Introduction

Groundwater is one of the most important environmental factors affecting the short or long-term stability of underground engineering, such as civil engineering, tunneling, and coal mining1,2,3. Groundwater (especially highly mineralized and acid/alkaline groundwater) significantly affects the mechanical properties of rocks, especially for those containing clay minerals4,5. Weakly cemented rock (WCR), which mainly appears in coal measures of Jurassic, Cretaceous, and Paleogene Periods6,7,8, deposits widely in the largest coal base in China, say Northwest China. Northwest China holds 74.1% of the whole country in coal reserves and produced 60.5% of the whole country in coal production in 2023. Due to the short period of diagenesis, WCR thereof is characterized by weak cementation, low strength, and high sensitivity to weathering and coal mining disturbance9,10. Mining-induced fractures easily trigger water flow from the upper water-bearing roofs into the lower roofs, with consequent water-rock interaction11,12. Moreover, mine water in Northwest China, rich in SO42−, Cl−, Ca2+, Mg2+, K+, Na+, HCO3−, always behaves with high mineralization and strong alkalinity13. When encountering mine water with various ion components, WCR is prone to be degraded in mechanical properties, thus resulting in catastrophic failures, such as roof caving, rib spalling, and mine inundation, which are significantly problematic in the coal mines of Northwest China14,15,16,17,18. Taking Da’nanhu No. 7 Coal Mine located in Hami, Xinjiang Uygur Autonomous Region, China as an example, a roof fall disaster occurred in the main roadway two years after being excavated, with the caving height of more than 1.8 m, the width of more than 2 m and the length of more than 15 m (see Fig. 1a). A large amount of yellow or green caved rocks were found on the site, which is evidence of corrosion by a large amount of alkaline water coming from the gravelly coarse-grained sandstone (see Fig. 1b & c). The bolts and other supporting bodies remained intact, but the roof fell down integrally, indicating that the degradation of WCR eroded by alkaline water is primarily responsible for the disaster. The control of WCR occurring in water-bearing strata disclosed by mining activities has attracted great concerns from engineering and academic fields.

The degradation effect of water-rock interaction on rocks is closely related to the coupling of physical, chemical, and mechanical fields19,20,21,22,23,24. Feng et al.25 studied the effect of chemical solutions on rock tensile strength, and found that the chemical compounds significantly decrease the fracture toughness of the specimen. Yang et al.26analyzed the change of P wave behaviors with different water saturation, found the clay mineral hydration is the key reason for P-wave attributes between kaolinite- and bentonite-filled rock joints. Zhou et al.27 reductions of the compressive and tensile strength of sandstone under static and dynamic states in different saturation processes, most specimens can recover their strength after drying. Yin et al.28 study the mechanical properties of containing coarse-grained gypsum mineral under long-term water immersion conditions, found the softening effect of water on rocks attenuates nonlinearly with increasing immersion time, and the UCS changes as a logarithmic function of immersion time. Some scholars analyzed the uneven distribution of swelling clay minerals hold a higher swelling potential under water chemical effects29,30,31. At the same time, the influence of stress and water chemical corrosion (including underground water) on WCR sample crack permeability has also been paid attention.

Fig. 1
Fig. 1
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WCR roof fall occurred in Dananhu No.7 Coal Mine, (a) roadway roof caving due to alkaline water effect, (b) caved weakly cemented sandstone, (c) eroded sandstone.

Scholars also have conducted numerous studies on WCR mechanical property and damage mechanism during the water-rock interaction process. Research found that when encountering mine water with different ion components, concentrations, and pH levels, WCR experiences significant changes in porosity, cementation degree, particle morphology due to hydrolysis reaction and ion exchange, further leading to the evolution of microstructure and mechanical property32,33. Guo et al.34 investigated to show that the calcareous shale uniaxial strength decreases linearly with increasing water content. Roy et al.35 found that the sedimentary rocks’ mechanical and fracture properties degrade with increasing degrees of saturation. Liu et al.36 studied the change in creep failure characteristics and creep rate of weakly cemented mudstone with different moisture contents, further establishing a fractional-order creep model. Wang et al.37suggested those lateral restraints can restrain water migration and water-rock interaction for weakly cemented mudstones. Liu et al.38 constructed a seepage model of straight capillary and theoretical permeability Formulass for the stable seepage stage and seepage mutation stage. Studying the degradation effect of alkaline water on WCR is critical for understanding the mechanical behavior of weakly cemented strata subjected to moisture circumstances, also laying a theoretical foundation for future research regarding water hazard, roadway stability, and roof control that are potentially operated in weakly cemented coal measure strata occurring in mine sites.

Hence, to study the variation law of mechanical properties of WCR with the impact of alkaline water and the reason for mechanical properties deterioration, various mechanical tests were carried out on weakly cemented fine-grained sandstone (WCFS) samples sampled from the coal mine roadway site. Combined with the chemical analysis, this paper probes into the mechanism of WCFS degradation due to alkaline environment. Based on all these results, a predict model describing WCFS chemical damage under the effect of alkaline water is constructed.

Materials and methods

Preparation and characterization of rock samples

The weakly cemented fine-grained sandstone tested in this paper were obtained from the Da’nanhu No. 7 Coal Mine in Hami, China. The original uneroded WCFS specimens, which were collected from the Jurassic Xishanyao Formation within the scope 7 to10 m above the 7# Coal Seam, see Fig. 2. According to the standards recommended by the International Society for Rock Mechanics and Rock Engineering (ISRM), the rock cores were processed at dry status into cylinder specimens of being 100 mm, 50 mm, and 25 mm in length, respectively, and about 50 mm in diameter. By comparing the geometry, quality, no parallelism, axial deviation, and longitudinal wave velocity of all specimens, 115 specimens with high concentrated wave velocity and density and high processing accuracy were selected as the standard samples for the following mechanical tests. The mineral compositions of WCFS specimens, including quartz (31%), kaolinite (36%), feldspar minerals (26%), white mica, and other clay minerals (7%), were tested in the dry state.

Fig. 2
Fig. 2
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Lithological column of study area, mineral composition and rock specimens.

Soaking solutions

Water quality tests on the chemical properties of the overlying aquifer of Dananhu Coal Mine showed that:

  1. (i)

    High mineralization, average level 11015.03 mg/L.

  2. (ii)

    Weak to medium-strong alkalinity, with pH value between 7.7 and 11.9.

  3. (iii)

    A chemical type featured by Cl·SO4—K + Na. High contents of K+ and Na+(1838～3256 mg/L, 2685 mg/L on average), Ca2+ (48～820 mg/L, 481 mg/L on average), Cl- (2761～5256 mg/L, 4182 mg/L on average), and SO42- (969～2723 mg/L, 2046 mg/L on average), accounting for 98.39% of the total ion equivalent weight.

Various solutions used for water-rock interaction tests were prepared based on the above chemical test results. Solid anhydrous CaCl2, NaCl, MgCl2, and K2SO4 were added into the deionized water according to a particular proportion, and the pH value of simulated solutions was adjusted using NaOH solution to 7, 10, and 12, respectively. In addition, deionized water was adopted as the blank controller group.

WCFS specimens were dried in an oven until reaching a constant weight, and such dried specimens were then soaked into the prepared alkaline solutions. Considering the disintegration characteristics of WCFS, the soaking durations were scheduled as 4 h, 8 h, 12 h, 16 h, and 20 h, respectively; the volume of solutions for each specimen was 500 mL.

Experiment method

MTS-810 triaxial testing system with three modes achieved by controlling load, displacement or time was adopted in the study, which is shown in Fig. 3. It can support 250 kN of maximum axial load, -85 ~ + 85 mm of axial displacement, 0 ~ 25 MPa of confining pressure. Confining pressure loading can be automatically controlled during the whole testing process, which made it acceptable in the test. Rock mechanics tests were conducted to understand the strength behavior of corroded WCFS by alkaline water. The tests adopted a displacement loading with a constant rate, both the uniaxial compression test and the Brazilian test were conducted at a constant loading rate of 0.005 mm/s39,40. The variable-angle shear tests were conducted to analyze the shear properties of the eroded samples at a loading rate of 0.002 mm/s with a maximum displacement of 10 mm, see Table 1.

Fig. 3
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MTS-810 triaxial testing system.

Table 1 Mechanical tests and physical parameters.
Full size table

Results

Uniaxial compression mechanics test

Stress-strain curve

Figure 4 presents the stress-strain curves of WCFS specimens soaked in the solutions of different pH levels for different soaking durations. All stress-strain curves are generally composed of: (I) initial compaction stage; (II) linear elastic stage; (III) yield and failure stage, and (IV) residual stage. In Figs. 3 (b) to (f), each stage is marked in black, red, blue, and green, respectively. The curves shows that at the beginning of loading process, dry WCFS specimens had an obvious initial compaction stage, influenced by alkaline water, the specimens witnessed axial strain increment in the initial compaction stage. The curve slope decreased with the enhancement of solution alkalinity. Moreover, the stronger the solution alkalinity, the more considerable the decrease of WCFS peak strength.

Fig. 4
Fig. 4
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Stress-strain curves of WCFS specimens soaked in different alkaline solutions for different durations: (a) natural state; (b) soaked 4 h; (c) soaked 8 h; (d) soaked 12 h; (e) soaked 16 h; (f) soaked 20 h.

Figure 5 shows that the uniaxial compressive strength (UCS) of soaked WCFS presents a nearly negative exponential relationship with the soaking duration, as expressed in Eq. (1):

$$UC{S_C}=Rc \times {e^{ - kt}}$$
(1)

where UCSC is the UCS of the chemically eroded sample; Rc is the UCS of the uneroded sample at natural state; t is the soaking duration; k is the chemical effect coefficient, the stronger the alkalinity of the solution, the greater the coefficient.

Fig. 5
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UCS vs. Soaking duration relation.

Compression modulus and elastic modulus

Compression modulus refers to the ratio of effective stress increment to axial compressive strain when the axial load is beginning applied, marked as dσ/dε 41,42. The curves in Fig. 6a describe the change of WCFS compression modulus with soaking duration, suggesting a negative correlation between them, except a relatively discrete data of a sample being soaked in the solution of pH = 10 for 8 h; compared with the initial level (5.22 GPa in the natural state), the compression modulus of the WCFS specimen chemically processed by the pH 12 solution for 20 h degraded by 58.2% to 2.17GPa. Such phenomena indicate that the alkaline corrosion led to further development of WCFS primary pores and fissures, and the total axial deformation went greater in the compaction stage.

As the soaking duration increased and the alkalinity intensified, the elastic modulus of weakly cemented fine-grained sandstone (WCFS) gradually decreased, as illustrated in Fig. 6b. Compared with the deionized water, other groups with different pH levels witnessed significantly low elastic modulus. In the shortest duration case (0 to 8 h), the elastic modulus degradation of WCFS specimens in deionized water was slower than that in the other three alkaline solutions. The elastic modulus degradation of WCFS was almost synchronous in both solutions of pH = 7 and 10, but much more drastic in the solution of pH = 12. With soaking duration beyond 8 h, the degradation in solution of pH = 10 got faster than that in solution of pH = 7, but changed slightly in solution of pH = 12. After soaking duration was greater than 16 h, the elastic modulus experienced a sharp degradation for WCFS specimen in deionized water, but slight changes for those in alkaline solutions. Ultimately, WCFS elastic modulus in the four circumstances reached a low level. After the soaking duration reached 20 h, the elastic modulus of the samples in different soaking solutions was reduced by 56.77%, 62.76%, 63.95%, and 74.82%, respectively.

Fig. 6
Fig. 6
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The change of WCFS modulus with pH levels, (a) compression modulus; (b) elastic modulus.

Strain energy evolution law

Based on the complete stress–strain curve, statistical calculations were conducted on the elastic energy Ue and dissipative energy Ud of WCFS during uniaxial compression under different soaking conditions43,44. Figure 7 shows the change of Ue and Ud nephogram of WCFS. It can be seen that there is a negative correlation among Ue, Ud with pH value and soaking duration. After soaking for 20 h in pH = 12 conditions, the elastic energy Ue and dissipative energy Ud of WCFS reach their lowest points in the energy distribution nephogram. As shown in Fig. 6a, Ue of WCFS in different pH value solutions exhibits a trend of decreasing first and then stabilizing as the soaking time increases. Taking WCFS in a pH = 12 solution as an example, as shown in Fig. 6b, during the initial soaking period (4 ~ 12 h), the Ue of WCFS decreased from 138.9 kJ in the dry state to 49.86 kJ. In the middle and later stages of soaking (12 ~ 20 h), the Ue varied little and gradually stabilized. The trend of Ud also demonstrates a sharp decrease followed by stabilization with the soaking time increases, in the pH = 12 solution, the Ud of WCFS decreased from 49.4 kJ in the dry state to 21.65 kJ during 4 ~ 12 h, then the variation remained relatively small. After soaking in alkaline solution, Ue and Ud of WCFS exhibited a synchronous decrease, indicating that the alkaline solution had damaged the internal structure of WCFS, leading to a reduction in the elastic energy stored within and the energy required for the development of micro-fractures.

Fig. 7
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The influence of pH value and soaking time on the energy distribution of WCFS, (a) elastic energy Ue, (b) dissipative energy Ud.

Shear properties

Cohesion and internal friction angle are two critical parameters for assessing the shear resistance capability of rock. Figure 8a shows the variation of WCFS cohesion and internal friction angle, suggesting that WCFS cohesion degradation mainly depends on the soaking duration. The degradation rate is much greater in the initial period (0 to 4 h) but gradually lower after that. Also, the higher the pH level, the lower the cohesion, but the effect of alkalinity is somewhat limited. Compared with the cohesion at the dry state, the cohesion of WCFS which were processed via solutions of deionized water, pH 7, 10, and 12 for 4 h led to cohesion decrease by 76.01 to 81.35%, and the decrease further accumulated accounting for 12.41% to 16.29% from 4 h to 12 h.

Internal friction angle decreased gradually with the increase of soaking duration (see Fig. 8b). Alkaline solutions exerted a more significant negative influence on internal friction angle than deionized water. The higher the pH level, the lower the internal friction angle and the faster the degradation. From 46.54° in the dry state, the internal friction angle decreased by 17.59%, 20.06%, 22.43%, and 24.25% in the group of deionized water, pH 7, 10, and 12 solutions, respectively, as the soaking duration reached 20 h.

Fig. 8
Fig. 8
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Variation of WCFS shear parameters during chemical corrosion:(a) cohesion; (b) internal friction angle.

Tensile strength

The curves in Fig. 9 describe the variation of WCFS tensile strength with soaking duration. In the initial stage of soaking (0 to 4 h), WCFS tensile strength decreased from 4.89 MPa by 13.49%, 87.05%, 87.19%, and 91.34% in the group of deionized water, pH 7, 10, and 12 solutions, respectively, suggesting a significant degradation effect of dissolved ions on tensile strength. WCFS tensile strength decreased gradually and almost leveled at 2.69 MPa as the specimen was soaked in deionized water for 20 h. By contrast, the strength of WCFS specimens processed via solutions of pH 7, 10, and 12 was much weaker, ranging from 0.21 to 0.31 MPa; Whilst, in the stage of being soaked from 4 h to 20 h, the tensile strength changed slightly either with soaking duration or with the pH levels, indicating that the chemical ion is responsible for tensile strength degradation of WCFS, rather than the pH level.

Fig. 9
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Variation of WCFS tensile strength with soaking duration.

The difference between WCFS and conventional rock

To further clarify the difference between weakly-cemented rocks and conventional rock in terms of mechanical degradation due to hydro-chemical corrosion, a comparison was made based on the results for sandstones from Yellow River Xiaolangdi Reservoir, limestones from a tunnel in Chongqing, and granites from Three Gorges Dam, respectively (data from Feng et al.41, Chen et al.42, Han et al.45), as shown in Fig. 10. Alkali corrosion WCFS specimens had a more considerable degradation in UCS and elastic modulus than sandstones, limestones, and granites within a short soaking duration. Taking pH = 12 as an example, sandstones (soaked for 90d) from Xiaolangdi witness a UCS decrease by 54.11% and an elastic modulus decrease by 34.31%, and the HSC (hydro-chemical softening coefficients) is 0.46; limestones (soaked for 30d) from Chongqing by 41.82%, 25.22%, and 0.58, and granites (soaked for 12d) from Three Gorges by 72.31%, 42.11%, and 0.28, respectively. By contrast, UCS and elastic modulus of WCFS (soaked for 20 h) from Da’nanhu in this paper dropped by 86% and 74.82%, respectively, and its softening coefficient was only 0.14. As WCFS had a significant degradation in a shorter corrosion period, WCFS is more sensitive to hydro-chemical corrosion with consequent degradation than conventional dense rocks. In view of geotechnical engineering, the field works for WCFS waterproof and reinforcement should be conducted immediately after the engineering disturbance.

Fig. 10
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Impact of alkalinity functioning on different rocks in terms of: (a) uniaxial compressive strength (UCS), (b) elastic modulus, and (c) hydro-chemical softening coefficient.

Discussion

Mechanism of hydro-chemical degradation

Water-rock interaction altered the chemical compositions of rock, essentially causing the degradation of mechanical properties46,47,48,49,50. The clay minerals, quartz and feldspar, are thought to be mainly responsible for hydro-chemical induced WCFS mechanical degradation.

Hydrolysis reaction

Figure 11 shows the variations of WCFS mineral composition after being exposed to diverse soaking environments for 20 h. In the case of pH = 7, with the increasing of soaking duration, feldspar (including potassium feldspar and sodium feldspar) decreased from 23.25% to 19.19%, and kaolinite significantly increased from 42.66% to 48.06%. It is inferred that the hydrolysis reaction of feldspar and mica contribute to the increase of kaolinite, see Eqs. (2) and  (3), which can be validated by the decrease of the total content of feldspar mineral. Alkaline solution of pH at 10, by contrast, contributed more increase of kaolinite and more decrease of feldspar. The hydrolysis reaction of white mica rarely occurred in alkaline solutions, resulting in the slight change of white mica content in the soaking solutions of pH at 10 and 12. The increase of soft mineral (kaolinite), as well as the decrease of hard mineral (feldspar), contribute to the sharp strength degradation (such as UCS, Cohesion, and Tensile strength) of WCFS in the initial stage of soaking.

$$4\left( {K,{\text{ }}Na} \right)\left[ {AlS{i_3}{O_8}} \right]\left( {feldspar} \right)+6{H_2}O \to A{l_4}\left[ {S{i_4}{O_{10}}} \right]{\left( {OH} \right)_8}\left( {kaolinite} \right)+2Si{O_2}+4\left( {K,{\text{ }}Na} \right)OH$$
(2)
$$4KA{l_2}\left[ {AlS{i_3}{O_{10}}} \right]{\left( {OH} \right)_2}\left( {White{\text{ }}mica} \right)+12{H_2}O \to 3A{l_4}\left[ {S{i_4}{O_{10}}} \right]{\left( {OH} \right)_8}\left( {kaolinite} \right)+4KOH$$
(3)
Fig. 11
Fig. 11
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WCFS mineral composition variation with pH levels and soaking durations. (a) deionized water, (b) pH = 7, (c) pH = 10, (d) pH = 12.

Alkaline corrosion

After being soaked in alkaline solutions pH = 10 and 12, potash feldspar even disappeared in the alkaline solutions of pH at 10 and 12. Due to the alkaline corrosion, the content of quartz slightly decreased in alkaline solutions, which indicates the reaction as Eq. (4) and Eq. (5). Part of quartz grains will be consequently degraded or even dissolved. Figure 12 shows the concentration variation of Al(OH)4− and SiO32− in alkaline solutions with soaking durations, which provide evidence of the occurrence of alkaline corrosions on feldspar and quartz. The longer the soaking duration and the stronger the alkalinity, the greater the Al(OH)4− and SiO32− concentration. In terms of the alkaline effect on WCFS, the higher the increase of the concentration of Al (OH)4− or SiO32− in solutions, the more vigorously feldspar or quartz reacts with OH− and the more severe the degradation of cementing material and silicate skeleton structures. As a result of hydrolysis reaction and alkaline corrosion, the minerals with high strength, say feldspar and quartz, decrease significantly with consequently WCFS degradation in mechanical strength.

$$KAlS{i_3}{O_8}\left( {feldspar} \right)+7O{H^ - } \to KOH+Al{\text{ }}{\left( {OH} \right)_4}^{ - }+3Si{O_3}^{{2 - }}+{H_2}O$$
(4)
$$Si{O_2}\left( {Quartz} \right)+2O{H^ - } \to Si{O_3}^{{2 - }}+{H_2}O$$
(5)
Fig. 12
Fig. 12
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Concentration variation of different ions in alkaline solutions with soaking durations: (a) Al (OH)4−, (b) SiO32−

Ion exchange and hydration of clay mineral

The ion exchange further aggravates the instability mineral alteration, especially for feldspar. The albitization of potash feldspar, see Eq. (6) and Eq. (7), essentially caused by ion exchange between Na+ and K+, resulted in the increase of soda feldspar. Due to the mineral alteration, the cementation of feldspar with other rock particles will be somewhat loosened, which further aggravates the occurrence of hydrolysis reaction and alkaline corrosion. Due to high richness in clay minerals, which easily attract water molecules to form a strong hydrated film51,52, the cementation of WCFS will be declined and the plasticity will be strengthened. The hydration of kaolinite will significantly affect the degradation of UCS, cohesion, friction angle and tensile strength.

$$KAlS{i_3}{O_8}\left( {potash{\text{ }}feldspar} \right){\text{ }}+N{a^+} \to NaAlS{i_3}{O_8}\left( {soda{\text{ }}feldspar} \right){\text{ }}+{K^+}$$
(6)
$$A{l_4}\left[ {S{i_4}{O_{10}}} \right]{\left( {OH} \right)_8}\left( {kaolinite} \right)+4{H_2}O \to A{l_4}\left[ {S{i_4}{O_{10}}} \right]{\left( {OH} \right)_8} \bullet 4{H_2}O$$
(7)

Micro-fracture and its implication

SEM results and uniaxial compression failure pattern

In order to investigate the reason for the deterioration of the mechanical properties of WCFS in this study, the scanning electron microscope tests were performed on WCFS subjected to different pH levels for 20 h, see Fig. 13. There was a mass of natural pores between particles in the natural state, and kalinite was the critical media cementing other mineral particles such as quartz and feldspar. In the uniaxial compression process, WCFS specimens presented classical single slope shear failure. After soaked in deionized water, the coarse crystal particles were eroded and peeled off from the surface, thus making mineral particles seemingly more obvious and surface roughness much larger. On the bottom of the soaking solutions were some sand-like settlings. In this state, the failure pattern was mainly characterized by tensile fracturing. In pH 7 solutions, the number of dissolution pores occurring on specimen surface increased. The mineral grain structure tended to be loose, accompanied by fractures arising between microstructures due to the feldspar hydrolysis and kaolinite hydration. The failure pattern was still dominated by tensile fracturing along the cementing media between particles in this state.

For the specimens soaked in pH 10 and 12 solutions, the number and dimension of dissolution pores increased evidently, and microfractures gathered and connected because of mineral crystalline lattice breaking, indicating that the rich OH− in medium to strong alkalinity can cause drastic erosion to mineral particles from microstructural perspective. This phenomenon can be attributed to the intensification of quartz and feldspar hydrolysis and kaolinite hydration in high pH level cases. In this state, the coexistence of tensile and shear fracturing featured the failure pattern; nearby the main facture developed a number of minor fractures, specimen completeness became worser, and masses of flake fragments spalled from the rock body.

Fig. 13
Fig. 13
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WCFS uniaxial compression failure pattern microstructure profile acquired by SEM in different cases. (a) natural state, (b) deionized water, (c) pH = 7, (d) pH = 10, (e) pH = 12.

Micro-fracture generate mechanism

The hydro-chemical weaken behavior not only reduces rock strength, elastic modulus, but also change the microcracks occur, accumulation and connection53,54. To study the micro-fracture failure mechanism of WCFS specimens during uniaxial compression tests under dry and alkali corrosion conditions, the loaded specimens were sectioned and observed with microscope. Figure 14a presents hydro-chemical corrosion effect on mineral particles change the morphological features, some mineral transformation as ions form into solutions, that caused the inter-particles porosity or that in the cement increased. On the other hand (see Fig. 14b), alkaline water lubricated and softened the interfaces between the mineral particles or the cement, thereby decreasing the friction coefficient and cohesion along these interfaces. Figure 14c and d presents two typical microscopic images of dry and alkali corrosion specimen, the microstructure of dry WCFS after uniaxial compression is primarily characterized by transgranular fracture, with numerous visible microstructural fractures in the SEM images. When zooming in on the fracture surface at ×1000 magnification, local crystal nucleation cracks can be observed on the fractured surface, indicating that the fracture mode of the WCFS microstructure in a dry state is transgranular model. Under loading conditions, most of microstructures are interconnected through transgranular fractures, leading to the formation of macroscopically shear fractures. Figure 14d also shows microscopic image of the fractured surface of WCFS affected by alkali corrosion and loaded. It can be seen that after alkali corrosion, the transgranular fractures in the sandstone microstructure decrease. Due to the alkaline water physicochemical deterioration of intergranular cementation, the paths of microcrack propagation along the grain boundaries are preferentially followed, thus not leading to grain fracture. Under loading conditions, it is easier for microstructures to form misalignments and slips, forming macroscopically tensile cracks.

Fig. 14
Fig. 14
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Hydro-chemical erosion process: (a) erosion, dispersion and transport action of mineral particles, (b) deterioration of cementation, (c) grains failure path, (d) grain loaded failure pattern.

Hydro chemical damage model

Model construction

The total damage of WCFS corroded by alkaline water can be expressed as Eq. (8):

$$D=1 - (1 - {D_C})(1 - {D_M})$$
(8)

Where, DC refers to the WCFS chemical damage due to alkaline water corrosion, and DM refers to the stress damage induced by external loads. Considering that the reaction of rocks and chemical solutions frequently leads to quality variation due to the generation of new minerals and dissolution of previous minerals, DC can be further expressed as Eq. (9):

$${D_C}{\text{=}}\frac{{\Delta m}}{{{m_0}}}$$
(9)

where Δm refers to the quality of rock media dissipated by chemical reactions, and m0 refers to the total reactant quality of rocks.

As WCFS hydro-chemical degradation is closely related to the chemical ions of solutions, the damage degree is mainly characterized by the rate of OH− (in solutions) reacting with effective minerals (in specimens) and the ion concentrations of products. Assume that the reacting Formulas for WCFS effective minerals and OH− in solutions can be expressed as Eq. (10):

$$aA+bO{H^ - }=B+C$$
(10)

where A and OH− are reactants, and B and C are products.

According to the chemical kinetic Formulas, Eq. (11):

$${V_0}=kC_{A}^{\alpha }C_{{O{H^ - }}}^{\beta }$$
(11)

where V0 refers to the instantaneous reaction rate of rock specimens and chemical solutions with different pH levels, k is the chemical reaction rate constant, CA and COH− are the instantaneous concentration of A and OH− at a specific time, respectively, and α and β the concentration indexes of their reactant.

Water can also pose damage to rocks in the hydro-chemical reaction process. As the chemical reaction between the primary reactants, rock mineral and OH− played a major role on WCFS degradation. Therefore, \(\:{C}_{A}^{\alpha\:}\) is considered a constant, and Eq. (11): can be simplified as Eq. (12):

$${V_0}=\lambda C_{{O{H^ - }}}^{\beta }$$
(12)

Assume that the duration time of rocks soaked in chemical solutions is t, the function of OH− concentration variation is COH−(t), in mol/L, and the volume of soaking solutions is V. The molar masses of the substances containing OH− and A consumed by chemical reactions after t are respectively, Eqs. (13) and  (14):

$${N_{O{H^ - }}}=\int_{0}^{t} {\lambda C_{{O{H^ - }}}^{\beta }} (t)Vdt$$
(13)
$${N_A}=\frac{b}{a}{N_{O{H^ - }}}=\frac{b}{a}\int_{0}^{t} {\lambda C_{{O{H^ - }}}^{\beta }} (t)Vdt$$
(14)

Assume that rock media are homogeneous. T refers to the time when OH− or A is consumed completely, at which the molar mass of the substances containing OH− consumed by chemical reaction is MOH−. Therefore, the consumption of substance A is Eq. (15):

$$\Delta m={N_A}{M_A}=\frac{{b{M_A}}}{a}\int_{0}^{T} {\lambda C_{{O{H^ - }}}^{\beta }} (t)Vdt$$
(15)

Substitute Eqs. (15) into  (9): to acquire the expression of DC, Eq. (16):

$${D_C}=\frac{{\Delta m}}{{{m_0}}}=\frac{{b{M_A}}}{{a{m_0}}}\int_{0}^{T} {\lambda C_{{O{H^ - }}}^{\beta }} (t)Vdt$$
(16)

Assume that there are n kinds of substances (in WCFS) reacting with OH− (in alkaline solutions), and the reaction rate is V1, V2… and Vi, respectively. The consumption of effective substances contained by rocks is Eq. (17):

$$\Delta m=\sum\limits_{{i=1}}^{i} {\frac{{{b_i}{M_{{A_i}}}}}{{{a_i}}}\int_{0}^{T} {\lambda C_{{O{H^ - }_{i}}}^{\beta }} (t)Vdt}$$
(17)

The corresponding total chemical damage of rocks can be expressed as Eq. (18):

$${D_C}=\frac{{\Delta m}}{{{m_0}}}=\frac{{\sum\limits_{{i=1}}^{i} {\frac{{{b_i}{M_{{A_i}}}}}{{{a_i}}}\int_{0}^{T} {\lambda C_{{O{H^ - }_{i}}}^{\beta }} (t)Vdt} }}{{{m_0}}}$$
(18)

The damage caused by the stress effect can be expressed according to55:

$${D_M}=A{(\frac{\varepsilon }{{{\varepsilon _C}}})^B}$$
(19)

where \(\:A=1-\frac{{E}_{C}}{E}\) and \(\:B=\frac{{E}_{C}}{E-{E}_{C}}\), where εc and Ec refer to the peak strain and elastic modulus of uneroded rocks, respectively.

Substitute Eqs. (18) and  (19) into (8) to acquire WCFS comprehensive damage factor under the condition of alkalinity-stress damage, which is expressed as Eq. (20):

$$D=1 - \left[ {(1 - \frac{{\sum\limits_{{i=1}}^{i} {\frac{{b{M_{{A_i}}}}}{{{a_i}}}\int_{0}^{T} {\lambda C_{{O{H^ - }_{i}}}^{\beta }} (t)Vdt} }}{{{m_0}}})(1 - A{{(\frac{\varepsilon }{{{\varepsilon _C}}})}^B})} \right]$$
(20)

According to the stress-strain relationship, the elastic-brittle constitutive model of damaged rock subjected to hydro-chemical effect is:

$$\sigma =(1 - D)E\varepsilon {\text{=}}(1 - {D_C})(1 - {D_M})E\varepsilon$$
(21)

The lab tests indicated that alkaline corrosion posed significant impacts in the compaction stages of WCFS specimens. Thus the above constitutive model should be classified into different stages. Assume that the relationship between strain and stress in the compaction stage conforms to a specific exponential function, that is, σ = εn, where n refers to the fitting parameter of the curve. No secondary fractures were generated in the compaction stage, meaning that rock specimens only experienced chemical damage. The stress-strain relationship is expressed as Eqs. (22) and  (23):

$$\varepsilon =(1 - {D_C})\varepsilon '$$
(22)
$$\sigma ={(1 - {D_C})^n}{\varepsilon ^n}$$
(23)

The damage in the elastic-brittle stage is Eq. (24):

$${D_M}=A{(\frac{{\varepsilon - {\varepsilon _n}}}{{{\varepsilon _C} - {\varepsilon _n}}})^B}$$
(24)

where εn is the strain corresponding to the compaction stage.

The piecewise expression of WCFS stress and chemical damage under alkaline corrosion is as follows, see Eq. (25):

$$\sigma =\left\{ \begin{gathered} {(1 - {D_C})^n}{\varepsilon ^n},{\text{ }}0<\varepsilon \leqslant {\varepsilon _n} \hfill \\ (1 - {D_C})(1 - {D_M})E(\varepsilon - {\varepsilon _{^{n}}})+{(1 - {D_C})^n}{\varepsilon ^n},{\text{ }}{\varepsilon _n} \leqslant \varepsilon \hfill \\ \end{gathered} \right.$$
(25)

Model verification

The stress-strain curves of WCFS, which had been soaked for 4 h in solutions of pH at pH 7, 10, and 12, respectively, were selected to verify the damage constitutive model. Table 2 lists the OH− concentration in different reaction periods under pH = 12 conditions. The functional relationship between COH− and t is obtained by data fitting, as expressed in Eq. (26). Differentiate Eq. (26) to acquire VOH− (Eq. 27), and substitute the value of COH− and VOH− to Eq. (12) to calculate out the λ. Then a, b, A, and B can be calculated out according to Eqs. (11, 20 and 25), respectively. The final calculation results are summarized as Table 3.

$${C_{OH - }}=0.003{t^2} - 0.1058t+0.949$$
(26)
$${V_{OH - }}=0.006t - 0.1058$$
(27)
Table 2 OH− concentration variation.
Full size table
Table 3 Parameters of WCFS damage constitutive model.
Full size table
Fig. 15
Fig. 15
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Comparison between model calculation results and experimental data.

Comparisons between the above model and the experimental data, as shown in Fig. 15, show a good match under different alkaline circumstances, especially for the pre-peak stages. Some scholars proposed chemical damage constitutive models of different types of rock under uniaxial compressive strength56,57, the specific form of the formula as follows:

Equation (28): Feng (limestone):

$$\sigma =\left\{ \begin{gathered} {\sigma _A}{(\varepsilon /{\varepsilon _A})^2},{\text{ }}\varepsilon \leqslant {\varepsilon _A} \hfill \\ {\sigma _A}+E\left[ {(1 - {D_0})(\varepsilon - {\varepsilon _A}) - m{{(\varepsilon - {\varepsilon _A})}^{k+1}}} \right],{\text{ }}\varepsilon \geqslant {\varepsilon _A} \hfill \\ \end{gathered} \right.$$
(28)

Equation (29): Huo (sandstone):

$$\sigma =(1 - D)(1 - D'){E_0}\varepsilon$$
(29)

Equation (30): Liu (sandstone):

$$\sigma =\left\{ \begin{gathered} {E_t}\varepsilon \left[ {1 - \exp [ - \frac{1}{m}{{(\frac{\varepsilon }{{{\varepsilon _{01}}}})}^m}^{{_{1}}}]} \right],0 \leqslant \varepsilon \leqslant {\varepsilon _e} \hfill \\ {E_t}(\varepsilon - {\varepsilon _e})+{\sigma _e},{\varepsilon _e} \leqslant \varepsilon \leqslant {\varepsilon _p} \hfill \\ {E_t}(\varepsilon - {\varepsilon _e})\exp [ - {(\frac{{\varepsilon - \varepsilon p}}{{{\varepsilon _{02}}}})^{{m_2}}}]+{\sigma _p},\varepsilon >{\varepsilon _p} \hfill \\ \end{gathered} \right.$$
(30)

Where “m” is the damage coefficient of rock material, “k” is the material coefficient of rock. “E” and “ε” can be obtained from the stress-strain curve of the specimen.

Using the above models to calculate the UCS of WCFS under the condition of pH = 12, corrosion duration time 20 h, Fig. 16 shows the stress-strain curve obtained by the damage constitutive models and experimental results. It can be seen that, except by Eq. (26), the curves calculated by other models have more considerable deviations with experimental data. In the initial compression stage, compared with other dense rock, WCFS existed a large number of pores, and is more vulnerable to corrosion by alkaline solution, Eq. (26) can better explain this process. In the linear elastic stage, elastic modules calculated by Eqs. (28) and  (29) are greater than the experimental result, and that by Eq. (30) is lower. At the yield and failure stage, the error of peak strength of Eq. (26) is the least. Thus, the hydrochemical damage model is appropriate for predicting the strength of alkaline corroded WCFS.

Fig. 16
Fig. 16
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Comparison stress-strain curve among four predict models.

Conclusion

Weakly cemented fine-grained sandstone (WCFS) uniaxial compressive strength, hydro-chemical softening coefficient, initial compression modulus, elastic modulus, cohesion, internal friction angle, and tensile strength decrease with pH levels and soaking durations. The UCS of soaked WCFS presents a nearly negative exponential relationship with the soaking duration. The degradation effect of alkalinity on elastic modulus was obvious in the initial soaking period, then went slight with alkalinity enhancement in the medium stage and reached a similar level after 20 h. The hydro-chemical softening coefficient gradually decreased with the time of soaking; the higher the pH level, the more rapid the UCS decrease in the initial period; soaking time also has approximately a negative exponent relation with the hydro-chemical softening rate. WCFS cohesion decrease was much faster within 4 h and gradually slower after this period; the higher the pH level of soaking solutions, the lower the cohesion, but the alkalinity effect on cohesion was limited. The impact of ion concentration in soaking solutions on tensile strength was significant. Also, in ionic solutions, WCFS tensile strength degraded faster within the first 4 h.

Alkaline circumstances contribute to the change of the proportions of quartz, feldspar, and kaolinite occurring in weakly cemented rocks, deteriorating the silicate skeleton and weakening the cementation degree of rock particles. Due to hydrolysis reaction and alkaline corrosion, the minerals with high strength decrease significantly with consequently WCFS degradation in mechanical strength. All potash feldspar was corroded after hydrolysis reaction and ion exchange, thus leading to a severe WCFS degradation. The hydration of kaolinite will further strengthen the plasticity and the degradation in UCS, cohesion, friction angle, and tensile strength. From the ion point of view, the higher the concentration of Al (OH)4− and SiO32− in solutions, the more significant WCFS degradation. Through SEM method found the controlling effect on the transformation in the micro-fracture form (from transgranular fracture to intergranular fracture) on the mechanical properties deterioration.

Considering that the chemical reactions between different pH level solutions and WCFS effective minerals were different, the molar mass of WCFS minerals participating in chemical reactions was obtained by calculating the consumption of OH− in solutions within different reaction periods, and a chemical damage Formulas for weakly cemented rocks was presented. In order to evaluate the WCFS performance in the elastic-brittle stage, a stress-chemical coupling constitutive model was constructed and verified with experimental data and other models presented by other scholars, which can be used to predict the mechanical properties of WCFS subjected to alkali water corrosion.