Impact of stylolite cementation on weathering rates of carbonate rocks

The weathering of carbonate rocks plays a significant role in the evolution of Earth’s surface. Such weathering is often accelerated by the presence of stylolites, which are rough, serrated surfaces that form by dissolution under burial or tectonic stresses. Stylolites are thought to represent zones of mechanical weakness in rocks, as well as regions in which chemical weathering is enhanced. However, a quantitative framework capable of predicting how stylolites accelerate weathering in carbonates has yet to be achieved. In this study, we first used scanning electron microscopy and wavelength dispersive spectroscopy to characterize the way in which the two sides of individual stylolites connect at the micrometer scale. In the samples we examined, we found that tiny calcite bridges span the opposing sides of the stylolites, effectively cementing the rock together. This cement filled 1–30% of the stylolite volume. We then used a numerical cellular automaton model to simulate the effect that different degrees of carbonate cementation have on stylolitic carbonate rock weathering. Our results show that weathering rates decrease non-linearly as the degree of stylolite cementation increases. The effect on overall rock weathering rates is significant: stylolite-bearing rocks with 1% cementation weathered as much as 37 times faster than limestone without stylolites, primarily because of accelerated mechanical erosion. Our results indicate that stylolites could be as important as joints and fractures in accelerating carbonate rock weathering and in the development of karst landscapes, potentially making a major contribution to global carbonate weathering.


Introduction
The weathering of carbonate rocks plays a major role in the evolution of Earth's surface.Carbonate rocks comprise 10-20% of Earth's crust (Morse et al. 2007) and cover about 25% of the continental surface (Wang et al. 1999;Goldscheider et al. 2020).On a global scale, the weathering of carbonate rocks is a significant sink for atmospheric CO 2 , contributing to the regulation of both short-term and longterm climate change (Liu et al. 2011(Liu et al. , 2018).On regional and local scales, carbonate weathering can control the evolution of soils and karst landscapes, the composition of groundwater, and the erosion of buildings, sculptures, and historical monuments (Buhmann and Dreybrodt 1985;Doherty et al. 2007).
Like all rocks, carbonate weathering rates are enhanced by the presence of fractures and joints (Goldscheider et al. 2020;Israeli et al. 2021;Zhao et al. 2022;Xu et al. 2022).However, many carbonate rocks also contain stylolites (Larbi 2003;Simpson 2009;Wangler et al. 2016;Aly et al. 2018;Davis 2018), which are rough, serrated surfaces that form by mineral dissolution as a result of diagenetic or epigenetic processes (Rolland et al. 2012;Kaduri 2013;Toussaint et al. 2018).Because stylolites, like fractures and joints, represent planes of discontinuity, they are also expected to accelerate weathering, and this is supported by both field observations and laboratory experiments.For example, at the Western Wall in Jerusalem, Israel, the average erosion rate in stylolitic limestone was found to be over an order of magnitude higher than in rocks that were stylolite-free (Fig. 1; Emmanuel and Levenson 2014;Emmanuel 2015).Similarly, an experimental study that tested the effects of heating and drying cycles on limestone cladding showed 56 Page 2 of 8 that stylolite-bearing rock was 3.5 times more susceptible to erosion than samples without stylolites (Aly et al. 2018).
Enhanced weathering in stylolitic rocks is likely to be the result of both physical and chemical processes.As well as representing planes of mechanical weakness (Simpson 2009;Baud et al. 2016;Koehn et al. 2016;Israeli et al. 2021), stylolites can also serve as conduits for fluid flow that facilitate chemical dissolution and the swelling of clay minerals (Larbi 2003;Wangler et al. 2016).These mechanisms work in concert because mechanical weathering exposes fresh reactive surfaces, while chemical weathering dissolves the mineral phases that bind the rock together.
One of the factors likely to determine the effect that stylolites have on weathering is cementation.While clay minerals, organic matter, and oxide phases often fill the gaps between the opposing sides of the stylolite surface (Rolland et al. 2012;Baud et al. 2016;Aly et al. 2018), calcareous cement plays a critical role in binding the rock together (e.g., Marfil et al. 2005).During the formation of stylolites in carbonate rocks, dissolved calcium carbonate often re-precipitates as cement within or in the vicinity of the stylolites, in micro-fractures, or in vugs.The precipitation of carbonate cement can also be related to diagenetic, epigenetic, and tectonic processes, or related to the penetration of hydrothermal fluids (Marfil et al. 2005;Paganoni et al. 2016;Gomez-Rivas et al. 2022).Such cementation strongly influences petrophysical properties: a recent study on the sealing potential of stylolitic carbonate rocks showed that a high degree of cementation along stylolites reduces permeability (Wu et al. 2022).Although stylolite cementation is expected to control the weathering rates of carbonate rocks, a complete quantitative understanding of this mechanism has yet to be achieved.
In this study, we use high-resolution imaging to characterize stylolite interfaces in calcareous rocks, and we propose a conceptual framework and numerical model to describe the impact of stylolite cementation on carbonate weathering rates.Our model includes the effects of both chemical and mechanical weathering, and simulates the rates of denudation in stylolite-bearing carbonate rocks possessing different degrees of cementation.We compare our results with reported field rates, and we discuss the implications of our analysis for karst formation and global carbonate weathering.

Conceptual model
Our model considers an outcrop of stylolite-bearing carbonate rock exposed to meteoric water that is undersaturated with respect to carbonate minerals.Fluid flows through the rock from one side to the other, and because the permeability of bulk rock is typically much lower than the permeability in the stylolites (Baud et al. 2016;Paganoni et al. 2016;Humphrey et al. 2020), we also assume that the stylolites represent conduits for flow.The rock surrounding the stylolite is assumed to comprise 100% calcareous minerals that can dissolve in contact with a reactive fluid.As it flows, the fluid in the system dissolves some of the calcite in the region directly adjacent to the reaction front, and the flow is slow enough to allow the fluid to reach equilibrium rapidly.No re-precipitation of calcite is allowed to occur.
In our model, we consider stylolites in carbonate rocks to be gaps that are partially filled by micrometer-scale calcareous cement bridges that connect the opposing sides of the stylolite.The remaining components filling the stylolite  Emmanuel and Levenson (2014) gap-clay minerals, metal oxides, organic matter, and voids-physically separate the carbonate cement bridges from one another.However, because these non-carbonate components usually weaken rocks (e.g., Mavko et al. 2009;Kumar et al. 2015), we assume that they do not play a significant role in binding the rock together.We also consider the non-carbonate minerals to be effectively unreactive because their dissolution rates are slower than carbonates by several orders of magnitude under typical weathering conditions (Wilson 2004;Brantley 2008;White and Buss 2014;Bufe et al. 2021).
Our model also assumes that the proportion of carbonate cement filling the stylolite will determine how rapidly dissolution occurs.This can be demonstrated by considering a system with a linear flow field.Mass balance considerations mean that the time, t, taken to dissolve all the carbonate mineral in a finite volume, F, of the stylolite can be approximated by: where V cement is the volumetric fraction of carbonate cement in the stylolite, ΔC is the change in dissolved concentration due to dissolution, q is the flow rate through the finite volume, and v m is the molar volume of the carbonate mineral.Thus, it can be seen that the time taken to dissolve all the carbonate mineral in a finite volume of the stylolite will be proportional to the proportion of cement.In other words, for a given set of environmental conditions, the dissolution rate at the reaction front will be inversely proportional to V cement .Thus, for a limestone in which 10% of the stylolite volume comprises calcite cement, the dissolution rate along the stylolite is 10 times faster than in the rock surrounding the stylolite.Such an approach does not account for the effect of flow on dissolution, although in principle this could be incorporated into the model by calculating the evolving flow field throughout the simulations.
Using this conceptual approach, the volumetric proportion of calcite along the stylolites (V cement ) can vary from zero to unity.In fully cemented stylolites (i.e., V cement = 1), there is no effective difference between the bulk rock and the stylolites, and weathering proceeds as if the rock was stylolite-free.By contrast, when V cement = 0 the rock has no effective cohesion and the rock will disintegrate immediately.However, at intermediate values (i.e., 0 < V cement < 1), the dissolution rate along the stylolites (i.e., perpendicular to the front with the reactive fluid) will be quicker than in the surrounding bulk rock.Because we assume that calcite cement is the only phase holding the opposing sides of the stylolite together, once all the cement surrounding a region of rock is dissolved, the region can become physically detached from the outcrop.The conceptual model described here serves as the basis for the numerical model described in the next section.

Numerical model
To determine the impact of carbonate cementation on weathering in stylolite-bearing rocks, we used a numerical code based on a previously published model (Israeli and Emmanuel 2018).The framework simulates the way a rock surface weathers, both chemically and mechanically, when it is in contact with an unsaturated solution that is dissolving minerals at the fluid-solid interface.In the new simulations presented here, the model rock was assigned a 2D stylolite network pattern (Fig. 2) that was based on the digitization of a stylolite-rich limestone quarry wall from the Avnon Formation in Mitzpe Ramon, Israel (Laronne Ben-Itzhak et al. 2014).
Coded in Matlab ® , the model is based on a cellular automaton algorithm.In our model domain, a 120 cm × 550 cm stylolite pattern is represented by a 1464 × 6710 pixel matrix with a resolution of 145 pixels cm −2 .The pattern is initially segmented into 2 phases: stylolites and surrounding carbonate rock.Each simulation begins by exposing the uppermost rock surface to fluid.The stylolite pixels do not initially contain a fluid phase.
In every simulation, each rock pixel is assigned a characteristic rate coefficient that represents the probability of undergoing chemical dissolution.This characteristic rate coefficient is distinct from a rate constant in chemical kinetics and is dependent on two factors: (i) the proportion of calcite in the pixel (i.e., V cement ); and (ii) the number of neighboring fluid pixels (only pixels that are in direct contact with the fluid can dissolve, and more neighboring fluid pixels will increase the rate of dissolution).Based on these characteristic rates, the algorithm determines stochastically which pixels will dissolve at every step.Every dissolved rock or stylolite pixel is re-designated as a fluid pixel.
After each stage of chemical dissolution, the rock matrix is scanned for pixel clusters that are entirely surrounded by fluid.We remove these surrounded clusters, simulating mechanical detachment, and re-designate the pixels as fluid.The new pattern becomes the input for the next step of dissolution.
To minimize possible boundary effects, we defined an internal bounding box that represented 53% of the domain.This bounding box began at the top of the domain and continued down to 200 cm above the bottom of the domain; the sides of the box began at a distance of 10 cm from each of the side boundaries.Simulations were terminated when half of the initial pixels inside the bounding box were disintegrated.We ran the simulations on the whole domain, but calculations of weathering rates exclusively stretched over the region within the bounding box.
To simulate the effect of micrometer-scale cementation on dissolution rates at the pixel scale, we assigned a rate coefficient to the stylolite pixels that was different from the surrounding rock.In each simulation, the rate coefficient in the stylolites was assumed to be uniform throughout the domain.We tested the effect of different stylolite rate coefficients on weathering rates.These values ranged from 1 to 100 times greater than the rate coefficient in the carbonate rock, corresponding to V cement = 1 and V cement = 0.01 respectively.In this study, we ran a total of 308 simulations, with 7 repeat realizations completed for each degree of carbonate cementation.The degree of cementation, simulated by the characteristic rate coefficient of the stylolite pixels was the only parameter that varied in the simulations.We normalized the weathering rates in all the simulations to the mean weathering rate calculated for the simulations with a rate coefficient of unity (i.e., stylolite-free rock).

Cement in stylolites at the micrometer scale
In all of the stylolitic limestones we examined, we found evidence of calcite cement at the micrometer scale.Elemental maps of calcium and carbon reveal that CaCO 3 bridges connect the bulk rock on opposing sides of the stylolites.These bridges are typically 2-50 μm wide.The degree of bridging, however, was not uniform, even within samples, and ranged from < 2% in the sample from Ramat Shlomo (Fig. 3a) to as high as 30% in the sample from Givat HaTanach (Fig. 3b).
Regions not filled by calcite contained a mixture of silicon, aluminum, magnesium, potassium, and iron, which is consistent with the presence of clay minerals and metal oxides.
Our observations are consistent with those from previous studies that showed that cementation in stylolites can vary significantly both within and between formations (e.g., Koepnick 1988;Araújo et al. 2021).Such variability could be due to both diagenetic and epigenetic processes.For example, clay minerals that fill stylolite gaps are thought to determine stylolite patterns and topology (Ehrenberg et al. 2006;Ebner et al. 2010), and variations in clay content could affect the local degree of cementation.Similarly, hydrocarbons are thought to inhibit calcite precipitation, and the presence of oil or gas during epigenesis could also cause non-uniform cement patterns (Padmanabhan et al. 2015;Humphrey et al. 2019;Koepnick 1988).Importantly, such heterogeneity means that determining a statistically representative value of stylolite cement for a given rock formation would require a high number of WDS or EDS analyses on different rock samples.
The high-resolution images of stylolites also lend support for our conceptual model of weathering in stylolitic rocks.While the images themselves do not provide evidence that bridging determines weathering rates, they do confirm the assumption that micrometer-scale bridges of calcite partially fill the stylolite gaps, and that the rest of the gap is filled with clay minerals, voids, and metal oxides.If water that is unsaturated with respect to calcite permeates through the stylolite, these calcite bridges will dissolve, creating a front of mechanical discontinuity that will enhance weathering.Moreover, the fewer the bridges, the more rapidly this front will progress, and such a mechanism could explain the enhanced dissolution along stylolites observed in some formations (Araújo et al. 2021).In the next section, we show quantitatively how this mechanism accelerates weathering in stylolite-bearing rocks.

Impact of carbonate cementation on weathering rates
Our numerical model shows that the level of cement has a significant effect on the overall weathering rate (Fig. 4a).Rocks with 1% cement in the stylolites (V cement = 0.01) were found to weather 37 times faster than rocks with no stylolites.However, this effect becomes less pronounced as cementation increases: at 20% carbonate cement (V cement = 0.2), the weathering rate is only about 2.5 times faster than stylolitefree limestone.
The simulations also indicate that accelerated weathering at low levels of carbonate cementation is mainly due to high levels of mechanical disintegration (Fig. 4b).When V cement = 0.01 the proportion of mechanical weathering is 65%; by contrast when V cement = 0.2, the proportion decreases to 13%.This is because when dissolution along the stylolites is rapid, islands of rock surrounded by interconnected stylolites become detached before significant levels of dissolution can occur in the rock matrix.Although the model does not account explicitly for fluid flow through stylolites, we expect that high flow rates will enhance this effect, so the elevated weathering rates we report should represent conservative estimates.

Comparison of field weathering rates with model results
By comparing the field weathering rates with our model results, we can estimate the degree of carbonate cementation along stylolites in real rocks.To demonstrate this, we used published data on weathering rates from the Western Wall in Jerusalem, Israel (Emmanuel and Levenson 2014).At that location, limestone building blocks containing stylolites weather at rates of 23-29 mm ky −1 , while the rate for stylolite-free blocks is estimated to be 1-2 mm ky −1 .These values imply that stylolites enhance weathering by a factor of 11.5-29, which, according to our model, would correspond to a degree of cementation of approximately 1-4% (Fig. 5).Significantly, the degree of carbonate cementation predicted by the model is in agreement with that observed in the electron microscopy images of the samples we collected from Ramat Shlomo (Fig. 3a), where quarries are thought to have provided stone for the Western Wall (Mazar 2011).
In addition to influencing the weathering rates in monuments and building infrastructure, our findings suggest that carbonate rocks that contain stylolites could be more susceptible to karst formation than stylolite-free rocks.Indeed, in Brazilian limestones from the Potiguar basin, caves, and other karst phenomena were found to be strongly associated with the presence of stylolites (Rabelo et al. 2020).In another study in the same region, Araújo et al. (2021) showed that stylolites control karst formation in carbonate rocks exposed to meteoric water, with stylolites increasing in size as a result of weathering until they merge, forming large cavities.Moreover, in a field study in South Italy, Magni (2020) showed that terra rossa soil, often associated with carbonate dissolution and karst development, was more common in areas with stylolites than in areas with fractures and joints.This could indicate that stylolites have a greater ability to accelerate weathering than other rock discontinuities.Clearly, such findings suggest that stylolites will enhance the dissolution of carbonate rock in other scenarios, such as the injection of reactive fluids into subsurface reservoirs for enhanced oil recovery and geological carbon storage.

Conclusions
In this study, we used high-resolution imaging to show that stylolites contain calcite bridges, at the microscopic scale, that cement the rock together.This cement plays a critical role during weathering rate, and numerical modeling suggests that stylolitic limestones with a low degree of cementation will weather more than 30 times faster than stylolite-free limestones.While our model focused on the effect of cement on stylolite-bearing rocks, cement is also likely to play a significant role in controlling the weathering rates of rocks with other kinds of discontinuities, such as fractures, joints, and cracks.
While our results demonstrate the importance of cementation in stylolites during carbonate weathering, our model has several limitations.First, we only tested one example of a 2D anastomosing stylolitic network; other kinds, such as isolated stylolites and bedding parallel stylolites, could behave in a different manner, particularly in 3 dimensions.Second, our model assumes that the degree of cementation is uniform throughout the stylolite network; in reality, cementation could exhibit significant spatial variability that could affect overall weathering patterns and rates.However, incorporating such variability into future simulations in a meaningful way would require quantitative data from real stylolite networks.To achieve this, a reliable method to quantify cementation patterns in stylolites at spatial scales beyond the micrometer scale would need to be developed.
Clearly, factors other than cementation are also likely to play an important role in determining the impact of stylolites on weathering rates.Stylolites often contain smectite clay minerals that expand in contact with water, increasing stress within the stylolite and enhancing the mechanical weathering rate.Fluid flow, too, is expected to accelerate the effects described here.Such effects could be included in more sophisticated models in future.
Because stylolites accelerate weathering at the outcrop scale, they will also contribute to enhanced carbonate weathering on the global scale.However, estimating this contribution is challenging.While stylolites are ubiquitous in carbonate rocks, there is no generally accepted value for their abundance, making any assessment of their global impact on weathering poorly constrained.To resolve this issue, further studies are required that provide reliable estimates for the frequency of stylolites in carbonate rocks.

Fig. 1
Fig.1Example of preferential weathering of stylolite-bearing rocks at the Western Wall, Israel.a Digital photograph; and b a surface retreat map.The two central blocks have average weathering rates of 23-29 mm ky −1 , in contrast to the flanking blocks at the sides that have weathered at a rate of 1-2 mm ky −1 .Modified fromEmmanuel and Levenson (2014)

Fig. 2
Fig. 2 Representation of the digitized stylolitic limestone used in the numerical model.(a) Model domain at the beginning of the simulation and (b) during the simulation.White regions represent the fluid phase, black lines represent the stylolites, and yellow represents the surrounding carbonate rock.Rock or stylolite pixels in contact with the fluid undergo chemical dissolution.When a cluster of pixels is surrounded by fluid it becomes physically detached.(c) Zoom in shows the roughness of the weathering interface resulting from mechanical detachment.(d) Sub-pixel scale representation of the carbonate cement bridges (highlighted by the white arrows) between two opposing stylolite sides.When there are fewer bridges, the rate at which the dissolution front moves along the stylolite will be greater.This results in the stylolite losing its cohesion more rapidly, leading to accelerated mechanical weathering (color figure online)

Fig. 3
Fig. 3 Backscattered electron (BSE) image and elemental (WDS) maps of stylolitic limestone from 2 different locations from the Bina Formation in the Judean Hills, Israel.(a) Sample with a low degree of cementation sampled from Ramat Shlomo exhibiting ~ 2% of calcite cementation (highlighted by the white arrow).(b) Region with a high degree of calcite cementation (~ 30%; white arrows) in a sample from Givat HaTanach.Elemental maps are shown for Ca, C, Fe, Si, Mg, Al, and K.In both samples, much of the stylolite is filled with clay minerals and Fe-oxides (color figure online)

Fig. 4
Fig. 4 Simulated weathering rates as a function of the degree of carbonate cementation.(a) Total rate; and (b) mechanical and chemical rates.Rates are normalized to the total rate of weathering at 100%