Influence of water content on the basic friction angle of porous limestones—experimental study using an automated tilting table

Rock masses typically consist of a rock matrix intersected by discontinuities such as shear zones, faults, joints, schistosity, bedding planes or flaws. This discontinuous nature of rock masses implies that their mechanical behaviour can sometimes be controlled by the presence and characteristics of discontinuities rather than by the intact rock (Ghazvinian et al. 2012). Considering this fact is especially relevant from a safety perspective in the execution and the design of civil engineering works and mining activities performed on shallow rock masses subjected to low confining pressures where instability phenomena are usually related to sliding or separation occurrences of rock blocks (e.g. rocky slopes, tunnels, open-pits, near-surface and underground excavations or rock-socketed piles) (Wines and Lilly 2003; Alejano et al. 2008, 2010, 2011, 2012b). Therefore, an accurate determination of the shear strength of discontinuities is of paramount importance for assessing and solving structurally controlled stability issues at rock mass scale (Kveldsvik et al. 2008; Ulusay and Karakul 2016; Pérez-Rey et al. 2019b).

Shear strength of discontinuities can be determined through in situ and laboratory investigation by carrying out direct shear tests or can be empirically estimated by using existing shear strength criteria (Hencher and Richards 2015). Because direct shear tests require an expensive shear test apparatus and involve difficult and time-consuming procedure of specimen preparation and data processing, many empirical shear strength criteria have been developed so far and their use have been widely expanded among rock engineering practitioners (Singh and Basu 2018).

The vast majority of these criteria are based on Coulomb’s linear formulation (1766); i.e. they relate the shear strength component, through normal stress, with different mechanical and surface-topography parameters of the joints. In particular, Patton’s bilinear model (1966), given by Eqs. (1) and (2), can be considered as the first attempt to describe the peak shear strength of discontinuities with asperities (saw-tooth shape joints). Originally, Patton proposed to consider first order asperities to evaluate shear strength (Wyllie and Mah 2004).

However, later, Barton (1973) stated that for low normal stress (σ_n), the second order roughness come into play:

In contrast, for high σ_n values, the asperities are sheared off with the displacement: where τ is the peak shear strength of the discontinuity, σ_n is the normal stress at which the discontinuity is subjected, φ_b is the basic friction angle, i is the angle of the saw-tooth face, c_a is the apparent cohesion and φ_r is the residual friction angle.

Subsequently, Barton and Choubey (1977) proposed an enhanced model applicable to rock joints with irregular surfaces (3), which has become one of the most widespread shear strength criteria, probably because of its simplicity, reliability on obtaining the input parameters and certain conservativeness (Pérez-Rey 2019). where JRC is the joint roughness coefficient, JCS is the joint-wall compressive strength and φ_r is the residual friction angle given by Eq. 4. where r and R are the Schmidt hammer rebound number for weathered and wet discontinuity surfaces and for dry non-weathered saw-cut surfaces of the same rock, respectively.

As is clear from Eqs. 1, 3 and 4, φ_b is a crucial input parameter for the determination of the shear strength of discontinuities. It symbolises the shear strength between two planar (non-dilating), unfilled, non-weathered and non-polished rock surfaces (Pérez-Rey 2019). This property can be obtained by means of different laboratory tests such as direct shear, push/pull and tilt tests. Nevertheless, among them, tilt test has been possibly the most widely used in rock engineering projects due to its greater simplicity, speed and low cost (Zhang et al. 2018).

Tilt test consists of placing rock specimens one on top to another in such a way that the surface of the plane of contact, which is initially horizontal, is progressively tilted until the upper specimen slides along the joint. The tilting angle with respect to the horizontal just at the instant when displacement begin is the φ_b. Different procedures have been historically used with regard the type of contact provided by the geometry of the samples: on the one hand, the three-core method (Stimpson 1981; Li et al. 2019), and the two-core method (Barton 2011; Ruiz and Li 2014) in which the contacts are linear; and on the other hand, the one-core method (Barton 1973; Zhang et al. 2018) and the block-based method (Alejano et al. 2012a; Ulusay and Karakul 2016) in which the contacts are planar surfaces. However, among them, the block-based method has proved to be the most suitable (specially, when slab-like specimens are used) because of core-based methods overestimate or do not provide reliable φ_b values (Alejano et al. 2012a; González et al. 2014). Furthermore, a great experimental effort has been done in previous works to detect other factors that influence tilt test results, such as the saw blades and cutting velocities (Alejano et al. 2017), the specimen size and shape (Hencher 1977; Alejano et al. 2012a; Kim et al. 2016; Jang et al. 2018), the test platform tilting rate and vibrations (Hencher 1977; Pérez-Rey et al. 2016, 2019a; Jang et al. 2018), the wear of rock surfaces due to multiple sliding on the same contact (Pérez-Rey et al. 2015, 2016, 2019a) or the time elapsing between cutting and testing (Pérez-Rey et al. 2015); as well as to evaluate the repeatability of tests carried out in different laboratories (Alejano et al. 2017). As a result of the conclusions derived from the abovementioned studies, an ISRM Suggested Method for determining the φ_b of planar rock surfaces using tilt tests has been recently published (Alejano et al. 2018). This document briefly points out that, although it is not fully recognised, other additional aspects such as environmental relative humidity (RH) or water content (w_c) of specimens may affect the results of tilt tests in some friable rocks due to water and could activate adhesion between slickensided rock surfaces (Mehrishal et al. 2016).

Contact mechanic approaches have also been widely applied for studying rock interfaces. Misra and Marangos (2011) used a micromechanical model that explicitly considers asperity interactions on joint surfaces to examine the rock-joint closure and wave propagation behaviour. They concluded that rock joints with the same roughness can display a variety of closure behaviours depending on initial overlap of the joints and rock intrinsic friction. Recently, Kasyap and Senetakis (2021) utilised micromechanical-based experiments to analyse the effect of shearing rate on the tangential contact behaviour of smooth flat quartz surfaces in the presence of plastic and non-plastic gouges. Their results indicated that important variations in the stick–slip instability (increase in force-drop, recurrence interval and slip velocity) occurred when the shearing rate was reduced by one order of magnitude. They also reported that the initial tangential stiffness raised when the shearing rate was diminished.

Conventional direct shear tests have frequently shown that moisture caused important reductions of the peak shear strength and friction angle (φ) of unfilled discontinuities of sedimentary weak rocks, such as marls (Pellet et al. 2013) or claystones (Zandarin et al. 2013). In this line, micromechanical experiments performed to understand the tribological behaviour of analog mudrock interfaces have also indicated that the presence of water at the interfaces of these materials resulted in a continuous decrease of the friction compared to the dry state due to a predominant effect of abrasion (Ren et al. 2022). Also, substantial water-induced decreases of the frictional strength have been found in unfilled joints of other rock types, such as granitic gneiss (Jaeger 1959), trachyte (Hoskins et al. 1968), chalks (Gutierrez et al. 2000) or coal measure rocks (Li et al. 2005). In the case of filled joints, there might be development of suction which may provide additional contributing mechanics of friction. In this connection, Kasyap and Senetakis (2020) conducted micromechanical shearing tests which demonstrated that the presence of gouge materials between nominally flat quartz grains resulted in a reduction of frictional strength in comparison with pure quartz surfaces. Furthermore, they observed that plastic gouge materials (montmorillonite) exhibited a significant reduction in friction coefficient (μ) due to water submersion at any state of the shearing while non-plastic gouge materials (silt) showed only a slight decrease in the μ.

Regarding the variations of the φ_b with moisture for saw-cut rock surfaces, inconsistent findings (reductions and increases) have been informed in literature. On the one hand, Barton (1973, 1977) collected the φ_b values of different rock types from earlier researchers (Patton (1966), Coulson (1972) and Richards (1975)) and concluded that dry specimens generally exhibited higher φ_b values than the wet ones. Subsequently, similar findings were also obtained by Aydan (1995), who attributed the results to the uncertainty of the effective normal stress over the shearing section. On the other hand, Ulusay and Karakul (2016) determined the φ_b values of 22 rock types from Turkey under dry, wet and submerged conditions using rectangular-based slabs. They found that in 13 rock types, wet φ_b was lower than dry φ_b (decreases between 1.4 and 10.6°) due to the predominance of the lubrication effect, while in the other 9 rock types, the wet φ_b was greater than the dry φ_b (increases between 0.2 and 6.5°) due to prevalence of the capillary action (suction). Furthermore, they reported that all dry samples displayed higher φ_b values than submerged ones and that the reductions of φ_b widely varied between 0.2 and 15.2° because the lubrication effect happened with different intensity according to the mineral composition of each rock type. In the same vein, Zhang et al. (2018) obtained the φ_b values of 46 rock types from Norway in dry and wet states using cylindrical specimens (three-core method). They reported that 21 rock types exhibited wet φ_b values smaller than the dry ones (with drops between 0.7 and 5.3°) while the remaining 25 rock types showed the opposite behaviour (with increments between 0.7 and 5.0°). These authors postulated that the impact of humidity on φ_b was not linked to lithology but rather to mineralogy. Later, Kim and Jeon (2019) evaluated the water-induced changes in φ_b on granite, diorite, sandstone and cement mortar and found increases ranging from 1 to 3°. Recently, Beyhan and Özdemir (2021) measured the φ_b of travertine’s samples under dry and different soaked conditions (i.e. water solutions with a pH of 2, 7 and 12) and observed that those conditioned at pH of 2 displayed the lowest values while those conditioned under the rest of conditions exhibited quite similar values between them. A summary of the φ_b values in dry and wet conditions found in preceding works for different rock types is given in Table 1.

Petrological characteristics and microstructure of geomaterials are also additional factors that affect frictional properties of rock surfaces and their water-induced changes. Cruden and Hu (1988) found that the φ_b of carbonate rocks depends on grain size and mineralogy. In particular, they obtained that for pure carbonate rocks, the φ_b reduces with increasing dolomite content and decreasing grain size. Ramana and Gogte (1989) reported that rocks rich in felsic minerals, quartz and calcite exhibit higher μ values than rocks with significant hydroxyl bearing minerals. Horn and Deere (1962) indicated that as surface moisture rises, the μ of massive-structured minerals (e.g. quartz, feldspar and calcite) increases. In contrast, they observed that the μ reduces when surface moisture increases for layer lattice minerals (e.g. muscovite, phlogopite, biotite, chlorite, serpentine, steatite and talc). Also, Morrow et al. (2000) reported that moisture caused no substantial or slight μ modifications for calcite, quartz, albite and zeolites (i.e. laumontite and clinoptilolite), dramatic drops for serpentinites (i.e. antigorite, lizardite and chrysotile) and moderate decreases for sheet-structures minerals (i.e. kaolinite, muscovite, chlorite, brucite and talc). Tembe et al. (2010) observed that the μ of saturated binary and ternary mixtures made up of quartz, montmorillonite and illite decreased with increasing clay content. Furthermore, Westbrook et al. (1968) and MacMillan et al. (1974) have demonstrated that the adsorption of fluids in mineral surfaces could cause significant variations in their surface microhardness.

The abovementioned background has shown that (1) there is a lack of studies regarding the effect of the environmental relative humidity and moisture content of samples on tilt test results; (2) inconsistent findings have been obtained concerning the water-induced changes in the φ_b of rocks; and (3) the underlying causes of this behaviour are unclear and may be related to petrophysical properties of rocks. This research addresses and tries to elucidate these points for carbonate rocks. To this aim, a tilt testing campaign was carried out in three limestone lithotypes (calcarenites). In particular, φ_b values were measured in saw-cut rock-like slab specimens tested under three different conditions: (1) oven-dry state, (2) non-submerged but fully water-saturated state achieved by using vacuum and (3) partially water-saturated state reached by equilibrating the rock samples with an environment of high relative humidity (90%). Complementarily, mineralogy and microstructural characteristics (grain and pore sizes) of these rocks are analysed with the aim of linking the φ_b values and their water-induced variations with them.

In this work, the petrological and microstructural characteristics as well as the sliding angle (β) values of three lithotypes of porous limestones under dry and saturated conditions, as well as after an exposition to an environment of high relative humidity (RH), have been determined by performing a large number of tilt tests. The results obtained have allowed to (1) evaluate the possible impact of the repetition of tilt test conducted on the same rock contact (a pair of rock surfaces) on β; (2) quantify the effect of water saturation and environmental RH on the basic friction angle (φ_b) value of these rocks; and (3) establish connections between properties such as grain size, mineralogical composition, porosity or pore size and φ_b or its moisture-induced variations. The obtained results are compared with those reported in previous investigations and their implications and limitations are discussed below.

A first finding of this work is that the β values obtained under dry conditions exhibited moderate standard deviations (always less than 3°) while the β values measured under fully water-saturated conditions displayed considerably higher standard deviations (between 3 and 4.2°). This result is in line with those obtained by Ulusay and Karakul (2016) in Turkish rocks and by Zhang et al. (2018) in Norwegian rocks, who reported that standard deviations were often greater in saturated specimens than in dry ones. This may be explained because water distribution on saturated slab surfaces is unavoidably slightly different for each test repetition and powder generated during sliding is more difficult to remove completely in this case. In addition, the standard deviations obtained in both conditions are generally higher than those informed in the previously cited studies, which may be attributed to the fact that they refined the raw data by discarding the maximum and minimum β values before their calculation. The standard deviations of β found in the sets of samples exposed to an RH equal to 90% were moderate (less than 3°) and quite similar to those obtained under dry conditions. This occurred despite the fact that the special test setup used on these specimens required to stop the tilting table in a manual way when sliding started (i.e. not automatically as in the dry and fully water-saturated specimens). This fact can be explained by the fast and efficient work of the laboratory operators in detecting the onset of sliding and stopping the tilting table, as well as by the low tilting velocity used during the tests (10°/min). In this sense, it is worth mentioning that a one-second variation in the reaction time of the operators to stop the tilting table would result in a variation of the measured β of less than 0.2°.

A second outcome of this study is the existence of several outliers in the β values obtained in the three limestones tested under different moisture conditions, as revealed by the box-and-whisker plots. This fact shows the recommendation proposed by Alejano et al. (2012a) to use the median of β values instead of the mean to determine a representative φ_b value, which has been included in the recently published ISRM Suggested Method (Alejano et al. 2018). Nevertheless, according to Gonzalez et al. (2014), the mean β value of the five first tests conducted on freshly saw-cut samples could also be used as the input φ_b parameter in the Barton’s model to realistically estimate the shear strength of unfilled discontinuities. In addition, the present investigation corroborates that tilt tests could be carried out using the two surfaces of each rock slab in order to have a larger number of β values from which to derive a representative φ_b, given that both rock surfaces are homogeneous and free of irregularities. The latter is not always easy to achieve in soft rocks such as tested limestones, despite the availability of modern cutting tools and skilled operators.

Furthermore, our tilt test results indicate that β values of calcarenites are not significantly affected by wear when only five test repetitions are conducted on the same rock contact and the debris generated by friction is removed between each repetition, which is consistent with the findings reported by Ulusay and Erguler (2016). Notwithstanding the foregoing, previous works have demonstrated that repeated tilt testing of saw-cut specimens could cause a β reduction when the rock debris is removed after every test repetition and a β increase when the rock debris is not removed (Hencher 1976, 2012; González et al. 2014; Pérez-Rey et al. 2015, 2016; Alejano et al. 2017). In this connection, Kasyap and Senetakis (2018) found that the debris scraped during micromechanical shearing tests could contribute to the increase of friction of kaolinite-coated sand grains. Also, Ren et al. (2022) suggested that the variations of the interface friction of miniature kaolinite specimens are strongly related with abrasion and the presence of water. In particular, they observed that the increase of shearing cycles leads to a slight increase of the interface friction in dry condition and, on the contrary, an important reduction of the interface friction in wet state. Therefore, although the level of normal stresses in tilt tests is very small, the choice of an appropriate number of test repetitions performed on the same rock contact could be an important matter to consider when conducting tilt tests, especially on weak rocks.

A third result of this research is that the φ_b values of tested calcarenites are in a range of 31.2–37.8, which are comparable to those obtained by other researchers in similar sedimentary rocks, such as dolomite (27–37°), limestone (35–40°) (Coulson 1972) or travertines (28.2–38.3°) (Ulusay and Karakul 2016). Furthermore, in the dry state, the φ_b value found in calcarenite S-1 (31.8°) was lower than those measured in calcarenites S-2 and S-3 (37.4 and 36.8°, respectively), which can be explained by its smaller grain size. This fact has also been noted by Cruden and Hu (1988), who reported that large grain sizes increase φ_b in Canadian pure carbonate rocks.

A fourth finding of this work is that moisture can cause both positive and negative φ_b increments in calcarenites. The φ_b increase of 6% obtained in calcarenite S-1 after its fully water-saturation could be attributed to the fact that in this variety, the capillary (suction) effect prevails over the lubrication effect (Ulusay and Karakul 2016). Previous research has found analogous φ_b increases in some sedimentary (i.e. sandstone, limestone and travertine) and volcanic (andesite granite, diorite and gabbro) rocks (Ulusay and Karakul 2016; Zhang et al. 2018; Kim and Jeon 2019). In contrast, the φ_b reductions of 18 and 11% obtained in the calcarenites S-2 and S-3 could be attributed to the occurrence of the opposite phenomenon, that is the dominance of the lubrication over the capillary effect (Ulusay and Karakul 2016). Similar φ_b decreases have been found by other academics in several types of sedimentary (sandstone, dolomite and limestone), metamorphic (slate and marble) and volcanic (basalt, granite, dolerite, pegmatite and migmatite) rocks (Coulson 1972; Richards 1975; Ulusay and Karakul 2016; Zhang et al. 2018).

In this connection, the different impact of water saturation on φ_b obtained in tested limestones may be related to the differences in their microstructure and mineralogical composition. On the one hand, the smaller pore and grain size of the calcarenite S-1 would promote the accumulation of water molecules on the voids of rock surface and their permanence despite its drying with a cloth just before conducting tilt tests. However, the larger grain and pore sizes of calcarenites S-2 and S-3 would cause a more effective removal of the water molecules lodged in the voids of the rock surface when wiping it with the cloth. Consequently, the effect of surface tension would be considerably more substantial in calcarenite S-1 than in the others. On the other hand, the higher content of clay minerals (phyllosilicates) and the lower quartz content of the calcarenites S-2 and S-3 compared to the calcarenite S-1 might be other reason to explain the dissimilar water-induced changes of φ_b found in each lithotype. In this line, former basic research has demonstrated that moisture caused important drops of the μ in clayey and sheet-structure minerals (e.g. chlorite, lizardite, kaolinite, talc and biotite) and slight increase or no change in minerals with a massive structure (e.g. calcite, quartz and feldspar) (Horn and Deere 1962; Morrow et al. 2000; Moore and Lockner 2004). In addition, the higher water-induced variations in φ_b exhibited by calcarenites S-2 and S-3 compared to S-1 may be related to their larger water absorption capacity, as well as to the fact that S-1 had greater mechanical properties and displayed a sparry and siliceous fibrous cement that makes its grains better cemented.

The variations of φ_b with environmental RH were slight in the three tested limestones. In particular, when the RH varied from 50 to 90%, the φ_b increased by 3% in calcarenite S-1 and by 1% in calcarenite S-2, while φ_b decreased by 3% in calcarenite S-3. These minor changes can be attributed to the small amount of water adsorbed by these rocks (0.64–1.08%) and its homogeneous distribution within the pores when subjected to the humidity chamber atmosphere. Therefore, to know the φ_b values of this rock types under RH conditions to which rock masses are commonly exposed, it is not necessary to conduct the test in a precise (and more complex) way, since the differences with the dry φ_b values are very small. Nevertheless, its generalisation for all rock types requires further research. In this sense, Westbrook and Jorgensen (1968) found that crystal planes of some synthetic minerals (i.e. bromellite, periclase, corundum, rutile and silicon carbide) and natural minerals (quartz, kyanite, topaz, tourmaline, fluorite, sphalerite, galena and calcite) exhibited substantial drops (up to 32%) in their relative values of the indention microhardness due to water adsorption from ambient air. Also, Macmillan et al. (1974) postulated that the increment in the μ of glass in wet environments could be attributed to chemically induced variations in surface microhardness.

Based on the experimental work and the analyses carried out in the present article, the following conclusions can be derived:

This study offers an in-depth understanding of the influence of water saturation and environmental RH on the φ_b of porous limestones that may be of interest for the design and execution of infrastructures (e.g. dams, ports, tunnels, mines and nuclear waste repositories) built in or on rock masses in which water or RH can play an important role in their stability. Furthermore, the findings related to the effect of wear and moisture on β values as well as its variability provide valuable knowledge that can serve as reference on how to perform tilt tests on porous calcareous rocks.