Using Experimental Models to Calibrate Numerical Models for Slope Stability and Deformation Analysis

Abstract

Landslides cause significant loss of lives and properties globally. Rainfall and earthquake are considered to be two frequent causes of landslides although there are dozens of natural or anthropogenic triggers of landslides. Experimental or numerical analyses by varying a single parameter—while keeping other triggers constant—help researchers/practitioners to understand the influence of each triggering factor on slope stability/landslides. However, experimental modeling of landslides in laboratory is exhaustive, time consuming, and expensive process. There are various experimental methods available for such modeling—ranging from centrifuge modeling to small scale 1 g models—depending on the need, available resources, and funds. With the wide availability of materials and development of better sensors/instruments, our capability to perform laboratory experiments, specifically for landslide modeling, has been much easier and accessible in recent decades. Such experiments are valuable to calibrate numerical models so that various analyses can be performed on the real-world problems. In this study, we prepared laboratory scale slopes in Plexiglas containers at varying densities and slope inclinations, and instrumented the slopes properly to measure real time suction, displacement, advancement of wetting front, and accelerations at various locations and depths within the model. The slopes were subjected to rainfall and/or earthquake shaking to evaluate the effect of rainfall and earthquakes—separately and combined—on slope stability. The experimental results were used to calibrate the numerical modeling effort so that a full spectrum of sensitivity analyses could be performed for a slope located in an expensive neighborhood of Southern California.

1 Background

Landslides cause billions of dollars of loss in properties and kill thousands of people annually worldwide. Causes of landslides span from many factors including heavy rainfall, snow melt, volcanic eruption, earthquake, changes in surface or ground water level, stream bank erosion, loss of vegetation cover, deforestation, wildfires, poor construction practice, improper design of infrastructure, and poor water management practice. These factors cause disturbance to naturally stable slopes and add into factors causing slope instability, which eventually yield mass movement in the form of landslides, slope failures, mudslides, and debris flows. While each of these factors either solely or in combination with two or more other factors are responsible for triggering hundreds of thousands of landslides every year, heavy rainfall, earthquake or combination of both account for majority of the mass movements. With a geometric increase in the number of significant earthquakes and a significant increase in global precipitation anomaly due to global warming associated climate change, there has been a geometric increase in the number of significant mass movements every year (Ajmera and Tiwari 2021).

Due the increase in the number of mass movements annually, there has been significant progress in research and development related to understanding behavior of mass movement caused by the triggers mentioned earlier through various methods including theoretical analyses, statistical analyses including artificial intelligence, remote sensing techniques, instrumentation with better equipment/tools including internet of the things, and experimental as well as numerical modeling techniques. Although some methods are better than others for specific projects depending on the scope of the project, availability of information, or implementation cost, each method has its own merit in analyzing landslide projects. However, if affordable, a combination of these methods will always provide the most accurate results.

Experimental modeling techniques, although very expensive, have been very effective in understanding the mechanism of slope stability or mass movement subjected to one or a combination of triggering factors. These experimental methods include element level flume tests, laboratory scale experimental slope models (Tiwari et al. 2018, 2013; Tiwari and Caballero 2015), field tests, and centrifuge modeling. Each of these techniques have their own benefits as well as limitations. However, the best method is generally chosen based on the scope of the project, availability of the equipment/tools, and project funds. While flume tests are generally performed to study the source and run-out of failed mass during rainfall events, laboratory scale experimental modeling are more appropriate to evaluate, numerically, the influence of triggers such as rainfall and earthquakes on seepage velocity and slope deformation. In the field tests, although very expensive, influence of rainfall on mass movement is studied on actual slopes. All these techniques offer 1 g level stresses only; as such, they may not represent actual field level stresses on slopes. Centrifuge models, although having their own merits and challenges, are helpful in studying slope behavior at high stress levels. Nonetheless these experimental models will help in calibrating numerical models, specifically for slopes subjected to different external triggers, so that multiple scenarios can be studied at the field scale. There are a large number of software available for such numerical modeling—ranging from simple to complicated or relatively low cost to expensive—in addition to the availability of several open source coding.

Although experimental modeling of various sizes and scopes are available in practice, this study focuses on a small scale, laboratory based, models to evaluate the seepage velocity, suction, and deformation of slopes subjected to rainfall and/or earthquake induced shaking. Ten different slopes were prepared with varying compaction densities and slope gradients, and subjected to different rainfall intensities and seismic accelerations. The results obtained from the experimental study have been used to calibrate the numerical models so that effect of different intensity of rainfall and earthquake shakings on slope stability could be observed for different gradients and densities using the numerical modeling exercise. The following sections will describe the experimental procedures, data analyses, results, discussion, and a brief summary based on the outcomes of this study.

2 Methodology

2.1 Experimental Modeling

A truck-full of soil was collected from a landslide site at Mission Viejo, Southern California. Various laboratory tests, such as sieve and hydrometer analyses, specific gravity tests, standard Proctor compaction tests, Atterberg limit tests, falling head permeability tests, and direct shear tests were performed on the collected soil samples following the guidelines outlined in the pertinent ASTM standards. Direct shear tests were conducted for soils at different degrees of saturation. The slope materials were sieved through 4.75 mm size sieve so that only smaller sized materials could be used in the laboratory scale models.

The air-dried soil was mixed with water uniformly to prepare a moist sample having ~12% moisture content. While preparing the model slopes, bottom of the 1.2 m × 1.2 m × 1.2 m sized Plexiglas container was installed with Polyethylene pipes having numerous holes—drilled in a staggered way and wrapped with geo-textile—that was buried under 5 cm thick gravel layer. A geotextile layer was installed between the compacted slope and the drainage layer to act as a filter layer. The moist soil was compacted on the geotextile layer—in 5 cm thick layers—at the pre-defined densities. Each layer of compacted soil slope was prepared until the desired height of the slope achieved. The desired geometries of the slopes were marked on the Plexiglas container to guide the compaction effort. Figure 1 illustrates the process involved in making the experimental model slopes. Separate slopes were prepared for two different slope gradients—40° and 45°—at three different void ratios (or densities)—0.89, 1.0, and 1.2—as illustrated in Table 1.

Fig. 1

Process for the preparation of experimental model slopes

Table 1 Geometries and densities of the model slopes used for this study

The compacted slopes were installed with miniature tensiometers that were calibrated prior to installation. Calibration of tensiometers prior to placement is extremely important to avoid erroneous suction measurements during the rainfall event. Small holes were drilled into the slope up to the desired depths at the spatial location (Fig. 2) to install the tensiometers (Fig. 3). Those holes were backfilled with the soil after the installation of tensiometers and then the top of the drill holes were sealed with bentonite slurry to avoid rainwater percolating down through the backfilled hole (Fig. 4). Moreover, several copper wire extensometers were installed at pre-defined locations (Fig. 5) as illustrated in Fig. 6 to measure the slope deformation at various locations during and at the end of the experiments.

Fig. 2

Locations of the tensiometers at different depths (Decagon T5 tensiometers)

Fig. 3

Drilling in the slope to install the miniature tensiometer

Fig. 4

Backfilling of the top surface of tensiometer location with bentonite slurry

Fig. 5

Location of copper wire inclinometers (units = cm)

Fig. 6

Installed copper wire inclinometers

The experimental models prepared as explained above were than subjected to two different rainfall intensities (1.68 and 3.6 cm/h) and three levels of seismic shaking events (0.1–0.3 g accelerations; 1–3 Hz frequencies), as illustrated in Table 2. The rainfall events were applied through a laboratory scaled custom designed sprinkler system (Fig. 7), and the seismic events were applied after preparing the model on the shaking table, shaking with actuators, and saturating them with rainfall (Fig. 8).

Table 2 Rainfall intensities (prior to seismic motion) and seismic motions applied to the models

Fig. 7

Custom designed sprinkler system used for this study

Fig. 8

Slope models prior to shaking on the shaking table

During the rainfall events, advancements of the wetting fronts were traced—every 15 min—while suction values were recorded with the tensiometers every second. Suction values were also recorded during the seismic events to measure the change in suction during seismic events. Moreover, deformations of the slopes were measured using high resolution cameras (surface, real time) and the copper wire extensometers (depth-wise, at the end of the test). Degrees of saturations for soil at the tensiometer locations were measured at the end of the rainfall event.

2.2 Numerical Modeling

Numerical models were developed for the slope models at the same geometry and densities as used in the experimental modeling. Slope/W, Seep/W, and Sigma/W platforms of the GeoStudio software were used for static analysis and Quake/W was used for the seismic analysis. Prior to the initiation of numerical modeling to acquire various parameters, numerical modeling parameters for Seep/W were calibrated with the experimental results, specifically with the wetting front locations and suctions at different locations and time spans. To perform finite element analysis for experimental models in this study, Sigma/W was used. Before performing the stability analysis, steady-state seepage analysis was performed first to obtain initial pore-water pressure condition to be matched with the experimental information, and then the model was imported into the Sigma/W for transient analysis state. Sigma/W allows simulating rainfall on the slope in desired amount of time. Change in pore-water pressure with rainfall duration was also calculated by using this module. The required parameters for the numerical analysis were taken from laboratory experiment (Table 3). There were a few assumptions made in this analysis: (a) infiltration was considered as the only effect on seepage condition within the slope, and the evaporation on the surface of the slope was ignored during the numerical analysis; (b) if rainfall intensity is smaller than the saturated hydraulic conductivity, all rainfall infiltrates into the surface, and the excess amount will runoff and flow down the slope. In Seep/W, a “q” unit flux boundary condition is assigned as the rainfall intensity, which was 1.68 or 3.6 cm/h. This flux value is applied along the surfaces of the slope, as shown in Fig. 9. In Sigma/W, there were a few assumptions for input parameters, such as Young’s modulus and Possion’s ratio. Typical values of Young’s modulus for cohesive material obtained from literature for high plasticity clay (CH)—7000 kPa for void ratio of 0.89, 5500 kPa for void ratio of 1, and 4000 kPa for void ratio of 1.2—were used. The value of Poisson’s ratio used was 0.45. Details of the numerical analysis using these platforms are available in Tran (2017).

Table 3 Parameters used in numerical modeling of model 1

Fig. 9

Boundary conditions and grid set-up for numerical modeling

3 Results and Discussion

3.1 Laboratory Experiments

Presented in Fig. 10 is a sample wetting front locations—separated every hour—for Model 2. Time vs suction recording at 5 tensiometer locations on this model are presented in Fig. 11. Results presented on Fig. 10 can be used to estimate the time required for the water to reach tensiometers and reduce the suction to ~0 kPa. Please note that tensiometers were installed half way from the edge of the slope while wetting fronts were measured at the edge of the slope. As can be observed in Table 4, time required for the tensiometer to cease suction is very close to the time the wetting front advanced to those tensiometers, except in Tensiometer 3 (T3). From the pattern of the suction variation with time, observed in Fig. 11, it is clear that this tensiometer had some recording issues during the initial period. Similar results were obtained for other models as well. Please also note that as the soil was compacted at higher density for this model, soil swelled after the slope became saturated as can be observed in Fig. 10 for the post-experiment slope.

Fig. 10

Advancement of wetting front with time—recorded by eye-observation through the Plexiglas container

Fig. 11

Variation of suction with time—recorded by the tensiometers

Table 4 Time required for the wetting fronts to reach tensiometers and the tensiometers to drop suction to ~0 kPa

Deflection of the copper wire extensometers with depth shows the location that had the maximum deformation. Presented in Fig. 12 are the deflections of copper wires for Model 3. Deflection of the copper wire extensometers helped to predict the plane that has maximum deformation for Model 3, as presented in Fig. 13.

Fig. 12

Copper wire deflections observed after the experiment in model 3 (x-axis exaggerated)

Fig. 13

Predicted weakest plane in model 3

The wetting front information presented in Fig. 10 has been used to calculate seepage velocity for all 10 models so that variation in seepage velocity on slopes with soil density and intensity of rainfall could be developed. Presented in Fig. 14 is the relationship between seepage velocity and void ratio for two different rainfall intensities. Likewise, Fig. 15 shows the variation in seepage velocity with infiltration rate. Similar results were obtained for the 45° slope as well.

Fig. 14

Variation of seepage velocity with void ratio for two different intensities of rainfall for 40° slope. Data for point ‘?’ was obtained from the numerical analysis

Fig. 15

Variation of seepage velocity with intensity of rainfall for three different void ratios for 40° slope

The results obtained from the experimental modeling were compared with the results obtained from the numerical analysis using Seep/W. As can be observed in Figs. 16 and 17, the results obtained from the numerical modeling in models with 40° slopes were close to that from the experimental modeling. This is the way how calibrations of the numerical models were performed. Similar results were observed for the 45° slopes as well.

Fig. 16

Seepage velocities from numerical and experimental models for 40° slope; rainfall intensity 1.68 cm/h

Fig. 17

Seepage velocities from numerical and experimental models for 40° slope; rainfall intensity 3.6 cm/h

Critical failure planes were also obtained through numerical analysis using Sigma/W, as presented in Fig. 18 (for Model 1). Presented in Figs. 19 and 20 are the comparison of weakest planes obtained with experimental and numerical analyses for Models 6 and 2, respectively.

Fig. 18

Weakest plane obtained from numerical analysis—Sigma/W for model 1

Fig. 19

Weakest plane obtained from numerical and experimental analyses—Sigma/W for model 6

Fig. 20

Weakest plane obtained from numerical and experimental analyses—Sigma/W for model 2

The comparison between seepage velocities and deformation obtained from both numerical and experimental modeling was useful to calibrate the numerical models, as explained earlier. With the Slope/W function of the Geo-Studio, reduction in safety factors with an increase in rainfall duration for the experimental models were calculated at the critical/weakest planes using Spencer’s Method. Although the factors of safety were higher than 1 and the models did not fail, there was a drastic reduction in safety factors with an increase in rainfall duration for all slopes, with denser slopes having a lower reduction rate. Results of the numerical analysis related to safety factor reduction with rainfall duration for 40° slopes having different soil densities, subjected rainfall intensities of 1.68 cm/h and 3.6 cm/h are presented in Figs. 21 and 22, respectively. Similar results for the 45° slopes at the rainfall intensity of 3.6 cm/h are presented in Fig. 23, for comparison.

Fig. 21

Variation in safety factor with rainfall duration in 40° slope model subjected to 1.68 cm/h rainfall

Fig. 22

Variation in safety factor with rainfall duration in 40° slope model subjected to 3.6 cm/h rainfall

Fig. 23

Variation in safety factor with rainfall duration in 45° slope model subjected to 1.68 cm/h rainfall

As explained in the previous section, slope models were prepared in the Plexiglas container to make a 40° slope at the void ratio of 1.2 (Model 10). Tensiometer devices and accelerometers were installed at different depths within the slope. First, the slopes were subjected to a series of sinusoidal waves for 20 cycles, separately at the frequencies of 1, 2, 3 Hz and accelerations of 0.1, 0.2, 0.24, and 0.3 g. In addition, ground motion recorded at station 90,095 during the 1994 Northridge Earthquake was also applied. Figure 24 shows the ground motion applied to the model.

Fig. 24

Ground motion applied to model 10 prior to the application of rainfall event

Right after the shaking event, the sprinkler system was set on the top of the Plexiglas container. Rainfall intensity of 3.6 cm/h was introduced to the slope. Figure 25 shows the variation in pore water pressure during the shaking stage. As can be observed in Fig. 25, there is no change in suction in the compacted soil during shaking. Presented in Fig. 26 is the variation in suction during the rainfall event, observed with the tensiometers. Deformation observed with the copper wire and the potential sliding plane obtained with Sigma/W for the slope subjected to rainfall after the seismic event is presented in Fig. 27. As can be observed in Fig. 27, deformation of the slope decreased after the model was shaken with a series of seismic events; and the potential sliding planes obtained from the numerical and experimental results were similar. Figure 28 shows the comparison of factors of safety obtained for static slope and same slope subjected to post-seismic event rainfall event. As observed in Fig. 28, safety factors have increased for the same slope after the shaking event due to the increase in soil density after the shaking event; please note that Model 10 had the highest void ratio, i.e. lowest compaction density.

Fig. 25

Variation in suction with time during the shaking event

Fig. 26

Variation in suction with time during the post-earthquake rainfall event

Fig. 27

Potential sliding planes observed on model 10 with experimental and numerical results

Fig. 28

Variation of the factors of Safety on Model 10 with time for static and seismic loading

4 Summary and Conclusion

Extensive experimental modeling efforts were made on slopes prepared at two different slope gradients and three different densities. Those experiments included preparing the slopes, instrumenting them with tensiometers and extensometers, and subjecting the slopes to two different intensities of rainfall until the slopes got saturated. The suction values and extensometer deformations were recorded and the results were compared with the results obtained from the wetting front advancement with time. Moreover, numerical analyses were performed on all the slopes to calibrate the numerical analyses parameters. Results obtained from Seep/W on seepage velocities and Sigma/W on deformation matched well with the results obtained from the wetting fronts/tensiometer recordings and copper wire deformation, respectively. The calibrated numerical models were used to calculate the factors of safety of slopes with the duration of rainfall using Slope/W module of GeoStudio. In addition to the static experiments, slope model that had the lowest density was shaken on the shaking table with a series of seismic motions and change in suction during the shaking was observed. It was observed that there was no change in suction with seismic shaking. When the shaken slope was subjected to a rainfall event, there was a reduction in seepage velocity and deformation compared to the same slope that was not subjected to seismic events. Such reduction in seepage velocity has been attributed to the increase in density of the soil during and after shaking. This study provides a complete information about how various soil and ground parameters influence stability of slopes and how numerical models can be calibrated with the experimental modeling results to apply the calibrated numerical models for field slopes/landslides.