Development of a Universal Landslide Hazard Potential Model for Mudrocks - Fuzzy Logic and Molecular-level Modeling approaches

doi:10.21203/rs.3.rs-2002444/v1

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Development of a Universal Landslide Hazard Potential Model for Mudrocks - Fuzzy Logic and Molecular-level Modeling approaches

https://doi.org/10.21203/rs.3.rs-2002444/v1

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published 19 Jan, 2023

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The phenomenon of the reduction of shear strength due to moisture-induced swelling and subsequent slaking of the mudrocks is one of the leading causes of landslide hazards in mountainous terrain. In the practice, empirical/semi-empirical approaches adopted for the determination of this hazard are mostly based on macro-level factors. But they do not comprehensively cover the micro-level factors, which contribute to the complex swelling/slaking process. Therefore, a comprehensive fuzzy-logic-based model was developed in this study, which includes both the macro-level landslide contributing factors and the micro-level factors, such as mineralogy, cementation, cation exchange capacity, in situ moisture content, density, and stress state. The model resulted from the molecular simulations of swelling and the subsequent slaking processes using Monte Carlo, molecular mechanics, and molecular dynamics. The results of the micro-level model are incorporated into the fuzzy-logic model to create a universal landslide hazard potential model for the slopes composed of mudrocks. The micro-level behaviour is incorporated in the coupled model via the cohesive energy density parameter for the mudrocks. The final coupled model was verified through the accurate prediction of the landslides and also by comparing the predicted terminal water content with the water content of the mudrock samples collected from the triggered landslides.

Landslide hazard potential

mudrocks

molecular-level simulations

fuzzy logic

Among other rock-forming mountainous slopes, clay-bearing mudrocks such as mudstone, shale, siltstone, and claystone have always been the major and integral parts of the fragile strata leading to landslides. Landslide Hazard Potential (LHP) in the slopes composed entirely or partially of mudrocks is quite a complex phenomenon and is controlled by multiple factors and processes occurring both at macro and micro levels. Even in slopes partially composed of mudrocks, the slope stability, in most cases, is exclusively controlled by these clay-bearing rocks. The macro-level factors leading to landslides include the slope configuration (height, slope, shape), surface and subsurface hydrological conditions, vegetation type and density, and local weather and climatic conditions. On the other hand, micro-level factors consist of the processes leading to the moisture-induced swelling and subsequent slaking of the structure of the mudrocks such as the type, nature, and content of the swelling-prone clay minerals, the interaction of these swelling clay minerals with both the non-swelling clay and the non-clay minerals, cementation/bonding due to the cementing agents, in situ moisture content, density, and the stress state. Stress relief and weathering forces induce negative pore pressures (suction) in the rock structure leading to the intrusion of the air and water into the microstructure consisting of nanopores and fissures. In addition to the volume change, this process may also result in the degeneration of the weak cementation/bonding among the particles. The resulting reduction in strength due to swelling and/or loss of cementation has always been considered as the major preparatory/conditioning and triggering factors resulting in the landslides in the mudrocks.

Existing research comprises several empirical and semi-empirical correlations/models and isolated studies on the effects of macro and micro-level factors on the swelling/slaking of mudrocks but no unanimous and comprehensive model that encompasses all these macro and micro-level factors simultaneously exists so far. Present general practice for the assessment of the slaking and swelling characteristics is to perform isolated laboratory tests on the field samples such as slake durability and/or swell potential. All these existing slake durability assessment approaches and tests (Deo, 1972; Franklin and Chandra, 1972; Wood and Deo, 1975; Chapman et al., 1976; Oakland and Lovell, 1982; Withiam and Andrews, 1982; Santi, 1995a, b; Walkinshaw and Santi, 1996; Santi and Koncagul, 1996; Santi and Higgins, 1998; Santi, 1998; ASTM D4644) and swell potential tests (ASTM D4546) are empirical and provide only an indirect and qualitative assessment of the durability of the tested samples. However, as enumerated earlier, weathering potential of intact mudrocks is controlled by many factors, including the properties of the constituent materials and the corresponding structure such as mineralogy, nature of minerals, porosity and fracturing (Franklin and Chandara, 1992; Olivier, 1990; Dick and Shakoor, 1992). The properties of the rock may be altered during the weathering or similar processes and will result in a weak and moisture-sensitive rock structure (Prodan and Arbanas, 2016), consisting of uncemented clay minerals. However, the rock may gain strength due to the cementation of the discontinuities through the cementation agents such as ferrous oxides, calcite, or siliceous filling material (Aydan et al., 2013). The interaction between rock constituents and the moisture results in the swelling and finally flaking of the surface matter (Santi and Koncagul, 1996; Erguler and Ulusay, 2009; Hu et al., 2017). Smectite, mixed-layer clays, and zeolites are generally responsible for the volume change of the rock structure (Vergara and Triantafyllidis, 2016; Selen et al., 2020). Slake durability is one of the procedures to determine the durability of the material from the engineering point of view (Czerewko and Cripps, 2006). The slake durability test simulates the acceleration of the weathering process by opting for slaking in a specified water-borne drum and the subsequent sieving procedures (Franklin, 1979). However, recent studies have emphasized the importance of clay mineralogy, micro fabric, and strength in the physical breakdown process of the rock structure (Taylor and Spears, 1970). They further emphasized the importance of the presence of expansive clay minerals in the degradation process. Another study (Gökceo et al., 2000) indicated that the type and amount of swelling clay minerals are the major factors controlling the slake durability. To measure the effect of initial wetting on the slake durability, a modified version of the test was also proposed (Selen et al., 2020).

In addition to the studies on the micro-level factors on the slake durability of the mudrocks, the assessment of the overall slope stability scenario requires the simultaneous consideration of several factors, which affect in varying degrees and several interaction levels. It is difficult to quantify these factors into a simple factor of safety. Such a complex scenario is usually quite effectively assessed using the artificial intelligence (AI) based technique. Fuzzy set theory or fuzzy logic is one of the AI techniques usually employed in landslide hazard analysis. Such a theory allows for studying the spatial objects as members of a set on a typical map in landslide susceptibility mapping (Tangestani, 2000). Since all the factors affecting the landslides are subjective or qualitative, a fuzzy logic-based technique is most appropriate for the analysis of landslide hazards. In essence, in a typical fuzzy logic process, all the contributing factors are assigned fuzzy attributes considering their comparative contribution to the slope stability process. Lee and Juang (1992) carried out failure potential mapping of mudstone slopes in Taiwan using fuzzy sets. They developed a qualitative evaluation technique for assessing the slope failure potential. The main thrust of the evaluation scheme was to design an evaluation tree consisting of two levels of factors that are known by experts to affect the stability of slopes. The selection of these factors, and the weights among them, were based on the results of a survey of expert opinions on slope failures in the Southwestern Taiwan mudstone area. Finally, a slope failure potential map was generated for the area under study. Likewise, Jawaid (2000) studied the use of the fuzzy theory for the hazard assessment of landslides. He prepared a low-cost quantitative landslide potential evaluation scheme using the fuzzy set theory and used an evaluation tree similar to Lee and Juang (1992). Whereas Lee and Juang (1992) considered the topography, geology, environment, and metrology as the primary factors affecting slope stability. Chi et al. (2002) also studied the usefulness of the spatial data in fuzzy set theory for landslide hazard mapping in Boeun Korea.

The review presented above was performed with the available bibliography in the field and summarizes the knowledge about a few macro- or micro-level aspects of landslide hazard potential. However, counting with a precise landslide hazard prediction model for the mudrocks requires the simultaneous consideration of both macro- and micro-level processes affecting slope stability. In turn, this requires the development of individual macro- and micro-level models and their integration into a comprehensive and universal nature model. Therefore, this study aimed to develop a comprehensive landslide hazard model combining both macro- and micro-level behaviour models, specifically for the mudrocks of the Murree hills in northern Pakistan. The macro-level factors were modelled by the fuzzy logic-based AI method, while the processes that contributed to the swelling and slaking of these mudrocks were incorporated via modelling the micro-processes and interactions through molecular-level simulations. The coupled model resulted in a Landslide Hazard Potential Indices (LHPI) map of the slopes composing the mudrocks. The results of the model were verified through the accurate prediction of the landslides and also by comparing the moisture content of the samples acquired from the triggered landslides with the ones estimated through the micro model.

Murree is a hill station in the North of Pakistan. It is located 65 km northwest of the national capital Islamabad, and 75 km southwest of Abbottabad city. Murree is one of the busiest hill stations in northern Pakistan and attracts a large number of tourists. It is estimated that there are 1000 + multistory hotels and guest houses in the Murree urban area. The local population of Murree urban area increases approximately from about 35,000 to 400,000 + during the peak summer season. The altitude of the Murree hills above the Mean Sea Level (MSL) ranges from 1600 m at Ghora Gali to a maximum of 2200 m at Kashmir Point. The location map of the Murree hills is shown in Fig. 1 (GSP, 1999), while the layout of the road network of the study area is shown in Fig. 2, highlighting the main highways and roads of the urban Murree area.

Geologically, the study area entirely consists of Murree Formation (Tmm). Murree Formation rocks are alternate sequences of Sandstone and mudrocks, i.e., Siltstone/Claystone and Shale with occasional intraformational conglomerate (GSP, 2000). The study area is characterized by both diurnal and seasonal variations in weather and climate (Khan et al., 1987). Generally, the climate is tropical but, at higher altitudes, the winters are very cold with subfreezing temperatures. According to Gohar (1987), the study area falls in the Maritime climatic zone, characterized by high rainfall and warmer temperatures. The area receives most of the rainfall from July to September, known as Monsoon rains, as snowfall. Moreover, the area receives winter rains in March accompanied by the thawing of snow. The average annual rainfall in the area is from 1200 to 1400 mm (Khan et al., 1987; Gohar, 1987). The summer temperatures in Murree and Galiat vary between 25°C to 30°C, and the humidity ranges between 50% and 60% (Khan et al., 1987). Generally, the hills around Murree and their southern slopes have a fairly thick growth of Pine trees, but slopes with grasses, bushes, and with very scanty vegetation are also common.

Among Murree Formation rocks, mudrocks and particularly shale and claystone are key contributors to the formulation and triggering of landslides in the area (Ahmed and Akram, 2018; Akram and Ahmed, 2006). Moreover, several factors, including deforestation, high precipitation, and intense weathering of the mudrocks, lead to minor to major landslides in the area, which disrupts the economic activity and loss of property and human life.

The study methodology comprised a multi-prong approach encompassing the assessment, determination, and coupling of macro- and micro-level factors contributing to the slope instability of the mudrocks composing the Murree hills. The study, in its first instance, consisted of developing a macro-level landslide hazard prediction model using the fuzzy logic technique. For this model, the causal and triggering factors affecting slope stability were assessed. For this purpose, field and laboratory studies, and ultimately LHPIs, were mapped for the mudrock strata of the Murree formation. One of the prime factors that affect the slope instability process is the swelling and subsequent slaking of these mudrocks upon adsorption of water. Since this behaviour is essentially controlled by the micro- or molecular-level processes contributing to the swelling and slaking of these mudrocks, molecular-level simulations of these processes were carried out using computer simulation software. The results of micro- and macro-level testing on the mudrock samples and laboratory control samples were used to acquire parameters for the formulation and verification of these molecular-level simulation models. The micro-level behaviour model of these mudrocks, developed as a result of these simulations, was then coupled with the fuzzy logic-based LHPI model to formulate a comprehensive and precise landslide hazard prediction model.

3.1 Macro-level modelling

Based on the relative intensity and gravity by which each of these factors affects the instability, they are generally divided into primary, secondary, and tertiary-level factors. Each primary factor, in turn, is further stemmed into secondary and tertiary factors; each one of these contributes to the stability process to a variable degree. As it is very difficult to translate all these factors into a determinate, closed-form or analytical solution, one of the most effective and practical ways of handling such scenarios is to use the fuzzy logic theory. In this method, a fuzzy attribute is allotted to all the factors affecting the instability process. These factors and the corresponding attributes are then fuzzified and converted to a crisp number. The crisp number is then attributed to the qualitative assessment of the level of the potential of instability. Based on the individual weightage of each factor in the stability process, these multi-level factors are integrated to generate LHPI.

As typical of any LHPI process, primary and secondary level factors, which result in the slope instability for a specific area and particular strata, are ascertained as a first step. In the second step, relative weightage/grade is awarded to the primary and secondary level factors. These grades are awarded considering the comparative contribution to the slope instability processes. In this regard, a detailed study of the natural- and human-induced processes contributing to the landslides in the area was previously conducted to determine these weightage/grades. Finally, based on these conditioning/triggering factors, the spatial and temporal variation of these processes was carried out. For the area under study, the required steps were accomplished by conducting an in-depth study of the existing landslide studies, the landslides-related projects executed in the area, and further comprehension of the slope instability problems through extensive reconnaissance of the study area. Finally, the primary and secondary level factors, considered responsible for the conditioning and triggering of the landslides in the study area, are tabulated in Table 1. Similarly, the tertiary level factors identified for the study area are listed in Table 2.

A. Collection of Landslide Hazard Potential (LHP) data

Tertiary level attributes of the primary and secondary level factors affecting the slope instability, assigned in the previous section, were recorded in the field by an experienced field team of geologists through walk-over surveys. These attributes, listed in Table 2, were collected along all the roads and other routes in the study area. The discrete data collected for the study area was then integrated as area maps for the geological strata, hydrological conditions, drainage conditions, vegetation type, vegetation density, and slope protection facilities.

B. Analysis of LHP data

Statistical analysis of the LHP data was carried out using the fuzzy logic technique. Fuzzy logic is one of the techniques classed under bivariate statistical analysis techniques, and as explained above, it has been widely used for the LHP analysis. The fuzzy logic analysis for this study consisted of a sequence of several steps for the conversion of LHP data into Landslide Hazard Potential Indices (LHPI). Various steps were carried out for the fuzzy logic analysis, including a fuzzy input, fuzzification to crisp value through certain rules, and defuzzification to the final LHPI crisp values.

In the fuzzy logic process, “input” means the input of primary, secondary, and tertiary level LHP data in the form of an evaluation tree. The values of the recorded LHP factors were input in the process as fuzzy expressions such as very high, high, medium, low, etc. After assigning numerical equivalents to all the recorded fuzzy data, these fuzzy expressions were transformed into crisp values. In this study, all the recorded LHP data were fed into a database for further analysis using a ‘fuzzifier engine’. In the fuzzy logic process, the function of a fuzzifier is to convert the crisp data into the equivalent fuzzy data. The entire process is governed by several in-built rules and inferences.

Based on the extensive investigations and observations carried out, several sets of rules were defined for the fuzzy logic process. For example, in the process, the intense rainfall was awarded a grade of ‘A’, which means that it has got a maximum effect on the slope stability. But, as a rule, the effect of intense rainfall will be maximum on the boulder clay/shale strata rather than on intact rock. Therefore, a rule is in-built into the process which controls the incorporation of the relative effect of intense rainfall on several types of strata. The analysis process is outlined below, while the typical calculations for mudrock are shown in Table 3. Fuzzy to the crisp conversion of the grades assigned to multi-level factors is carried out as A + = 1, A = 0.93, B = 0.78, C = 0.58, D = 0.35, and E = 0.13.

LHPI = [{(T-S)1^P1} x {(T-S)2^P2} x ---- x {(T-S)n^Pn)}]/(SP) ………………………………………(1)

n is the total number of primary level factors; P is the crisp value for each primary factor; (T-S) is the conversion of tertiary to secondary level factors stemming from the fuzzy logic evaluation tree.

T-S = [{T1^S1} x {T2^S2} x ---- x {Tn^Sn}]/(SS) ……………………………………...…..………….(2)

The outcome of Eq. 1 is a crisp value of LHPI ranging from 0 to 1, which is finally transformed to the equivalent fuzzy attribute via the following relation:

LHPI > 0.85 = very high, LHPI: 0.70–0.85 = high, LHPI: 0.45–0.70 = medium, LHPI: 0.25–0.45 = low, LHPI < 0.25 = very low

The final result of the above process was an LHPI for about 30 m sections along all the surveyed routes of the study site. These discrete LHPIs were then integrated and plotted as surface maps for the entire study area. In addition to the collection of the data related to the specified factors during the field survey, a landslide survey was also carried out along the study routes based on observations and interviews with the local population. The information gathered included the type and nature of landslides, intensity, and frequency of occurrence, season and soil conditions in which triggering mostly occurred, and the maintenance/rehabilitation history.

C. Sampling of mudrock samples

Since mudrocks and particularly shale and claystone in the Murree Formation are key contributors to the formulation and triggering of landslides in the area, shale and claystone samples were acquired from several locations where landslides were observed. At each location, samples were acquired both from the intact shale strata present in the areas adjacent to the landslides and from the landslide material itself. Data collected against several multi-level factors were verified and confirmed by performing laboratory testing on these collected samples. The test procedures and details are provided below, in section 3.3, along with the testing details on laboratory control specimens for the verification/calibration of micro-level simulation results.

3.2 Micro-level simulations and modelling

In this study, molecular-level simulations were carried out to reproduce the molecular-level interaction processes of a clay-bearing rock. The simulations were accomplished through the Materials Studio software package (2017) and the interactions were simulated using Monte Carlo (MC) technique aided by molecular mechanics (MM) and molecular dynamics (MD) procedures. These simulations were carried out through the software running on high-performance computing (HPC) facilities available at KFUPM, KSA.

The molecular simulation scheme was carried out following the procedures described by Ahmed and Abduljauwad (2017), with minor modifications, for natural and compacted swelling clay structures. Such modifications aimed to modify and augment the procedures to incorporate the variations specific to the structure of clay-bearing rocks. For simulation of the structure of these rocks, higher compaction pressures of an order of 1–10 GPa were used to simulate the pressures borne during geologic formation procedures. All the corresponding parameters and properties were then evaluated accordingly. The micro-level study consisted of molecular-level simulations of the interaction of various constituents of the clay-bearing rock structure. The simulations were performed for all the possible interactions between swelling clay minerals, non-swelling clay minerals, cementing agents, and the water interacting with these solids in various forms (Tables 4 and 5). In the molecular-level modelling of the clay matrix, simulations were performed for the formation of clay minerals (e.g., montmorillonite/illite) matrix structure, and the interaction of this matrix with the pore water and the dissolved salts (e.g., gypsum, calcite). Views of single clay particles in dry and hydrated states and several possible clay structures created during the simulations are shown in Fig. 3. The results of molecular simulations were finally presented as a set of equations relating the cohesive energy density (CED) to the swell per cent and the terminal moisture content leading to the complete swelling of the clay structure. CED, a measure of the cohesiveness/bonding of the molecules in any molecular-level interaction simulations, was used as a state parameter in the current study, relating all the possible volume change behaviour.

3.3 Laboratory testing and evaluations

Disturbed and undisturbed mudrock samples (shale, siltstone, and claystone), retrieved during field studies, were subjected to mineralogical analysis, swell, moisture content, density, and slake durability characteristics in addition to the soil/rock classification tests. In addition, laboratory control samples were also prepared and subjected to mineralogical/chemical characterization and per cent swell tests (ASTM D4546) (Tables 4 and 5).

To acquire parameters to be used as input in the simulation schemes and also the verification of the molecular simulations model, X-ray diffraction (XRD) tests were performed using Rigaku Miniflex II equipment. XRD analysis and cation exchange capacity (CEC) tests were carried out on all the samples acquired from the landslide locations, and the results are summarized in Tables 4 and 5. In addition, the triaxial Unconsolidated-Undrained (UU) tests were performed on undisturbed shale/claystone samples (ASTM D2850). These tests were performed on specimens prepared at various saturation levels of 30, 50, 75, and 100%. Furthermore, the slake durability tests were also conducted on the natural mudrock samples (shale, claystone, and siltstone) according to ASTM D4644.

For a better organization of the results and analyses derived from the multi-level research activities performed in the current study, three separate sections are presented, namely the fuzzy logic-based macro model, the molecular-level swelling and slaking model, and the coupled model.

4.1 Macro-level model

The results of the field survey were prepared in the form of area maps representing the various factors affecting the slope instability in the study area. Typical maps, prepared for the near-surface/local geological strata, vegetation type, and vegetation density, are shown in Fig. 4. The geological strata maps mark the distribution of various forms of near-surface strata such as intact shale, shale bedded with sandstone/siltstone/claystone, highly weathered sandstone with clay matrix, and weathered shale. Using the fuzzy-logic analysis procedure, each of these geological strata maps, integrated with other factors such as slope configuration, vegetation type and extent, hydrological conditions, drainage conditions, and protection facility resulted in LHPI maps. For the LHPIs representative of different seasons, the moisture content/saturation levels were varied according to the precipitation expected in each season. The highest saturation levels were considered for the monsoon (July-September) and spring (March-April) seasons.

As the LHPIs developed from the macro model were based on observational assessments of the in situ state of mudrock strata, the observational assessments were verified by the moisture-strength relation (Table 7) and the rock slaking potential results (Table 8). Despite verifying these data, the current nature of the mudrocks could not be assessed accurately by just observational assessments. The assessment of the current in situ swelling and slaking state requires input from the microstructure of these rocks such as the mineralogy, the swelling nature of these minerals, and the nature, type and extent of cementation present among the minerals. Therefore, LHPIs calculated as a result of just observational assessments and supported by the laboratory-developed correlations were not accurate. The lack of accuracy of these LHPIs was demonstrated by the low LHPIs at some of the unstable/landslide-prone sections and vice versa.

4.2 Molecular-level swelling and slaking model

The molecular-level simulations resulted in a model which can predict the volume change of the mudrocks with the variation in moisture content, maximum possible volume change, and the corresponding maximum or terminal moisture content. Maximum swelling indicates the point at which the strength of the rock structure reaches its minimum. Similarly, a comparison of current in situ moisture content with the terminal one represents how far the current saturation state is from the one that results in minimum possible strength. This information can be acquired by inputting the mineralogical and chemical composition of these rocks into the micro model. The model has resulted in four distinct zones of density versus CED (Fig. 5), which besides being indicative of maximum volume change also provides knowledge of the slaking potential. The details of the model and the developed equations are provided in the following paragraphs.

All the above-explained phenomena in the molecular simulations have resulted in a model that closely simulates the natural behaviour of the clay-bearing structure. In the below maximum swell per cent Eq. 3, final dry density can be assessed using the relations (4a to 4d).

Swell (%) = (FDD – IDD) / FDD × 100 ……………………..……………………………………(3)

where IDD = initial dry density, FDD = final dry density

FDD_I=[IDD + {(0.000006 x TCEDm + 0.3443)–IDD}] x (102/P)^0.5 TCEDm < 1610 …………..……...(4a)

FDD_II=[IDD + {(0.0004 x TCEDm-0.4517) – IDD}] x (102/P)^0.5 TCEDm > 1610 and < 3360………..(4b)

FDD_III=[IDD+ {(0.00005 x TCEDm + 1.0082) – IDD}] x (102/P)^0.5 TCEDm > 3360……….…….……(4c)

FDD_IV=[IDD+ {(0.0004 x TCEDm-0.7252) – IDD}] x (102/P)^0.5 TCEDm > 5000……………………(4d)

where FDD is g/cm ³, IDD = initial dry density in g/cm³, TCEDm = Total CED in J/cm³, P = seating/confining pressure in kPa

Final water content has been found to exhibit a very close relationship with the van der Waals CED (CED_vw) expressed in Eq. 6. These equations 5 and 6 are plotted in Fig. 6.

FWC = 4E-06xCED_vw³ + 0.0035xCED_vw² + 0.9291xCEDvw + 109.83………………………………......…(5)

where FWC = final water content in per cent, IWC in per cent, CED _vw in J/cm³

CED_vw=-0.0525xIWC² + 6.1935xIWC-118.46+(-162xG/0.2) +(-362xC/0.1) …………………....….......(6)

The molecular-level model was used to plot the terminal/final water content leading to maximum swelling using the basic input parameters such as in situ water content, CEC, calcite content, and the stress state for two clay minerals (smectite) contents (Fig. 7). From the analysis of Fig. 7, we confirm that high cementation causes a reduction in the maximum swell and the corresponding final water content.

As TCED is a required parameter in Eq. 4, Eq. 7 is developed comprising the basic relationship between CED and initial water content.

CED = 0.0625(IWC)³-3.575(IWC)²+10.5(IWC) + 2830 + ΔTCED_CEC + ΔTCED_{cat ------------}......................…..(7)

where TCED = total cohesive energy density in J/cm ³, IWC = initial water content in per cent, ΔTCED_CEC = correction due to CEC, ΔTCED_cat=correction due to binding/cementing minerals/salts and exchangeable cations

In this model, the CED has been correlated to various molecular-level processes and interactions taking place during the complete volume change process in a clay mineral matrix of mudrocks (Ahmed and Abduljauwad, 2017). Due to its sensitivity to the variations in the CEC, interlayer and intralayer cations, anions, water content and density conditions, CED has been correlated with all the possible swelling processes. CED is expressed as the energy required for the transition of a molecule from the liquid phase, with closely placed strongly interacting molecules, to the gaseous phase with distant molecules having minimal interactions (Ahmed and Abduljauwad, 2017). For any group of molecules, total cohesive energy density (TCED) is divided into two components: the electrostatic CED and van der Waals CED. The van der Waals forces may either be repulsive or attractive, while the nature of electrostatic CED is always attractive.

The above-explained model was verified by the swell tests on natural and laboratory control samples. The swell test results on natural samples, including per cent swell and the final water contents, are summarized in Table 6. A quite close correlation with the ones obtained in the molecular simulations (equations 5 and 6) is observed. Likewise, the swell test results from the laboratory control specimens were also consistent with the ones resulting from the molecular simulations.

4.3 Coupled landslide hazard model

As mentioned above, data regarding the contribution of mudrocks to the overall instability or landslide hazard potential were collected through an observational assessment of the weathering/swelling state of these rocks. These observational assessments coupled with the strength and slaking potential laboratory testing results were not successful to forecast the real behaviour of these mudrocks. Therefore, the results of the micro-level model developed from molecular-level simulations were used to incorporate some rational input parameters in the fuzzy-logic-based macro model. In this respect, two aspects of the micro-model were incorporated into the macro-model to assess the swelling and slaking properties of the mudrocks. One of the parameters is the maximum or terminal moisture content that leads to the maximum swelling of the rock structure; the other is the slaking potential. Both of them require input from the CED of the mudrocks encountered and were added to the list of secondary attributes and the corresponding tertiary factors in Table 9 (modified from Table 2).

The final results of LHPIs for various seasons (saturation levels) are shown in Fig. 9. This final model was confirmed through the data acquired regarding the triggered landslides in the last 7 years (2015–2021) and is marked in Fig. 10. Finally, to verify the model, water content measured from the samples acquired from the active/triggered landslides was compared to the final water content determined from the model using equations 6 and 7. The comparison in Fig. 11 reveals a very close prediction by the model and thus establishes the validity and accuracy of the model.

Density versus CED plots presented in Fig. 5 could be divided into four distinct zones. These zones are distinguished based on various clay-bearing structures created due to various types and extent of cementation and/or adhesion among the clay particles. Zone I is marked by the structure owing to a minimal level of cementation and hence swelling is directly proportional to the CED of the mix. CEC, one of the inputs in CED equations, is a measure of the swelling ability of different clay minerals in this zone. On the other hand, in zone II, swelling behaviour is primarily controlled by the cementation among the clay particles in the compacted structure: the higher the cementation or the corresponding CED, the lesser the swelling. In zone III, higher CED is due to the high packing density of the compacted structure of the clay particles and/or cementation among them. The swelling, in this case, increases with CED and is mainly due to the rebound of the highly packed clay particles upon contact with water content. Zone IV represents the rock-like structure created by strong cementation and high density. Due to the presence of this cementation/adhesion, swelling in zone IV decreases with an increase in CED.

In addition to the role of these zones in defining the swell potential, final water content or terminal water content that leads to complete swelling of a particular clay-bearing structure can be calculated using Eq. 5. The micro-model predicts the maximum or threshold water content (Eq. 5) at which maximum swelling occurs and the rock may be subjected to its minimum strength. This threshold water content could be used as one of the indicators of the in situ strength state of the mudrocks. However, the type and extent of cementation among the clay and non-clay particles also play a role in the determination of the slaking potential at this minimum strength level. The minimum strength may still be higher enough to resist slaking. Therefore, the slaking potential at this state may be quite low if a high percentage of cementation is present in the structure of the rock and this cementation will resist the disintegration of the rock structure. This aspect was studied in the light of CED-density zonation in Fig. 5. For the sake of comparison, slaking potential results (Table 8) were superimposed on different zones of Fig. 5 and presented in Fig. 8. This superimposition shows that samples falling in zones I and II have a high slaking potential, while it is least in zone IV. However, zone III represents the samples with an intermediate slaking potential. For the study area, most of the shale samples fell in zones I and II, while claystone samples were mapped in zone III. The siltstone samples got plotted in zone IV and showed the least slaking potential due to the presence of high cementation and the absence of high swelling potential clay minerals. Looking at the slaking potential results of these samples, it could be ascertained that all the samples having CED of greater than 5000 J/cm³ are not slakable or are least slakable. Therefore, based on this observation, a threshold CED of 5000 J/cm³ can be defined as a dividing line between skalable and least slakable rocks. Similarly, samples with CED between 3300 J/cm³ and 5000 J/cm³ could be considered as the ones with medium slaking potential. Based on the above findings, CED and final water content have been added as another set of tertiary-level factors to Table 9 of the fuzzy logic-based macro model. For the study area, claystone and siltstone were considered resistant to slaking, while shale samples with the least cementation were classed as highly slakable in nature.

To verify the universal nature of the micro-level model developed in the current study, it was used to forecast and compare the results of the swell and slakability potential of the mudrocks present elsewhere in the world. In this regard, the data from the two studies (Sarman et al., 1994 and Pejon and Zuquette, 2002) were compared with the ones predicted from the micro model developed in the current study. Sarman et al. (1994) tested the volumetric potential and slaking potential of the forty-two mudrock samples collected across the United States. They also conducted physical, chemical, and mineralogical characterization of these samples. Using this characterization as input to the micro-model developed in the current study was used to predict the swelling potential of these mudrocks. The results, comparing the predicted and the actual results from Sarman et al. (1994) are presented in Fig. 12. The close correlation between the predicted and the actual test results show the comprehensive and universal nature of the micro-model developed in this study. Sarman et al. (1994) concluded that there are factors other than just the clay mineralogy that also control the swelling behaviour of the mudrocks. The close predictions through our micro-model are due to the incorporation of factors such as the cementation due to the presence of salts such as carbonates, high densities resulting in van der Waals repulsions, and initial moisture/water content with respect to the final water content. In addition to the prediction of the swelling behaviour, the slaking potential results from Sarman et al. (1994) were also plotted on the CED and density plot (Fig. 13). The slakability results were also found to have a good correlation with the slakability zones defined and discussed in earlier sections and shown in Fig. 11. Similarly, a comparison was carried out between the predicted results from the micro-model of this study and the one carried out by Pejon and Zuquette (2002). The results in Fig. 14 also indicate a close correlation and confirm the universal and precise nature of the micro-model developed in the study.

The fuzzy-logic-based macro model developed for the mudrocks of the study area has been found lacking in precisely predicting the landslide hazard. However, this model coupled with the micro-model was found to be accurate in such predictions. The parameters and procedures provided in this universal model can be used to predict the swelling and slaking potential of the slopes composed of mudrocks.

For the study area, shale was found to be highly slakable, while siltstone with cementation proved to be the least slakable. The slaking potential of claystone was dependent on the extent of cementation and the nature of swelling clay and non-clay minerals.

The good agreement found between the predicted and the actual landslides and the terminal water content of the samples from the landslide material and few studies elsewhere in the world suggests that the current model can effectively be used universally for the assessment of the landslide potential of the slopes made of mudrocks.

The van der Waals CED was demonstrated to be an indicator of the interaction of the constituents of the rock structure to water sorption and subsequent volume changes, whereas total CED is sensitive to the various volume change variables, such as water content, density, CEC, type and percentage of the exchangeable and non-exchangeable cations.

As the developed model predicts the onset of the landslides in mudrocks concerning the water content, the same model may be associated with any Geographic Information System (GIS) and satellite data-based hazard management system. In this system, the water content information could be assessed at regular intervals from remote-sensed electromagnetic and/or radar data and comparing it to the threshold water content could help in the forecast of landslides.

Acknowledgement

The authors would like to highly acknowledge the support provided by King Fahd University of Petroleum & Minerals (KFUPM), Dhahran, Saudi Arabia and Murree Kahuta Development Authority, Pakistan for the support during the execution of this research.

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Data availability

Data generated or analyzed during this study are provided in full within the published article.

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Development of a Universal Landslide Hazard Potential Model for Mudrocks - Fuzzy Logic and Molecular-level Modeling approaches

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Abstract

Figures

1. Introduction

2 Study Area

3 Methods

3.1 Macro-level modelling

3.2 Micro-level simulations and modelling

3.3 Laboratory testing and evaluations

4. Results And Analysis

4.1 Macro-level model

4.2 Molecular-level swelling and slaking model

4.3 Coupled landslide hazard model

5 Discussion

6. Conclusion And Recommendations

Declarations

References

Tables

Supplementary Files

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