted as Pp) and S (denoted as Ps) waves.Since the wetted part has a higher acoustic impedance (Z p = 1.21 × 10 7 Pa ⋅ s/m 3 ) compared to the dry part (Z p = 1.08 × 10 7 Pa ⋅ s/m 3 ), the refracted waves remain in phase with the direct P-waves propagating along the T-R path and contribute to the synthesized waveform.This explains the amplification observed in ΔT f and ΔT i at time i.When the wetting front arrives at the position of the T-R raypath at time ii, there is a phase shift of 180° between the refracted and direct P-waves.This explains the monotonic decrease of ΔT f and ΔT i from time i to ii.
However, the three notable deviations between ΔT f and ΔT i indicate the effect of the fracture.Before time ii, ΔT i exhibits more prominent variations compared with ΔT f .This occurs because the refracted waves at the wetting front undergo seismic attenuation while traveling across the fracture.If these attenuated refracted waves are in or out of phase with the direct P-waves, ΔT f will show less variation.
After time ii, the refracted waves remain out of phase with the direct P-waves but their amplitudes decrease to the incident angle as the wetting front progresses.Consequently, when refracted waves are synthesized with direct P-waves in the intact rock, a partial recovery of ΔT i is observed.In contrast, ΔT f shows little variation.We propose that the enhanced seismic attenuation across the progressively wetted fracture offsets the recovery in the intact rock.
After time iii, ΔT i generally plateaus as the elastic properties within the P-FFZ become more homogeneous.However, ΔT f decreases significantly until it becomes indistinguishable from the noise.This indicates that the fracture remains an active role, making it difficult for the elastic waves to transmit.

How Does Fracture Stiffness Vary Due To Gradual Wetting?
The fracture can be modeled as a non-welded interface, characterized by contact asperities and adjacent voids (Johnson, 1985;Persson, 2006;Tsang & Witherspoon, 1981).Across the fracture, stress remains continuous, but displacement is discontinuous (Cook, 1992;Pyrak-Nolte et al., 1990;Schoenberg, 1980).For P-waves incident  (Wu, Selvadurai, Li, Sun, et al., 2023), in response to the wetting front migration.(b) Top: Representative waveforms.Bottom: Schematic illustration of elastic wave interaction with the fracture associated with a migrating wetting front.
normal to the fracture, the ratio of normal stress to displacement discontinuity across the fracture gives the specific normal stiffness, κ n .The magnitude of the transmission coefficient, |T(ω)|, responds to κ n : where ω and    are the angular frequency and dimensionless angular frequency, respectively.As κ n approaches infinity, |T(ω)| becomes unity, indicative of the absence of a fracture.For our analysis, |T(ω)| of the intact dry specimen is set to unity.For the fractured specimen, despite small deflection (less than 2°), we assume the fracture to be vertically planar, allowing the application of Equation 2. Following these assumptions, we measure |T(ω)| as 0.2 and calculate     as 4,320 GPa/m for the dry fracture (orange circle in Figure 4a).We decipher the evolution of the fracture stiffness,     , as the fractured rock undergoes progressive wetting.By directly inserting ΔT f into Equation 2, we observe that     (black dotted line in Figure 4b) decreases completely by over two orders of magnitude since the water reaches the top end of the fracture (Y f = 0).Y f denotes the wetted depth of the fracture.Derived     may be subject to some bias, as the refraction of elastic waves at the migrating wetting front could affect ΔT f .We further develop an inverse model with parameters constrained by experimental data.A 2D finite element model, simulating elastic wave propagation in a bi-layered fractured medium, is constructed in Figure S7 in Supporting Information S1.The fracture is represented by a non-welded interface assuming uniform stiffness.The wetting front, which we assume to be flat and sharply defined, is modeled as a welded interface (Knott, 1899;Kovalyshen, 2018;Wu, Selvadurai, Li, Sun, et al., 2023;Zoeppritz, 1919) with the parameters constrained by the water imbibition test of the fractured specimen.The fracture stiffness is calibrated by minimizing the discrepancy in amplitude changes between numerical and experimental waveforms (see their close match in Figure 2a).The modeling methodology is detailed in Text S7 in Supporting Information S1.
In Figure 4b, the back-calculated stiffness     (orange solid line) evolves from     = 4,320 GPa/m at time i and exponentially decays as the wetting front progressively migrates downwards.The difference in     between inverse modeling and experiment up to time iii indicates the effect of wetting front movement on the elastic wave transmission across the fracture.The Pearson correlation coefficient between  ln   (inverse modeling) and Y f is 0.98 at 95% confidence level, indicating a strong correlation.An empirical relationship between     and Y f is obtained as: and shown as blue dashed line in Figure 4b.a is a constant, taking 0.1444 for our specimen.
Once the wetting front completely passes the P-FFZ (time iii), no elastic wave reflection/refraction occurs at the wetting front.Consequently, the wetting front will no longer affect the amplitude; thus,     from the inverse modeling (orange solid line) and experiment (black dotted line) are observed to agree well (Figure 4b) which will be further discussed in Section 4.3.After time iv, the waveforms are completely immersed in the background noise (Figure S1b in Supporting Information S1), and     eventually stabilizes at around 17 ± 2 GPa/m (Figure 4b).The implementation of such an inverse modeling methodology allows us to better determine the moisture-dependent fracture stiffness.

Why Does Fracture Stiffness Decrease as the Wetting Front Migrates Along the Fracture?
The exponential decay of fracture stiffness with the wetting front migration (Figure 4b and Equation 3) highlights inherent relationships among the water imbibition, mechanical deformation, and seismic attenuation of a single wetted fracture (Figure 4c).Along the rough interfaces, there is a sparse set of dilute contacts at different length scales (Persson, 2006).During water imbibition, the adsorption of water molecules onto the contact patches at asperities leads to a reduction in the free surface energy of the asperity minerals, followed by a volumetric expansion at the asperities (Dobrzanski et al., 2021).This causes an increased separation distance between the opposing walls and a decreased real contact area.As a result, the mechanical interactions at these asperities become less intense (analogous to a release of contact force) and the total number of asperities in contact decreases.At the macroscopic level, as the wetting front progresses along the fracture, the opposing rough walls tend to separate, decreasing the fracture stiffness.When elastic waves impinge almost normally on the fracture and transmit through the reduced contact area, more high-frequency, short-wavelength elastic waves are reflected where some low-frequency, long-wavelength portions can still pass through.
At ultrasonic frequencies, elastic waves through wetted microcracks can generate local pressure gradients, resulting in fluid flow and viscous dissipation (Müller et al., 2010).This wave-induced flow could lead to decreased fracture stiffness and wave transmission.Imbibed water may also aid the contact by volumetrically filling the fracture voids, thereby promoting transmission, as observed for saturated fractures under compression (Pyrak-Nolte et al., 1990).These processes however are expected to have minor effects on our results.
In this work, we have experimentally derived a formulation to describe the seismo-hydro-mechanical behavior of wetted single fractures under tension, which opens the door to use seismic waves for characterizing fracture geometry and tracking water infiltration along fractures, which play an essential role in unsaturated flow in near-surface bedrocks (Pruess, 1999).This could help us better understand and predict landslide behavior that is strongly affected by seasonal rainwater infiltration into basal shear zones (Finnegan et al., 2021(Finnegan et al., , 2022)).Useful insights can also be yielded into the spatiotemporal evolution of fracture stiffness in unsaturated bedrocks, which may play an important role in groundwater recharge-induced reversible ground surface displacements (Oestreicher et al., 2023) and landslide motion driven by moisture changes (Whiteley et al., 2019).The experimentally derived formulation in our study can be combined with the discrete fracture network modeling approach (Lei & Sornette, 2021a, 2021b) and seismic attenuation modeling in unsaturated fractures (Solazzi et al., 2020) to unravel and predict the seismo-hydro-mechanical behavior of complex fracture systems subject to water infiltration in near-surface environments.We will explore these topics in our future work.

Conclusions
Based on well-controlled laboratory experiments, we investigated the relationships among water imbibition, mechanical deformation, and seismic attenuation in single fractures subjected to tension and progressive wetting.We found that wave transmission strongly correlates with the wetting front movement of infiltrated water along the fracture where significant attenuation occurs since adsorption-induced expansion at asperities reduces the real contact area and the number of contact patches.As a result, less seismic energy can be transmitted across the fracture whose stiffness undergoes moisture-dependent weakening.Using an inverse modeling approach, we found the fracture stiffness follows an exponential decrease over about two orders of magnitude with the wetting front position as it moves along the fracture.Our results, elucidating the strong control of water infiltration on seismic wave propagation in fractured rocks, have important implications for many geophysical and geoengineering applications.

Figure 1 .
Figure 1.Schematic of the experimental setup.(a) A free-standing granite prism containing a fracture (gray curved plane) undergoing progressive wetting.(b) Acousto-mechanical monitoring using digital image correlation and ultrasonic pulse transmission.(c) Stacked waveforms received over a 16-hr drying stage followed by a 270-hr wetting stage.(d) Direct waves centered around the P-wave arrival within a time window of 20 μs.

Figure 2 .
Figure 2. (a) Amplitude changes of direct waves in response to the wetting process, obtained from the experimental measurement (red solid line) and inverse modeling (blue crosses).Vertical blue lines indicate the main turning points of amplitude changes.(b) Vertical strain ϵ yy and (c) horizontal strain ϵ xx evolution on the frontal face of the specimen as the water is introduced.Black solid line denotes the location of the fracture.
ϵ yy evolution indicates the history of the moisture profile in the matrix, while the ϵ xx evolution indicates the deformation history of the material surrounding the fracture.Strain contour at 100 μϵ (white dashed line) is chosen to delineate (a) the movement of the wetting front in the host rock using ϵ yy and (b) the fracture deformation using ϵ xx .The ellipses show the size (minor axis R 1 of approximately 12.5 and 10 mm) of P-FFZ at 500 and 700 kHz.A white area (dimension: 9 × 7 mm) near the top surface is the notch used to create the fracture in the bending test, for which DIC results are not available.The black line around the central region indicates the fracture profile.

Figure 3 .
Figure3.(a) Amplitude changes in the fractured (red) specimens, compared with the intact (blue) specimen(Wu, Selvadurai, Li, Sun, et al., 2023), in response to the wetting front migration.(b) Top: Representative waveforms.Bottom: Schematic illustration of elastic wave interaction with the fracture associated with a migrating wetting front.
Measurements and calculations of     are detailed in Text S6 in Supporting Information S1.If κ n decreases while Z p and ω maintain, |T(ω)| will decrease.According to Pyrak-Nolte et al. (1990), there is no effect of viscous coupling from the water on |T(ω)| of incident P-waves normal to the fracture.

Figure 4 .
Figure 4. (a) Variations of the transmission coefficient for incident P-waves normal to the fracture as a function of the fracture specific normal stiffness, κ n .(b) Evolution of fracture stiffness subject to gradual wetting derived from inverse modeling (orange) and direct ultrasonic measurements (black).(c) Schematic showing the inherent relationships between the water imbibition, mechanical deformation, and seismic attenuation of a single wetted fracture.
for their hardware and software support for this research.R.W. and Y.L. are financially supported by the Chair of Engineering Geology and China Scholarship Council.This work is supported by the Swiss National Science Foundation R'Equip (Project 170746 and 170766).Q.L. is grateful for the support from the Swiss National Science Foundation (Grant 189882) and the National Natural Science Foundation of China (Grant 41961134032).Partial funding for P.A.S. is provided by the European Research Council (ERC) project FEAR (Grant 856559) under the European Community's Horizon 2020 Framework Programme.Grant from CCTEG Coal Mining Research Institute, China (Grant KCYJY-2024-SYS-01) is thanked.We acknowledge valuable discussions on the (a) numerical simulations in COMSOL Multiphysics with Chenxi Zhao and Dr. Shuaifeng Wang and (b) P-wave arrival picking with Dr. Peidong Shi.