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Air temperature fluctuations cause intermittent shrinkage and expansion of rock blocks close to the surface. These cyclic deformations can bring cumulative and irreversible displacement of blocks down rock slopes, creating potentially dangerous conditions. This chapter presents examples from stations monitoring various slopes and natural cliffs that illustrate this phenomenon. The chapter will also present the results of a laboratory experiment performed on a block system that simulates the typical geological structure of a slope in a stratified and cracked rock mass. Inside a tensile crack, a prismatic rock block serves as a wedge capable of accelerating the cumulative displacement. The results obtained from the laboratory measurements serve as a basis for calibrating analytical and numerical 3D models of the problem. The results of the laboratory experiment and the numerical models clearly show that the wedge is of great importance in accelerating the rate of movement of the blocks on the slope. Further numerical analysis performed on blocks on the slopes of Mount Masada shows that temperature changes alone could explain the blocks’ detachment from the slope.
Shamoon College of Engineering, Beer-Sheva, Israel
*Address all correspondence to: daganba@sce.ac.il
1. Introduction
Observations from monitoring stations in rock slopes around the world indicate thermally induced cumulative deformations of removable rock blocks. Although temperature fluctuations are cyclical, the reaction of the rock is not necessarily so, indicating that the mere accumulation of plastic deformations that weaken the mass of the rock can lead to rock failure.
The first time the research group of which I was a member noticed the phenomenon was when monitoring blocks that had detached from the rock mass in the eastern cliff of Mount Masada, in Israel’s Judean Desert. During 1998, as part of a project to build a new cable car to the mountaintop, the group monitored blocks whose stability was questionable [1]. Joint meters were installed to measure joint displacement along the tensile joints that separate the blocks from the rock mass. Temperature and humidity meters were also installed.
The location of Mount Masada along the Dead Sea transform, just near the Dead Sea, is shown in Figure 1A. The main monitored block (referred to as “Block 1”) is shown in the picture in Figure 1B, taken before the construction of the new station. (The old cable car station is shown beneath the block.) In the picture in Figure 1C, taken after the completion of the new station and the access road from it to the mountaintop, you can see the proximity of the block to the visitor area. The results of the monitoring station are shown in Figure 1D. The results indicate a direct relationship between seasonal temperature changes and joint displacement [1]. At the end of that monitoring campaign, it was decided to anchor the block to the rock mass.
Figure 1.
Observation from a monitoring station at the eastern cliff of Masada. A) Location map, B) the snake path cliff with the old cable car station, C) the monitored sliding block (“Block 1”), and D) the obtained monitoring results during 1998 (After Hatzor et al. [1]).
Another observation from Masada was obtained from a research station installed on the western side of the mountain in 2009 [2]. This station was installed near the Roman Ramp (Figure 2A). The station consisted of four joint meters, an air temperature sensor, and a humidity sensor (Figure 2B). The monitoring results over 2 years are shown in Figure 2C, where joint openings are shown in black lines, and air temperature is in blue. A cumulative opening of the joints can be seen as a function of air temperature.
Figure 2.
Observation from the monitoring station at the western cliff of Masada. A) Station location, B) station setup, and C) obtained results (After Bakun-Mazor et al. [2]).
Various other studies by worldwide monitoring stations noticed the cumulative displacement of blocks on rock slopes as a response to temperature fluctuations. For example, Vlcko et al. [3] monitored selected castles on rock cliffs to preserve cultural heritage sites. They reported a thermal response of rocks as a result of seasonal periodic temperature changes.
Gischig et al. [4] monitored the rock slope instability above Randa (Switzerland) and measured temperature-controlled deformation trends at depths up to 68 meters. They interpreted this seasonal deformation trend as being controlled by thermomechanical effects driven by near-surface temperature cycles. Natural rock slope deformations across fractures, predominantly in a chert rock mass, were monitored by Mufundirwa et al. [5]. They proposed a new method to minimize displacement proportional to temperature and reported thermally induced rock mass movements. In their pioneering study, Gunzburger et al. [6] suggested that temperature fluctuations cause cumulative deformations in systems with a preferred sliding surface directionality.
These are just a few works from a wide variety of projects for monitoring rock movements along slopes. One of the difficulties is isolating the temperature’s effect from the other factors that can lead to slope failure, as discussed by Fiorucci et al. [7]. Moreover, asymmetry in the block system leads to the development of preferred directional stresses that can induce permanent displacement of rock blocks.
This chapter demonstrates a mechanism capable of explaining the cumulative displacement of rock blocks on a slope due to temperature fluctuations. First, I present the mechanism and describe laboratory procedures that tested the mechanism and, and then the use of numerical simulations to analyze a case study in the field.
The ratchet model is one of the mechanisms that can explain cumulative displacement driven by temperature changes. A schematic diagram depicting the mechanism in a stratified and jointed rock mass is shown in Figure 3. The components of the mechanism are shown in Figure 3A. A sliding block detached from the rock mass at a tension crack lies on a sliding surface. Rock fragments inside the tension crack function as wedge blocks in the ratchet mechanism. During cooling episodes (Figure 3B), the system contracts, and the tension crack opens. As a result, the rock fragments slide into the gradual opening of the crack. During heating episodes (Figure 3C), the system expands. The sliding block also expands and aims to close the tension crack. However, the rock fragments inside the crack are locked in place, resulting in the sliding block moving down the slope.
Figure 3.
The ratchet model. A) Model components along a rock slope, B) rock contraction at cooling episode, and C) rock expansion at heating episode.
A striking example of this can be inferred along a rock column in the Larzac Plateau (Southern France), as reported by Taboada et al. [8] and shown in Figure 4. It has nicely appeared that the rock column has a thermomechanical creep, and permanent deformations are associated with mechanical forces induced by short-term thermal cycles. Additional examples of potential wedging mechanisms are shown in the images in Figure 5.
Figure 4.
Example from monitoring station at Larzac Plateau (Southern France), measuring thermally induced rock column displacement. A) The rock column with the wedge blocks, and B) temperature and displacement data from the rock column (After Taboada et al. [8]).
Figure 5.
Photos of blocks from the field that illustrate the ratchet mechanism, A) Masada Mountain, Israel, B) Arugot Valley, Israel, C) Yellow Mountain, China, D) Zohar Valley, Israel, and E) Machtesh Ramon, Israel. The scale of each bar in the inset represents 1 m.
A one-dimensional analytical solution to the mechanism mentioned above was developed by Pasten [9]. The solution, which also is presented in detail in Bakun-Mazor et al. [10], consists of three displacement components. One component depends on the thermal expansion of the block system. The other two components depend on the ability of the sliding block to absorb some of the deformations elastically through elastic deformation of both the sliding block and the sliding surface upon which it rests. However, if the thermal expansion component is greater than the elastic components, the block is expected to accumulate plastic deformations reflected in its relative sliding down the slope.
Since the proposal of the mechanism, it has been tested by several researchers in the laboratory. The first to test the feasibility of measuring cumulative displacement as a result of a temperature change were Pasten et al. [11]. Their model, built from an acrylic block and wedge system, was placed in a temperature-controlled chamber that was heated and cooled using a light bulb and a fan. They showed that the wedge slides down due to temperature fluctuations and that the accumulation of plastic displacement, induced by temperature cycling, are proportional to the period and amplitude of the input temperature signal.
Another work that examined the mechanism in the laboratory was conducted by Greif et al. [12], who tested sandstone samples. As part of the work, the researchers examined how the ratio between the wedge length and the sliding block length affects the cumulative displacement. They then compared the measured results to those obtained from the analytical model. They reported that the results of the physical model agreed with Pasten’s analytical solution [9].
2.3 Lab experiment on a large scale
The two studies mentioned above tested the mechanism on relatively small models inside thermal chambers in the laboratory. On the other hand, a research work I carried out with the research group examined the mechanism of a model representing the dimensions of blocks in the field. The model was prepared using concrete castings formed as a block assembly representing a typical situation in stratified and jointed rock slopes found in the field. Figure 6A shows the block system with its dimensions in cm. The system model was placed on a tilted steel table and placed inside a temperature-controlled room (Figure 6B).
Figure 6.
The physical model in the lab. A) Concrete block system with the location of the displacement transducers (dimensions in cm), and B) the block system on an inclined steel table inside a temperature-controlled room.
Figure 6 shows the four locations where displacement transducers were installed to measure: A) the relative displacement between the sliding block and the fixed block, B) the vertical displacement of the wedge, C) the displacement of the front of the sliding block, and D) the thermal response of the concrete block (this transducer used as a dummy).
The relative displacement of the block assembly was measured using both displacement transducers and a high-resolution visual range camera (Figure 7). The visual range camera tracked the junction area between the four blocks, as shown in Figure 7. Screws were installed on the blocks to serve as markers for image processing (Figure 7D). The material properties of the concrete were measured in the laboratory and are detailed in Table 1. The room temperature is heated using electrical furnaces and cooled using an air conditioning system that operates inside air sleeves to prevent air movement inside the room. A controller regulates the thermal system. In a preliminary phase of the laboratory experiment, we tested the time needed for the center of the sliding block to reach the target temperature of the room. The measurements from the thermocouples inside the block showed that it takes about 3 days for the block to reach room temperature in its center. During the experiment, the room temperature changed intermittently from 35 degrees to 5 degrees, with a delay of about 75 hours between one target temperature and another.
Figure 7.
The experiment measurement setup. A) Displacement transducers, B) the focus area along the junction between the blocks, C) visual range camera tracing the focus area, and D) markers on the blocks for image processing.
Parameter
Symbol
Units
Value
Material properties
Elastic modulus
E
GPa
24.5
Poisson’s ratio
ν
-
0.251
Bulk density
ρ
kg/m3
2140
Joint properties
Friction angle
ϕ
°
21
Normal stiffness
Kn
GPa/m
5
Shear stiffness
Ks
GPa/m
0.5
Thermal properties
Thermal expansion coefficient
α
10−6/°C
3.22
Thermal diffusivity
DT
10−7m2/sec
5.44
Specific heat capacity (assumed)
Cp
J/kg/K
850
Table 1.
Thermomechanical properties of the concrete used for the experiments.
The experiment’s results indicate cumulative sliding of the block down the slope, depending on the temperature cycles. Figure 8A shows time-dependent cumulative displacement over three and a half temperature cycles. The block responds to the temperature cycles but accumulates a one-directional slip down the slope. The slip reaches about 0.06 mm at the end of three temperature cycles, that is, a rate of about 0.02 mm per cycle. Figure 8B shows the wedge sliding down to the gradual opening of the crack.
Figure 8.
Physical model results. Displacement obtained by two different measurement methods (colored lines) is shown on the right y-axis, room and block temperature (gray lines) are shown on the left y-axis, for A) sliding block and B) wedge block.
To deeply study the mechanism and carry out simulations of a case study in the field, we performed a numerical analysis using a three-dimensional version of the Distinct Element Code (3DEC) [13, 14]. The theoretical foundation of this method is the formulation and solution of equations of motion of deformable blocks by an explicit time-marching scheme using the finite volume method. The code can simulate the response of discontinuous media to static, dynamic, or thermal loading and can provide the corresponding deformation.
We first reproduced the geometry of the physical model in the 3DEC environment for validation. We applied the thermal boundary conditions on all exposed faces as the temperature-time histories recorded in the lab. The model was fixed in all directions at the bottom of the sliding surface, and in the normal direction behind the rock mass. The numerical simulation was performed with the thermomechanical parameters exactly as measured in the laboratory. The response of the block system in the numerical model is shown in Figure 9. The block’s response in the numerical analysis appears slightly greater than the displacement measured in the experiment. The numerical model, however, captures the expected physics of the failure mode very well. We performed sensitivity analyses to better explore the relative influence of the controlling parameters. We found that the numerical model is most sensitive to the chosen values of the normal stiffness in the contact between the blocks, and to the thermal expansion coefficient. The value of the thermal expansion coefficient that we used in the analysis represents linear expansion, while the problem in reality is affected by volumetric expansion. We assume this is one of the reasons for the differences between the laboratory measurements and the numerical results.
Figure 9.
Comparison between numerical 3DEC results (purple lines) and physical model results obtained by the displacement transducer (blue lines). Displacement (colored lines) is shown on the right y-axis, and room and block temperature (gray lines) are shown on the left y-axis for A) sliding block and B) wedge block.
3.2 Field case study
After confirming that the numerical analysis captured the thermally induced ratchet mechanism, we used the code to test a case study in the field, returning to the case of Block 1 on the eastern slope of Masada. We used 3DEC to model the geometry of Block 1. The block rests on an inclined bedding plane (j1) with a dip angle of 20o toward the east (the free space). The maximum (peak) friction angle measured in the laboratory is 41o, and the residual (saw-cut) friction angle is 28o [1]. The block is separated from the mountain by two tensile joints—one joint, referred to as j2, is open, and fragments of rock can be seen inside the joint (Figure 10A), while the second joint, referred to as j3, is relatively closed (Figure 10B). Therefore, in the numerical model, we added a wedge block only inside j2 (Figure 10D). A temperature function, representing the air temperature as recorded at a nearby meteorological station, was applied to the free surfaces in the model. The numerical parameters used for the analysis are detailed in Table 2, assigned to the rock mass in Masada [1, 2]. A video describing the simulation over three seasonal cycles is attached to this chapter. The response of the block for three annual cycles is shown in Figure 11. The cumulative response of the block after three years is about 0.6 mm when considering a friction angle of the sliding surface of 41o and about 1.0 mm when considering a friction angle of 28o.
Figure 10.
The analyzed Block 1 in Masada. A) J2 with the wedge fragments. B) The trace of J3 with no wedge blocks, C) the block near the cable car station, and D) the 3DEC model of the block.
Thermally induced displacements in Block 1 in Masada, as computed with 3DEC for peak and residual (saw-cut) friction. The applied temperature to the block boundaries is shown on the upper panel; the normal compressive stresses that evolve at the back of the wedge in response to thermal oscillations are shown on the lower panel.
Temperature fluctuations under conditions of biased forces are capable of causing geological materials to creep in accumulative plastic displacement [16]. Hence, it is assumed that rock blocks tend to creep on an inclined plane even without the wedge inside the joint, as also inferred by Gunzburgeret et al. [6]. To study the role of the wedge, we performed both the experiment and the numerical 3DEC analysis without a wedge block. The comparison between the two configurations, with and without a wedge, is shown in Figure 12. In our tested geometry, we infer that the wedge accelerates the cumulative slip rates approximately three times, compared to the situation where the tensile crack is empty for both the experiment and the numerical analysis.
Figure 12.
Cumulative displacements for each thermal cycle as obtained with the numerical and physical models for the “Ratcheting” (left) and crawling (right) failure mechanisms.
We also analyzed Block 1 in Masada without a wedge block inside the tensile crack. Similar to the comparison made in the laboratory geometry, we numerically examined the effect of the wedge on the displacement rate of Block 1 in Masada. The results showed that the slip rate wedge acceleration was two times faster.
We used also the analytical solution to evaluate the annual displacement rate, as a function of the ratio between wedge and block length, for varied values of slope inclination (Figure 13). We use relevant physical and mechanical properties of Masada dolomite (Table 2). It seems that the mechanism becomes most effective when the length of the wedge is about a third of the length of the sliding block.
Figure 13.
One cycle plastic displacement for several plane inclination angles for Masada dolomite, as calculated by the analytical expressions suggested by Pasten [9].
4.2 Daily vs. seasonal cycles
The rock mass response to temperature fluctuations occurs at relatively shallow depths because the temperature changes in the atmosphere do not penetrate too deeply into the rock. The extent of thermal penetration depends on the thermal conductivity of the material and the duration of the thermal cycle. Daily changes are sensed at depths of only a few cm, while seasonal changes can be discerned several meters into the rock. Therefore, we assumed that the larger the blocks on the slope, the more likely they will be affected by seasonal changes rather than daily changes. To test this on Block 1 at Masada, we implemented the temperature function in two ways: 1) using a full record that also contains the daily measurements, and 2) using a smoothed record that contains only the seasonal changes. The results are shown in Figure 14. It is indicated that the daily changes do not affect the cumulative response of the block; namely, the cycle duration is too short to affect the heating and cooling of the block. However, several consecutive days of extreme temperature can lead to a cumulative response, as seen in the gray areas in Figure 14 and in Figure 1D.
Figure 14.
The influence of short-term thermal fluctuations on block displacement. Top) Temperature input for the simulations. Bottom) Block displacement as computed with 3DEC for the two input temperature records.
4.3 Rock types affected by the mechanism
Thermally induced rock displacement depends mainly on the rock material’s thermal conductivity and the thermal expansion coefficient. To examine which rock types are more responsive to the ratchet mechanism, we performed a numerical analysis using 3DEC on the system geometry of the blocks representing the physical model. We used a different type of rock in each analysis, with physical properties taken from the literature (Table 3). The results of the analysis for different types of rock are shown in Figure 15. It is clearly that sandstone reacts to the thermally induced ratchet mechanism more extensively, probably because of the high value of the thermal expansion coefficient.
Typical thermomechanical properties of some rocks.
Figure 15.
Response to the thermal ratcheting mechanism; a comparison between different rock types. The analyses were done using 3DEC on the geometry and thermal boundary conditions used on the physical model inside the climate-controlled room.
This chapter presented observations showing that a jointed rock mass responds to temperature fluctuations. First, we presented a few examples of measurements observed at several monitoring stations around the world. The difficulty in field measurements is to isolate the effect of temperature from other environmental factors, such as water pressure in joints due to a freezing and thawing process. For this reason, Mount Masada is a preferred site for testing thermal mechanisms because of the prevailing desert conditions, where there is usually no pore pressure or freezing of underground water.
Then, a ratchet mechanism was used to explain how temperature changes can lead to cumulative displacement along a rock slope. Laboratory results of models of different sizes were presented, and the effect of the wedge size was demonstrated. Numerical analyses using 3DEC illustrate the effect of the wedge inside the tensile crack. We have seen that the wedge generally accelerates the cumulative response of the block system, and the maximum response occurs where the wedge length in about a third of the length of the sliding block.
The numerical analyses also make it possible to examine the contribution of daily and annual fluctuations. We saw that in the model of the block in Masada, the daily temperature fluctuations do not affect the block due to its large size. However, a sequence of several days with extreme temperatures for the season can lead to a cumulative response. Finally, based on the numerical analysis, rocks made of material with a high thermal expansion coefficient will respond more to the thermal mechanism.
I thank Prof. Yossi Hazor for his support throughout the research. The laboratory work and the numerical analyses were carried out by Aviran Feldheim and Yuval Keissar, with the support of the Israel Science Foundation under contract no. ISF 1442/13. Christine Detournay from Itasca Consulting Group is thanked for her contribution.
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Written By
Dagan Bakun-Mazor
Submitted: 13 September 2022Reviewed: 05 October 2022Published: 09 November 2022
Open access peer-reviewed chapter
