DO SLOPES HAVE A FAVORITE SHAPE? Innovative slope profiles for remediation of landslides and the extractive industry.


Key remediation methods post small landslides consist of the use of heavy engineering solutions such as anchors, nails and /or geosynthetics or the reprofiling of the slope into a straight planar profile. The second solution is preferable from an environmental and aesthetical point of view (Schor and Gray, 2008). However, the vast majority of natural slopes manifest non-linear profiles. Several geomorphological studies of landscape evolution accounting for slope erosion and deposition phenomena point to the fact that straight profiles are never stable whereas landscapes undisturbed by anthropic activities tend to evolve towards equilibrium profiles whose shape in the cross section is partly concave and partly convex (Jeldes et al., 2018).
In the last 10 years, 4 independent systematic studies on the mechanical stability of slopes (Utili and Nova, 2007; Jeldes et al., 2015; Vahedifard et al., 2016; Vo & Russell, 2017), conclude that non-linear concave slope profiles are significantly more stable than the equivalent straight profile. Profiles of the same average inclination, i.e. sharing the same crest and toe points are considered equivalent, see Figure 1. Also Rieke-Zapp & Nearing (2005) and Jeldes et al., (2015) show that concave profiles are better to reduce slope erosion.
Recent theoretical studies have led to a software (Utili, 2016) that systematically determines the optimal profile from a mechanical stability point of view for a given average slope inclination and ground type. These profiles (see the figure) exhibit a significant increase of the factor of safety, up to 40%, over their equivalent straight profile as long as the ground exhibits some degree of cohesion. These findings have a number of implications. First, slopes at risk of impending failure and slow-moving landslides could be remediated by slope reprofiling alone avoiding the use of hard engineering solutions. Second, adoption of these profiles in quarries and open cast mines could allow steeper safe-excavation achieving significant saving on the amount of material to be excavated. Third, these profiles represent a hypothesis for equilibrium form of landscapes responding to topographic perturbation whether by excavation or through a natural process (e.g. river incision, earthquake, or deglaciation).


The geomorphic significance of this work is in a confronting theory with the extensive and high resolution topographic data to understand where real landscapes do and don’t conform to the theory. This work has implications for both landscape evolution and for hazard mapping – though the possibility of identifying out of equilibrium landscape locations.

Project Timeline

Year 1

i) Training in the use of the software coded in Matlab for the design of optimal slope profiles.
ii) Extension of the numerical model to 3D topographies.
iii) Inclusion of erosion resistance among the criteria to determine the optimal profile

Year 2

i) Identification of suitable sites.
ii) Secondment at Aggregates UK to identify quarry sites and need for any geotechnical investigation to properly characterise the chosen sites.
iii) construction of a few optimal profiles by re-profiling existing slopes at risk of impending failures and quarries in the UK.
iv) Setting up of the geotechnical instrumentation for the long-term monitoring of the optimal profile slopes.
v) Local scale (fine resolution) topographic analysis and development of topographic analysis methodology.

Year 3

i) Analysis of the monitoring data against the expected behaviour from the model in terms of mechanical stability and erosion resistance.
ii) Global scale topographic analysis in Google Earth Engine.
iii) Refinement of the model in the light of the monitoring results

Year 3.5

i) submission of relevant publications to Journals
ii) PhD thesis write up

& Skills

The School of Engineering requires each student to collect at least 60 PGRDP credits, corresponding to attendance of in-school delivered workshops, taught modules and other activities that display further engagement. The training in (a) research skills and techniques and (b) research environment are provided through four mechanisms: (i) a programme of taught modules; (ii) internal training ‘workshops’ that focus on key geographical research skills and techniques; (iii) input from supervisors; and (iv) School and academic Group seminars by visiting and internal speakers and presentations by postgraduate students themselves.
In addition to generic training offered by the University, the School also provides training through a series of in-house ‘workshops’. Engineering research postgraduates normally take the following Workshops: ‘Scientific Writing’, ‘Research Ethics (Theory)’, ‘Data Management’, ‘Time management’, ‘Document Management – Content and Layout’, ‘Introduction to Learning and Teaching’ during their first year. Also, it is envisaged that the student will undertake from 2 to 4 taught modules depending on the academic background of the appointed student of the MSc in ‘Engineering Geology’ and ‘Mapping and Geospatial Data Science’ . Modules particularly relevant for the project are ‘Geotechnical design’, ‘Geomechanics’, ‘Observation processes and analysis’, ‘Geohazards and Deformation of the Earth’. Most of these modules are delivered in one intensive week so well suited for PhD students.
Research training continues through the second and third years, and is based around a number of themes: (i) Recognition and validation of problems; (ii) Demonstration of original, independent and critical thinking, and the ability to develop theoretical concepts; (iii) Knowledge of recent advances within the research field and in related areas; (iv) Understanding relevant research methodologies and techniques and their appropriate application within the research field; (v) Ability to analyse and critically evaluate findings and those of others; and (vi) Summarising, documenting, reporting and reflecting on progress.
Bespoke technical training will also be provided by the research supervisors (numerical and analytical modelling of slope instabilities, geomechanical principles for the design of slope profiles, use of the National Landslide database,) and technical staff in the School of Engineering.

References & further reading

Abd, A. 2017 Geosynthetic-reinforced and unreinforced soil slopes subject to cracks and seismic action: stability assessment and engineered slopes. PhD thesis, Warwick.
Crosta GB., Utili S., De Blasio, Castellanza R. 2014. Reassessing rock mass properties and slope instability triggering conditions in Valles Marineris, Mars. Earth and Planetary Science Letters, 388: 329-342.
Eurogeosurveys, 2010. Annual report. Available at
Guzzetti, F., Ardizzone, F., Cardinali, M., Rossi, M. and Valigi, D., 2009. Landslide volumes and landslide mobilization rates in Umbria, central Italy. Earth and Planetary Science Letters, 279(3), pp.222-229.
Jeldes, I.A, Drumm E.C., Yoder D.C. 2018. Sustainable slopes satisfying rainfall-erosion equilibrium and mechanical stability. Transactions of Am. Soc. Agricultural & Biological Engineers, 61(4): 1323-1333.
Jeldes, I.A, Drumm E.C., Yoder D.C. 2015. Design of stable concave slopes for reduced sedimentary delivery. ASCE Jnl Geotech & Geoenv Eng, 141:4040-93.
Petley, D., 2012. Global patterns of loss of life from landslides. Geology, 40(10), pp.927-930.
Safeland, 2012. Living with landslide risk in Europe; Assessment, effects of global change, and risk management strategies. Summary report, available at
Schor, H.J., Grey, D.H. 2008 Landforming an environmental approach to hillside development mine reclamation and watershed restoration. John Wiley and Sons, New York, N.Y. (USA).
Schor, H.J., Grey, D.H. 2013 Landform/geomorphic grading for sustainable hillside developments. ASCE Congress on Stability and Performance of Slopes and Embankments III, Geo-Congress Issue 231 Geotechnical Special Publication: 1460-1471
Rieke-Zapp, D.H., Nearing, M. 2005. Slope shape effects on erosion: A lab study. SSSA J., 69:1463-71.
Utili, S., 2013. Investigation by limit analysis on the stability of slopes with cracks. Geotechnique, 63(2),140.
Utili, S., Abd, A. 2016. On the stability of fissured slopes subject to seismic action. International Journal for Numerical and Analytical Methods in Geomech, 40:785–6.
Utili, S., 2016. Software for the determination of optimal profiles for slopes and pitwalls.
Utili, S., Nova R. 2007. On the optimal profile of a slope. Soils and foundations, 47(4): 717-729.
Vahedifard, F., Shahrokhabadi, S., Leshchinsky, D. 2016. Optimal profile for concave slopes under static and seismic conditions. Canadian Geotechnical J., 53:1522-32.
Vo, T., Russell, AR. 2017. Stability charts for curvilinear slopes in unsaturated soil.Soils & Foundations, 57: 543-56.

Further Information

Prof Stefano Utili

Apply Now