Using Slide and Phase2 to Model Slope Failure in Impact Crater Rims on Mars

The modelling presented in this article likely differs from the more typical engineering application. This work provides insight into our understanding of the outermost crustal layers of Mars, where information is difficult to obtain, and limited. We found the Rocscience software suite was a valuable tool when per-forming inverse modelling. That is, when the rock parameters are not known. In the case of the newly recognized impact crater morphol-ogy, the Peripheral Peak Ring (PPR) described in this article, slope stability modelling conducted using Slide and Phase2 show that, using reasonable input rock properties, the proposed model of formation, which produces the observed morphology and topography, is both possible and reasonable. Using the Rocscience suite, we were able to confirm that our proposed formation model is valid. In ad-dition, it was possible to gain valuable insight into the strength parameters of the uppermost layers of the Martian crust.

We constrained the problem to determine whether failure is facilitated by:

an overall weakening of the rimrock during the cratering process, or

whether the sub horizontal faults created during the impact cratering process are suf-ficiently weak to facilitate failure for a wide range of properties for the rimrock.

Failure of the crater rim will produce a block slide if competent rimrock overlies a weak slip plane, or if weaker rimrock overlies a slip plane with marginally less strength. In order to match the observed topography, however, failure will only occur with the addition of sub horizontal slip plane(s) and a tension crack.

We would further argue that our model-ling shows, to a first degree, our proposed formation model is a unique solution. We will discuss how PPR formation can be modelled as a block slide, which takes place after the crater has formed, as opposed to being a feature formed during the cratering process.

Until now, although the PPR morphology has been recognized (Nycz and Hildebrand, 2003), its formation has never been explained. Using the Rocscience software not only assisted in characterizing this new impact crater morphol-ogy, it also allowed for the further constraints of the properties of the Martian near surface.

There are several challenges facing planetary scientists when studying an object remotely from space. These include data acquisition, processing, and at most times, little supporting information with which to put the information into a larger context. When studying the earth via spacecraft, we have the luxury of being able to ground truth our observations. For example, when using near infra-red spectro-graphic data, if the spectrum of the observed data over a mountainous area suggest the sur-face lithology is granite, it is usually possible to travel to the site and not only confirm that the lithology is indeed granite, but the samples can be analyzed to determine the amount of feldspar or quartz it contains, which then al-lows for the observed IR spectrum to be more accurately typed in the future. For an example of various IR spectra, please visit:

www.speclib.asu.edu

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Digital Elevation Models (DEM’s) of a Martian impact crater were used as topographic inputs into both Slide and Phase2.

When observing the other bodies in our solar system, ground truthing of observations is only possible in the most limited sense. This would consist of the return visits to the moon, and the various rovers and landers dispatched to Mars. In conjunction with these data where available, we must try to determine the story from our observations (satellite data). Fortunately, in recent years our remote sensing capabilities of the other planets have become quite sophisticated. Over the past decade or so, various spacecraft have analyzed other objects in our solar system (the Moon and Mars in particular) in unprecedented detail. This article will describe how we used Digital Elevation Models (DEM’s) of a Martian impact crater as topographic inputs into both Slide and Phase2. The purpose of our research was to describe, characterize, and develop a working plausible formation model for a newly recognized impact crater morphology. The Rocscience software was very helpful towards moving the research forward.

PPR and Data AnalysisThe morphological feature we are analyzing is shown in Figure 1. The image in Figure 1a is a 13km diameter complex impact crater located at 10.6°N and 249.9°E. As the mechanics of impact cratering will not be covered in this paper (the interested reader is directed to Me-losh, 1989 for a thorough introduction on the topic), it is sufficient enough for the reader to note the central peak and the Peripheral Peak Ring (PPR). It is the PPR that is being investi-gated in our research. The PPR is a topographi-cally symmetric ring, and roughly concentric to the crater rim. It has been found to occur in craters having a diameter between 4 and 200km. They are thought to be caused when instabilities in the rim post crater modification, cause all or a portion of the rim to detach and slide into the crater. These instabilities are caused by increased loading due to basalt lay-ers in the near surface, and fractures (planar, radial, and concentric) generated during the crater excavation process.

Figure 1a - 13km diameter complex impact crater located just south of Olympus Mons at 10.6°N, 224.9°E. Background underlay is 256 pixel/degree MOC wide angle image. Overlays are .25m/pixel HiRISE visual images. Crater has a central peak, and well developed Peripheral Peak Ring (PPR). Dark layer in the upper crater rim has a similar spectral signature as Basalt. The Central Peak is generated when the transient (in-termediate) crater collapses due to Martian gravity. The PPR is thought to form after crater collapse due to instabilities in the crater rim combined with increased loading due to the Basalt.

Figure 1b is a composite composed of two Digital Elevation Models (DEM’s) created from Mars Reconnaissance Orbiter HiRISE image pairs. DEM’s were generated from stereo pairs having a resolution of .25m/pixel using stereo workstations and BAE’s SOCET SET® photo-grammetry software, and using a processing sequence developed by the Astrogeology branch of the USGS. Because HiRISE DEM’s are derived from Photogrammetric methods as opposed to laser measurements, we calculate the expected vertical precision (EP) when describing the relative error within a DEM. EP is a function of image resolution, stereo view-ing geometry and the RMS stereo matching

Figure 1b - 10m/pixel Digital Elevation model (DEM) of the crater generated from HiRISE ste-reo pairs. Data is produced using the Planetary Photogrammetry facility at the USGS Astrogeology centre, established under the NASA Planetary Major Equip-ment Program and run under the NASA Planetary Geology and Geophysics Cartography Pro-gram. Expected vertical precision between two DEM posts based on HiRISE stereo geometry is approximately .25m. Data shows the PPR fits in the recessional alcove of the rim from which it came. Elevation of the PPR rela-tive to the crater rim shows the movement was mostly lateral, as opposed to vertical. Eastings, northings, and elevations are based on the Mars 2000 datum.

error. Assuming a stereo matching error of 0.2 pixel, the expected precision (relative error) between two DEM posts based on HiRISE ste-reo geometry is approximately 0.25m. Stereo workstations used in the processing allow for any absolute errors within the DEM to be visu-ally identified and manually corrected through a comprehensive editing process.

Impact Crater TootingThe 29km diameter Tooting Impact crater is lo-cated at 23.4°N, 207.5°E (Figure 2). Mouginis-Mark and Garbiel (2007) determined the age of Tooting to be between 0.4 and 1.7Myr. As such, Tooting represents one of the youngest large, most preserved complex impact craters on Mars. Figure 2 shows the well-developed monolithic PPR in the NW portion of the cra-ter. Recently, Tooting has been completely cov-ered by HiRISE stereo pairs which allow for the generation of Digital Elevation Models having sub meter resolution. Figure 3 shows a portion of a DEM which covers the NW rim of Tooting. It is the Tooting crater where our slope failure research was carried out. Before discussing our modeling using Rocscience, our proposed model of formation will be presented so the reader may fully understand what we were trying to achieve.

Figure 2 - HiRISE mosaic of the 29km diameter impact crater Tooting. Located on Amazonis Planitia at 23.4°N, 207.5°E, Tooting represents one of the youngest, best preserved impact craters on Mars. Green ellipse is estimated position of crater rim immediately following crater collapse (Pre PPR formation). Blue box is the area of the DEM shown in Figure 3, and red line is location of topographic profile shown in Figure 3. Resolution of HiRISE images are .25m/pixel. The NW portion of the Tooting crater contains a single monolithic PPR.

Figure 3 - A portion of a DEM over the NW rim of the Tooting crater generated from HiRISE stereo pairs. Area of the Dem covers the blue box in Figure 2. Resolution is 5m/pixel. Illumination is from the SE and resultant shading shows the Basalt in the crater rim. Black line is the location of the radial topographic profile shown in Figure 4a. Of particular note is the height of the PPR is actually higher than that of the resulting rim. Again, this is definitive proof that PPR movement is mostly lateral, and translational. The topographic profile extracted from this DEM was used as the initial input into the Slide and Phase2 slope stability modelling.

PPR ModelPPR formation and the resulting morphology can be categorized as a translational block slide (Nycz and Hildeband 2010). These are slides which involve translational motion (movement that involves changes in position as opposed to rotation) on a near planar, low angle slip surface. They are initiated when excavation undercuts or unloads the toe of an area of developed joints or planes (bedding or faults) which then act as weak layers, facilitat-ing movement as discussed. Many concentric and radial faults are generated in crater rims during the cratering process (Osinski and Spary, 2005). The Bindon Block slide of 1839 on the SE coast of England (Pitts and Bruns-den, 1987) is a well documented block slide whose characteristics are similar to what is seen in many Martian PPR. In the Bindon slide, a single (500m by 400m by 140m) discrete block detached from the English coastline after strong marine erosion removed the toe of the landmass. The detached block remained intact through movement on a slide angle of 4.5°. In the general case of PPR development, whether a PPR stays intact after detachment (monolithic PPR) or breaks up into smaller blocks (rubbly PPR) depends on the cohesion of the block, the velocity of the slide, and therefore the amount of internal stress gener-ated during sliding.

The first stage of our formation model involved reconstruction of the original crater rim to when before the PPR was formed. This begins with considering the present day topographic profile shown in Figure 4a. The location of the topographic profile shown is indicated by the red line in Figure 2, and the black line overlying the DEM in Figure 3. A plausible model for PPR formation must result in the final, observed profile. Reconstruction of the original rim of Tooting pre PPR forma-tion is facilitated by using portions of the present day rim that remain unslumped as inner “anchor” points. The ellipse denoting the estimated position of the original rim is seen in Figure 2 (green circle). Restored rim height was estimated based on extrapolation of the DEM generated by us, and from Mars Orbital Laser Altimeter (MOLA) heights of the unslumped rim around the crater as shown by Mouginis-Mark and Garbeil. Shape (i.e. slope)

of the restored rim was based on MOLA pro-files through the crater in places where no rim slumping post crater modification was evident.

When doing this, we considered the lateral position and height of the original unslumped rim as “semi hard” constraints. That is, al-though the lateral position of the original rim didn’t have to be exactly on the green ellipse, it had to be close. The crater slope had even less variability because it would primarily be result of the strength of the rimrock.

Figure 4a - Graph showing observed topography from HiRISE DEM for the tran-sect shown in Figure 3. Elevations are datumed on the Mars 2000 geoid. Data is sampled approximately every 5m laterally, and vertical precision is estimated to be approximately .25m per pixel. The data from these DEM’s represents the most detailed topographic information ever derived for Mars. The sub vertical striped pattern represents the location and thickness of Basalt seen in the rim and PPR derived from THEMIS spectroscopy data, and the HiRISE visual images.

As such, we fit the crater slope to match the slope of profiles through the unslumped rim of the crater. The final constraint, which was the hardest, was that through the entire PPR formation process, unit volume had to be conserved. At every stage of PPR develop-ment, the unit volume of rock underneath the profiles had to be equal (although there would be slight changes due to changes in porosity during compaction post formation, these were neglected). Using these constraints, the re-stored rim of our profile is shown in Figure 4b.

We would argue that the restored rim is, to a first order, a unique solution. Changing any parameter a significant amount would either make that value unreasonable (i.e. crater rim too high, slope unrealistic), or would violate the volume conservation to a significant degree.

The next step in the formation of the PPR is when the PPR detaches from the crater rim and slides laterally and downward toward the crater center. Movement of the PPR is thought to occur along near planes of weakness that are generated behind the disruption cavity during the excavation process (Osiniski and Spray). If we assume a planar slip surface and the simple case of a single block detaching and sliding, the result is an intermediate step in the formation of a PPR that is shown in Figure 4c. The constraint to note in this diagram is the outcropping of the slip plane at the base of the PPR as it is observed in the topographic profile. The tension fracture backward of the rim and angle of the slip plane will be justified further in later sections. The final step in the formation of the PPR consists of our interme-diate “newly formed” PPR block undergoing transformation to the observed profile. The most logical and straightforward process to achieve this is through mass wasting of unsta-ble material from the steeply dipping (nearly vertical in the case of the back scarp) flanks of the PPR. Once again, volume conservation plays an important role in the final stage of PPR development, including the distance the PPR slides, the angle of the slip plane, and the location of the tension crack which is the point where the PPR detaches from the rim. This step of the process is shown in Figure 4d. In order for the general geometry of Figure 4c to be valid, the unit volume of material from the intermediate PPR must equate within a

reasonable amount to the unit volume of the observed profile. This is valid as long as the amount of material from the resulting rim and backside of the PPR equals the material filled in the recessional alcove, and the material from the front side of the PPR equals the ma-terial which is presumed to be shed from the front side of the PPR.

Figure 4b - Graph showing the estimated position and shape of the crater rim as it was post crater collapse, and before PPR formation. As described in the text, various constraints restrict this profile, including height and lateral position of the original rim, slope of the original rim, and unit volume conservation. Basalt is dipping because during the crater excavation process, the rim undergoes structural uplift. This profile is used as topographic input to the slope stability modelling using Slide and Phase2.

It is important to once again mention that in going through the above modeling process, it was found that palinspatic restoration of the PPR and the PPR formation process are very restricted. We submit that in the case of the observed profile, that the process described above is, to a first order, the only method possible that will generate the observed topography. If for example, the slip plane is made steeper or shallower, not only will the observed profile not be achieved, but volume conservation will be violated. The modeling shows that during the initial and intermediate stages of PPR formation, changing the non-constrained variables even slightly will result in the observed topography not being realized.

Figure 4c - Graph showing PPR formation. Modelled as a translational block slide, the PPR is thought to form when a portion of the rim detaches, and slides crater-ward along a low angle slip plane. The position of the tension crack where the PPR detaches, and how far it slides is constrained by volume conservation.

Figure 4d - Graph showing unit volume conservation and how it constrains the model of PPR formation. To achieve the present day observed topographic profile, the intermediate PPR (shown in Figure 4c) must undergo mass wasting resulting in the observed profile. However, volume conservation throughout the entire process must be maintained. This means the unit volume of blocks A+B must equal block C, and the unit volume of block D must equal Block E. This volume conservation also constrains the position and angle of the slip plane.

Slope Stability Modeling As mentioned in the introduction, we cannot ground truth our model. On earth, although there are some large impact craters, they are all far too degraded and eroded thanks to plate tectonics and our climate to definitively determine the presence of, or formation mechanism for PPR. However, that does not preclude us from determining if using reason-able rock parameters, whether our formation model is reasonable or possible. This is how we employed Slide and Phase2. Using our initial model (the restored profile shown in Figure 4b), we used Slide to determine what rock properties and under which subsurface conditions a FOS of less than 1 could exist. In other words, given the observed profile (which we are assuming is the “truth”), and using other available information about Mars, land-slides and Impact cratering, can we determine if our model is valid, and if so, what are some of the necessary conditions for PPR formation?

Our initial input model into Slide is shown in Figure 5. As mentioned previously, the location of the PPR failure surfaces is well constrained: we know the near horizontal slip plane out-crops at the base of the PPR, and we know that tension cracks distal to the crater rim are produced as shown by Morris et al. (2010), and Nycz and Hildebrand 2010. Justification for each lithologies initial rock properties is as follows:

a. Ejecta/Regolith- Sullivan et al (2011) used information from the wheel trenches and wheel scuffs from the two Mars Explora-tion Rovers (Spirit and Opportunity) to derive the Cohesions and friction angles from the Gusev crater and Meridiani Planum. Of their two methods, the specialized wheel trench-ing sequences was the method they had the most confidence in, and determined was the most robust. From their analysis, they found cohesion values of the regolith to range from 0-2kPa, and friction angles ranging from 30°-37°. As such, the initial values for the Regolith in our model were initially chosen to have a cohesion of 1kPa and a friction angle of 33°.

b. Basalt- Density values were based on the average of SNC meteorites as determined by Mackie at al, 2011. Other Hoek-Brown parameters are the average measured values of 30 samples analyzed in the lab which are contained in the Rocscience database. In their work on slope stability in Valles Marineris, Neuffer and Schultz (2006) used minimum terrestrial rock strengths as a substitute for the parameters in their “wall deposits”, which according to Schultz (2002) and Caruso (2002), are consistent with layered igneous rocks (ba-salt). Although our initial values for basalt are slightly stronger than those used by Neuffer and Schultz, they concede that minimum ter-restrial rock strength parameters should be lower than corresponding Martian strengths due to the reduced influence of water on rock weathering and alteration on Mars.

c. Rimrock- Values taken from the average of various sandstones and siltstones from the Rocscience database. Again, Schultz and Neuffer found the ILD’s (interior layered de-posits) of Valles could consist of a wide range of lithologies from sandstone to welded tuff. In addition, Nahm et al (2007) used the Op-portunity rover to investigate the properties of the Burns formation at Meridiani Planum. Interpreted by Squyers and Knoll (2005) to be a sequence of sedimentary rocks formed in a wind-swept, arid surface environment with a variable water table, the Burns formation is a reasonable model for what we are calling the rimrock. Although our initial strength values for the rimrock are not exactly those determined by Nahm et al, the range used in the sensitivity analysis cover their calculated values, as well as all the ILD values determined by Schultz and Neuffer.

Figure 5 - Initial input model for Slide. Topography is the restored crater rim shown in Figure 4b. Location of sub horizontal slip plane outcrop, tension crack are constrained by the high resolution visual images of the Tooting crater. The position and thick-ness of Basalt is based on IR spectroscopy and HiRISE images. Locations of Melt and Breccia are based on the general model of a complex impact crater derived from terrestrial craters such as Ries, Lockne and Manicouagan. The slump blocks shown in the model are simplified, and are formed when the newly excavated, deep transient impact crater undergoes gravitational collapse. Initial rock properties for the model are as follows:

Lithology (Unit weight) UCS Mi GSI Disturbance FactorRimrock (8.74kN/m³) 50MPa 8 38 .37Breccia (10kN/m³) 80MPa 19 20 .6Basalt (11.9kN/m³) 160MPa 25 65 .3Slip Plane (6kN/m³) 50MPa 8 18 .74

Because the lightly consolidated Ejecta/Regolith layer is more suitably modeled as a soil than an intact rock, its parameters

were entered using the Mohr-Coulomb criterion (Phi=33°, Cohesion=1kN/m², Unit weight 5kN/m³).

d. Melt-Values taken from the average of 16 melt samples analyzed in the lab and kept in the Rocscience database.

e. Breccia- Values taken from the average of 22 Breccia samples analyzed in the lab and kept in the Rocscience database.

f. Slip Plane - Of all the lithologies, the strength properties of the slip plane is perhaps the most problematic. Of course, the lower strength limit would be to simply make the slip plane have no strength at all. In such a case, the material over such a surface would fail along it no matter what its constituent strengths were. However, we know that the surface must have some strength for the fol-lowing reasons:

PPR are only observed in a fraction of impact craters. Whereas, the weak planes we are describing would exist in almost every single impact crater on Mars. Although the geometry of these sub parallel detachment faults would vary from crater to crater, because they are a product of the cratering process, it is reason-able to expect they exist in all craters. If these features were ubiquitous and had no strength, we would see rim failures in almost every crater. In reality, the PPR is a distinct morphol-ogy, seen only in a fraction of Martian Impact craters.

Even after peak friction is reached, and the rocks composing the slip plane reach their critical state and strain at a constant rate without the addition of further stress, they will still have a residual strength. Finally, studies have been carried out examining the rocks of terrestrial shear zones (Laws et al, 2003), and Cataclastic rocks (Habimana, Labiouse, and Descoeudres, 2002) and both were found to have measurable rock strength. Using the work of Laws and Habimana as a guide, the initial properties of the slip plane were chosen as the upper strength range of highly altered, “tectonized” rocks having the same lithology as the Rimrock.

Slide Modelling ResultsDue to the number of models run (in terms of both rock properties and initial configura-tion), only the results of our modelling will be presented in this article. If interested, the reader is encouraged to contact the author for more details.

In the models run without both a slip plane or tension crack, failure did not occur using a reasonable range of rock properties. Using probabilistic analysis, the “minimum” strength for rim stability of each lithology was deter-mined. Using rock properties lower than these minimum values would produce failure along circular surfaces. Because this type of failure is not seen in any Martian impact crater, these minimum values were used as the lowest strength rock properties possible in the Mar-tian rims that could still produce the failure observed in Martian PPR craters.

Adding in a tension crack and a slip plane in the locations suggested by the HiRISE images reduced the FOS. Sensitivity analysis run on this model (Figure 6) showed that not surpris-ingly, the FOS was overwhelmingly sensitive to the primary strength parameter of the Slip Plane, Hoek-Brown m.

Figure 6 - Sensitivity plot showing the dependence of Janbu corrected FOS to various rock properties used in the model shown in Figure 5. Although the sensitivity for all properties for all lithologies were determined, only the properties shown to have an appreciable effect on the FOS are plotted. Not surprisingly, the FOS is most and highly sensitive to the primary strength parameter of the Slip Plane. Observed failure then, can be modeled in two ways. The strength of the slip plane can be reduced un-til the FOS is reduced to below 1.0 or, properties of the other lithologies can be modi-fied (i.e. rimrock unit weight increased) until failure is achieved. The latter method is constrained however in that because circular failure is not observed in Martian craters, it cannot occur in the models. Also, variation of all rock parameters must be reasonable (i.e. Martian rimrock could not have a density of 4g/cc).

The surface of Mars exhibits numerous features which point to the presence of surface water in the recent past, (Williams and Malin, 2004). Hy-drological modelling shows that heat generated during impact facilitates movement of liquid water for an extended period of time in the region around and underneath a newly formed impact crater (Ivanov and Pierazzo, 2011). In addition, there is ample high resolution visual evidence (Morris, Mouginis-Mark, and Gabriel, 2010) to support the idea that the impact cratering process releases significant amount of volatiles (liquid water) during the crater-ing process. It is reasonable then, to consider a subsurface fully saturated with liquid water for a significant time after an impact event. To model this, we used a water table at the surface and a fully saturated tension crack. In Slide, the ground water method used was a water surface, with a pore fluid unit weight of 3.72kN/m3 (water having a density of 1g/cc in Martian gravity). The Hu Coefficient was set to 1.

The model run with the effects of pore pressure considered further reduced the factor of safety. The probabilistic analysis found a probability of failure of 3.33%. However, upon analysis of the parameters that result in a specific Monte Carlo model having a factor of safety less than one, it was found that many of the material properties were not valid. This should serve as a caution to any Rocscience user carrying out this type of inverse modelling.

Because when performing the Monte Carlo probabilistic analysis, the parameters that may be varied are Hoek-Brown m, Hoek-Brown s, and Hoek-Brown a. These are the parameters that rely on the strength reduction of the mate-rial (that is, they are dependent on GSI and D). It was found that when performing the proba-bilistic analysis, although the program would calculate the factor of safety by adhering to the range of values input for the Hoek-Brown pa-rameters, the values for GSI and D which make up those parameters would not be constrained. As a result, some material properties retuned in the analysis would be unreasonable. For ex-ample, to determine the range of parameters to be used in the probabilistic analysis, an upper and lower strength range of the slip plane was determined using RocLab. A “high strength” GSI, and D would be chosen, and RocLab would return the corresponding Hoek-Brown m, Hoek-Brown s, and Hoek-Brown a parameters.

The same process would then be repeated for a “low strength” slip plane. The range of Hoek-Brown Parameters between the “high” and “low” strength slip planes would then be used as the range for the probabilistic analysis (UCS and Mi were kept constant, as those are properties which represent the intact rock pieces, whereas the “tectonism” or weakening of the slip plane would be represented by an increase in D, a decrease in GSI, or a combina-tion of both). Once the probabilistic analysis was run, a particular set of material properties for a FOS of less than one (in this case, .996) would be:

Hoek-Brown a=.53489, Hoek-Brown m=0.01075, Hoek-Brown s=7.371E-7.

In converting these values back to determine what the corresponding D and GSI would be using the following formulas:

It is found that D=1.15. Obviously, this is invalid as D cannot be larger than 1. In other

returned values, some of the GSI values would be outside of the range of the “high” and “low” GSI range, and in others, retuned values would be outside the range of Mi values. In no way should this be interpreted as a shortcom-ing of the software. As in all modeling, the user must make sure that the values produced by the model make sense and are reasonable.

Hydrological modelling shows that heat generated during impact facilitates movement of liquid water for an extended period of time in the region around and underneath a newly formed impact crater.

Once all the invalid results were removed, a plot of the GSI vs. Disturbance factor for all cases where the probabilistic analysis resulted in a factor of safety less than 1 was generated and is shown in Figure 7. The relationship between the Factor of safety and factors af-fecting the tectonism is clear. From this graph, the critical strength of the slip plane can be determined by fitting a line to the highest GSI values that still provide a FOS<1. The equation of this line is:

GSI=39.64-10.128(D)

Where 1.0>D>.35

Of course, the above equation would repre-sent the limit of tectonism values for the Slip plane that would still result in slope failure.

It is worthwhile to have a discussion on the relationship between GSI and the Disturbance factor. In normal conditions, the undamaged, intact rock mass should be used to deter-mine the GSI, whereas the Disturbance factor should only apply to the blast damaged zone and not the entire rock mass. For example, in tunnels the blast damage is generally limited to a 1 or 2 m thick zone around the tunnel, (Hoek 1992). Both Faulted zones and the rocks surrounding impact craters are special cases however.

In the case of faults and shear zones, Laws et al discovered that shear zones generally can be mechanically separated into three zones. These include a strongly foliated zone, a frac-tured zone, and a heavily fractured, cohesion-less zone. This represents some modelling challenges. When taken together, a reduction in GSI and/or an increase in D will result in a combined strength reduction of the rock. In the case of a fault zone, whether to reduce the strength via GSI reduction or an increase in D becomes difficult to determine. In the case of impact cratering, it is likely both. Passage of the plastic wave which causes the fault zone will both change the structure of the rock, thereby lowering the GSI, and weaken the structure which will cause an increase in D. This concept will especially hold in areas

Figure 7 - Graph showing the relationship between GSI, Disturbance Factor and FOS (Janbu corrected) for the lithological parameters listed in Figure 5. Values were determined by solving a system of equations from the sensitivity analysis to calculate corresponding GSI and D. The stability line in the graph determines the combination of “tectonism” or strength reduction of the slip plane via a decrease in GSI, increase in Disturbance factor (or both), that will result in a FOS of less than one. Invalid results from the sensitivity analysis were removed from these results.

where the wave pressure is greater than the Hugoniot elastic limit of the rocks. In his work examining cataclastic rocks in Switzerland, Habimana proposes an extension to the gener-alized Hoek-Brown criterion which treats these tectonized regions as not rocks, but pseudo soils. In general, use of both a reduced GSI and an increased D to describe the weakening of the fault zones is likely a simplification of the actual case. However, the main point is that in these fault zones, the rocks will be weaker. Although the exact mechanism of weakness cannot be determined, it does not affect the overall result of the model.

If we consider the finite element analysis of the model, we can see the modeling predicts many of the features observed in the pro-posed PPR formation model for the Tooting crater. Figure 8 shows various aspects of the above Slide model run in Phase2. When con-verting the input model from Slide to Phase2, there were issues which made the finite element model conversion problematic. The first was dealing with the fact that the FEM method cannot handle a strengthless material. As such, we cannot have a tension crack as an input into Phase2. The second issue was in dealing with the slip plane. After running models using the slip plane as a material layer in Phase2 with unstable results, consulta-tion with Rocscience staff determined that modelling stability in thin layers using the FEM method is sensitive to meshing and discretiza-tion parameters. It was recommended that the slip plane lithology be modelled as a Joint in Phase2. Mohr-Coulomb properties for both the tension crack and joint were determined using RocProp. In the case of the Slip Plane, the Slide Hoek-Brown properties were converted to Mohr-Coulomb, and the result was used for the joint properties in Phase2. In the case of the Tension crack, a range of Mohr-Coulomb properties were used, with mixed results. For example, if an extremely weak tension crack was used, the model would collapse in on itself in the location of the vertical joint (ten-sion crack).

Phase2 is a complex FEM modelling package. In our case, we are hindered because the stress on each node (and therefore the overall displacement in the system of equations) is determined by additional elastic constants that are unknown (e.g. stiffness and Young’s modulus). As such, inverse modelling with Phase2 must be undertaken with care. Figure 8 shows the results of a Phase2 Model where both the vertical and horizontal joint have the same Mohr Coulomb properties. Despite the issues mentioned above, the Phase2 FEM mod-el agrees with many of the features concluded by the Slide SLE model. These include tensile stress in the region where the tension crack is observed to form, yielded joints (these could represent failure of the slip plane), and most notably, the detachment of a single monolithic PPR which slides craterward along the sub horizontal joint. The deformation contours predicted by the model show a clear resem-

blance to the PPR generation model presented earlier, and the final observed topography of the Tooting PPR.

Figure 8a - Phase² model based on the Slide model in Figure 5. Because the FEM method is not compatible with a strengthless material, the tension crack in Slide is represented by a joint in Phase². The thin lithological layer in Slide representing the Slip Plane is also a joint in Phase² because thin layers in Phase² can result in unstable results. FEM analysis in this case is beneficial because it allows the user to examine the stress and strain on each node of the model.

Figure 8b - Results of the Phase² model with deformation contours and yielded el-ements displayed. Differences in the critical SRF in the Phase² model and the Slide model could be attributed to the need to use a joint in place of a tension crack and slip plane, or due to varying values for the Young’s modulus and Poisson’s Ratio, parameters not considered in the SLE method. As such, caution must be used when employing Phase² for inverse modeling such as this. However, it is noted that the model calculates many of the features predicted by the PPR formation model, and matches observations. These would include failure in tension at the position of the tension crack. The deformation contours show a single, monolithic block detaching form the crater and sliding until the force of internal friction resists further movement. The observed topographical profile is overlain in red. Additional modeling should derive parameters for the slip joint which result in the modeled PPR being transported closer to where it is observed.

Conclusions and DiscussionIt is worth noting that when conducting this research, the heuristic model was generated first, and the slope stability modelling followed. The Rocscience suite was employed to determine whether the proposed model of formation was both possible and realistic. Not only did it conclude both, but inverse modelling using Slide also allows for significant constraints to be applied to the properties of the rock composing the uppermost Martian crust.

References

Caruso, P.A. (2002). Seismic triggering of Martian landslides and slope stability for Valles Marineris, Mars. M.Sc Thesis. Univer-sity of Nevada, Reno.

Habimana J., Labiouse V., and Descoeudres F. (2002). Geomechanical characterisation of cataclastic rocks: experience from the Cleuson-Dixence project. International Journal of Rock mechanics and Mining Sciences, 39. 677-693.

Hoek, E. (2002). Rock Mass Properties. Available from www.rocscience.com/education/hoeks_corner.com.

Ivanov, B.A., and Pierazzo, E. (2011). Impact cratering in H₂O-bearing targets on Mars: Thermal field under craters as starting conditions for hydrothermal activity. Meteoritics & Planetary Science, 46. 601-619.

Laws, s.,et al. (2003). Geomechanical properties of shear zones in eastern Aar Massif, Switzerland and their Implication on Tun-nelling. Rock Mechanics and Rock Engineering, 36. 271-303. Doi: 10.1007/s00603-003-0050-8.

Macke, R.J, Britt, D.T., and Consolmagno, G.J. (2011). Density, porosity and magnetic susceptibility of achondritic meteorites. Meteoritics and planetary Science 46. 311-326.

Melosh, H.J. (1989). Impact Cratering: A Geologic Process. Oxford University Press. 245pp.

Morris, A.R, Mouginis-Mark, P.J., and Garbiel, H. (2010). Possible impact melt and debris flows at Tooting Crater, Mars. Icarus, 209. 369-389.

Mouginis-Mark, P.J., and Garbiel, H. (2007). Crater geometry and ejecta thickness of the Martian impact crater Tooting. Meteor-itics and Planetary Science, 42, 1615-1626.

Nahm, A.L, and Schultz, R.A, (2007). Outcrop-scalephysical properties of Burns Formation at Meridiani Planum, Mars. Geophysi-cal Research Letters, 34. doi:10.1029/2007GL031005.

Neuffer, D.P, and Schultz, R.A. (2006). Mechanisms of slope failure in Valles Marineris, Mars. Quarterly Journal of Engineering Geology and Hydrogeology, 39. 227-240.

Nycz J.C., and Hildebrand. A.R. (2003). Martian Complex Impact Craters: A size and morphology progression, and a newly recog-nized Structural element, The Peripheral Peak Ring. Abstract #5255. 66th Annual meeting of the Meteoritical Society.

Nycz, J.C., and Hildebrand, A.R. (2010). Using HiRISE digital elevation models to investigate the Peripheral Peak Ring morphology in the Martian impact crater Tooting. Abstract #1982. 41st Lunar and planetary Science Conference.

Osinski, G.R., and Spray, J.G. (2005). Tectonics of complex crater formation as revealed by the Haughton impact structure, Devon Island, Canadian High Arctic. Meteoritics and Planetary Science, 40, 1789-1812.

Pitts, J, and Brunsden, D. (1987). A reconsideration of the Bindon landslide of 1839. Proceedings of the Geological Association, 98. 1-18.

Schultz, R.A. (2002). Stability of rock slopes in Valles Marineris, Mars. Geophysical Research Letters, 29. doi:10.1029/2002GL015728.

Squyres, S.W., and Knoll, A.H. (2005). Sedimentary rocks at Meridiani Planum: Origin, diagenesis, and implications for life on Mars. Earth Planet. Sci Letters, 240. 1-10.

Sullivan, R, et al. (2011). Cohesions, friction angles, and other physical properties of Martian regolith from Mars Exploration Rover wheel trenches and wheel scuffs. Journal of Geophysical Research, 116. doi:10.1029/2010JE003625.

Williams, R.M.E., and Malin, M.C. (2004). Evidence for late stage fluvial activity in Kasei Valles, Mars. Journal of Geophysical Research, 109. Doi:10.1029/2003JE002178.