Tag Archives: slope stability

Mohr – Coulomb failure criterion continued

Landslide, soil mechanics, ,

Things to remember when using the Mohr – Coulomb failure criterion:

  • The linear failure envelope is just an approximation to simplify calculations
  • The failure envelope is stress dependent and will produce some kind of curvature if shear strength tests are executed in much different confining stresses (fig 1, from Duncan and Write, 2005).

 

  • According to Lade, 2010 the failure envelope is curved and at low effective stresses which can be found in superficial failures on slopes, the use of linear Mohr – Coulomb may be in the unsafe side. Soils without cementation do not provide any effective cohesion in very low effective stresses (fig 2, from Lade, 2010).

 

  • When the linear Mohr – Coulomb criterion is used it must be evaluated for the expected stress range in the field.
  • Small cohesion values will not produce significant errors when high effective stresses are anticipated in the calculation.
  • In low effective stress even minimum values of effective cohesion (in cohesionless soils) can produce significant errors in factor of Safety (FS) calculations.

References:

Duncan J. M.,  Wright S. G., (2005). “Soil Strength and Slope Stability”. Wiley, New York.

Lade P. V. (2010). “The mechanics of surficial failure in soil slopes”. Engineering Geology 114, pp 57-64.

Slope stability and scale effects

Engineering Geology, Landslide, ,

In previous entries the issue of stiff fissured clays and the time to failure was briefly touched. The design of such slopes is not a trivial matter and requires significant knowledge of soil mechanics, geology, hydrogeology etc. One additional issue mentioned (one that sometimes is neglected) is the scale effect. This was presented in the previous entry for a very deep mine in rock. This issue of scale effect in relation to stress field will be briefly presented for the case of stiff fissured clays and hard soils.

In the following picture a large highway cut of about 30m is shown. For a civil engineering project this is a significantly high cut. The effective stress filed in this cut can range from of 50 – 500kPa which is the normal range for laboratory testing.

Highway cut

In the second picture a large excavation for a lignite mine is presented. The depth of excavation of this multi bench cut is around 135m. The excavation of this type needs to consider bench stability of slopes with heights of around 18m and also overall slope stability for highs above 135m. In the second case a large part of a possible failure surface could be in a stress field of around 1500-2000kPa or even more.

Coal mine slopes

In the following figure the two types of cuts are compared and one can easily understand the significance of scale effects in the design of the different cuts.

Scale difference of coal mine and highway slopes

The scale of the mine excavation is such that even in one cross section, one has to consider besides the stress field, differing geology (pic 4), presence of faults, ground water locations and pore pressures etc. We will focus on the stress dependency at this point.

mine slopes

According to Stark et al, (2005) both fully softened and residual failure envelopes are stress dependent. In this work Stark et al provides an empirical graph regarding the stress dependency until 700kPa of normal stress for residual friction angle and 400kPa for fully softened friction angle.

Shear strength information for higher effective stresses >1MPa are not readily available. Furthermore execution of such tests in very high effective loads is not easy for most commercial laboratories. It may even be very difficult to execute ring shear tests in very high loads due to sample thickness and squeezing out from the sides.

In such high slopes the failure surface can pass from a number of soil layers with different shear strength properties. It is not easy to evaluate the “average” shear strength of layers involved in a possible failure surface. Unfortunately a rule of thumb for selecting shear strength parameters for such slopes cannot be provided. Engineering judgment is required in selecting such parameters and the stress conditions must not be ignored. Shear strength tests should be evaluated in relation to the expected stress field.

Slope failures, landslides and mines

Geotechnical information, Landslide, Site Features, ,

On 11 of April 2013, around 9:30 p.m. a large slide (maybe the largest) in the northeast section of the Kennecott mine occured (fig 1). The slide was preceded by slope movements that reached ~50mm per day. Two major questions could be raised, why this slide occurred and could it have been predicted before hand and remediated?

Kennecott mine

These are very difficult questions and require significant knowledge of the geology, geotechnical conditions of the area, operational practices, climatic conditions etc. In the following paragraphs some initial ideas regarding the stability of high mine slopes and some interesting references will be provided for interested individuals. The incident in Kennecott is an important lesson of how important continuous monitoring of slopes is in such mine operations.

I would like to start with a very interesting graph published by Hoek et al (2000), “Large-scale slope Design – A Review of the State of the Art”.

This chart presents slope height versus overall angle with solid markers representing unstable slopes and open markers represent stable slopes. This chart is for copper porphyry open pits. In this graph the Kennocott mine (Bingham Canyon) is also shown but not the April 2013 one.

It is very interesting to note that most of the unstable markers are located in a range between 35 and 45 degrees of slope angle. Although much information is required for detail evaluation of each point and why instability occurred, a trend can be seen. Can we assume that slopes designed bellow 32-35o would not provide stability problems?

In the next figure I would like to focus on scale effects when dealing with mine slopes in rock or even hard rock materials. In the down left side of the figure 2 a slope with 30 meters height is depicted. In the upper left one of 90m with the same spacing of joints and finaly on the right a slope of 500m again with the same spacing and trance length of discontinuities (figures adopted from Sjoberg, 1996).

What can be seen from this slope scale is that even solid lightly fractured hard rock can be seen as an accumulation of infinite rock items such as a gravel slope or sand slope, just with better interlocking. One additional question can be, “what is the effect of bridging (intact rock between discontinuities) in such large scale slopes”? Very difficult question but maybe the previous graph provides an explanation (maybe negligible?).

Is the scale effect, in relation to joint spacing, orientation and stress field producing a ductile (sand or gravel like) behavior that may control the overall stability?

In the left graph (Ross, 1949) tests on intact marble with different confining pressures are presented. On the right (Holtz, 1981) normalized stress – strain with different confining pressures for dense Sacramento sand are presented. As can be seen, both materials in low confining pressures present a brittle behavior and as confining pressure increases, the behavior becomes more ductile and strain hardening.

Strong rock and dense sand can have the same behavior in different stress scale? And if this is the case, should high slopes be treated in a different way? Neglecting cohesion and using a possible “critical state friction angle” approach in slope stability? This issue requires additional research and detailed case studies but at least we can have some perspective regarding to scale effects.

References:

Sjoberg J., (1996). Large scale slope stability in open pit mining – a review. Technical Report 1996:10T, Lulea University of Technology

Hoek E., Rippere K. H. and Stacey P.F. (2000). Chapter 1, Slope stability in surface mining, Hustrulid, McCarter, VanZyl (eds), Society for Mining, Metallurgy and Exploration

Ros Μ. und Eichinger Α. (1949). Die Bruchgefahr fester Korper (Eidgenoss. Material prufungs versuchsanstalt, Ind., Bauw. Gewerbe. ZUrich, l72), 246 pp.

Holtz R. D., Kovacs W. D., (1981). “An Introduction to Geotechnical Engineering”, Prentice Hall.

How long can stiff fissured clay slopes stand?

Landslide,

Coming back to the issue of stiff fissured clay slopes, one very important question is the standup time of a slope excavated or formed (natural erosion etc) with higher inclination than the one that would be the outcome using fully softened shear strength.

Skempton (1970) in his paper “First time slides in over consolidated clays”, provided a graph presenting the decay of strength with time to almost fully softened where failure of slopes in London clay occurred (pic 1).

Strength changes with time for London Clay (from Skempton, 1970)

Mesri et al (2003) in his paper provides a graph (pic 2) compiled from numerous case studies of failed slopes in stiff fissured clays in which the vertical axis presents the percent of failure surface length (Lr) in residual condition to the total observed failure surface length (Lt)  and on the horizontal axis the age when the slopes failed. The far left points are of unidentified time. Time to failure range from a couple of years to decades.

Ratio of slip surface segment assumed at residual condition to total slip surface length ploted against age of slope

VandenBerge et al (2013), mention that “The time required to reach fully softened strength might be as little as ten years in some cases, and as long as 60 years in others”.

Potts et al (1997) in the paper “Delayed collapse of cut slopes in stiff clay” presented complex coupled finite element analyses assuming strain softening soil behavior capable of swelling. The analysis requires among other parameters the coefficient of permeability which varies with depth, and coefficient of earth pressure at rest. With this complex parametric analysis they conclude that 3:1 (H:V) slopes produced failures between 11 and 45 years. And steeper slopes fail in less than a decade. 15m high slopes failed after 145 years. All these slopes produced deep seated progressive failure.

It is very interesting to note that they evaluated deep seated failures although the problem of investigation was recent shallow failures in highway cuts and embankments.

Another attempt from Kovacevic et al (2007) presented in the paper “Predicting the stand up time of temporary London Clay slopes at Terminal 5, Heathrow Airport” in which again a complex finite element analysis with swelling behavior and differing Ko was executed. The investigation was for both shallow and deep seated failure. The conclusion of the study was that shallow failures occurred earlier than deep seated and the time to failure was influenced most by the assumptions of permeability and the effect of suction.

Cuts in stiff fissured clays will stand up for an undetermined time before failure occurs when inclined steeper than fully softened strength requires. The time may be from six months to hundred or more years. Investigating the stand up time is very complex and requires sophisticated numerical analysis which also utilizes assumptions in many of the parameters used. Very important parameter is the permeability of the clay in the development of swelling and softening.

This is captured in the classical Terzaghi, Peck and Mesri, 1996 book in which it is stated that “If the surfaces of weakness subdivide the clay into fragments smaller than about 25mm, a slope may become unstable during construction or shortly thereafter. On the other hand, if the spacing of the joints is greater, failure may not occur until many years after the cut is made.”

In my opinion the spacing and orientation of joints is the controlling parameter of permeability in such materials. So highly fissured materials with very close spacing may develop shallow slope failures very quickly. More widely spaced  stiff fissured clays with fewer joint systems can provide significant delay time to failure.

A second important issue is the evaluation of shallow or deep seated failure and how a deep seated failure can be defined. This is something very important that will be covered in another entry.

Slope design in stiff fissured clays

Landslide, ,

A very difficult issue is the design of slopes or cuts in stiff fissured clays (pic 1). The difficulty lies in the evaluation of shear strength for stability calculations. Much work has been done on this issue especially by Skempton (1964) with his excellent Forth Ranking Lecture titled: “Long-term stability of clay slopes” and many others have contributed significantly on this issue.stiff fissured clay

In the classical Terzaghi, Peck and Mesri, 1996 book the following is mentioned regarding this issue: “Almost every stiff clay is weakened by a network of hair cracks or slickensides.” (pic.2). “If the surfaces of weakness subdivide the clay into fragments smaller than about 25mm, a slope may become unstable during construction or shortly thereafter. On the other hand, if the spacing of the joints is greater, failure may not occur until many years after the cut is made.”Stiff fissured clay exposed next to a sliding soil mass

The reduction in strength with time, due to the presence of fissures, has been attributed to swelling and softening due to water infiltration in this hairline cracks especially when stress relaxation and crack opening occurs in excavated slopes.

Laboratory shear strength evaluation of such stiff fissured clays is difficult because large samples are required in order to include significant number of hairline cracks and even if such samples can be tested, the long term swelling and softening cannot be fully developed in the laboratory.

Duncan and Wright (2005) propose, based also on the work of Skempton (1970) to use the fully softened strength for long term slope stability evaluation of stiff fissured clays that have not undergone any prior movement or failure. This fully softened strength can be correlated to the peak strength of normally consolidated clays. In the laboratory the fully softened strength is evaluated on remolded samples of stiff fissured clays.

A very recent paper by VandenBerge, Duncan and Brandon, 2013 presents the outcome of a workshop that took place in 2011 at Virginia Tech, regarding the fully softened shear strength for stability of slopes in highly plastic clays.

In this paper the most recent views regarding the softening process, the way to measure or estimate the fully softened strength and how and when to use it in stability analysis are presented. Together with the paper of Vanderberge et al, it is worth reading the Lade paper in Engineering Geology (2010), titled “The mechanics of surficial failure in soil slopes” where a power function failure model is proposed for the shear strength of clay for shallow stability evaluation. This criterion is mentioned also in the paper by VandenBerge et al (2013).

I would like to bring attention on some issues which are mentioned also in the papers but relate more to practical issues of the subject:

  1. Great care should be given when site investigation is executed and evaluated in such stiff fissured caly materialsFissured clay. If core samples are not collected then it is very difficult to distinguish between stiff clay and stiff fissured clay. Even when samples are collected, great care should be given to break up some core samples because the fissuring will not be observed as can be seen in the picture 3.
  2. In situ tests such as SPT will produce high values, misleading the investigator to think that a very strong (even cemented) material is found.
  3. Shear strength tests on intact samples will produce high values of cohesion, again misleading the investigator to believe that a very strong material is present. In the laboratory the fissuring may not be reported during sample preparation due to the small sizes required.
  4. The additional difficulty comes on how to persuade the Owner or Contractor about the problems (failures) that Steep stable excavation in stiff fissured clay may be formed after the slope has been excavated (maybe after very long time). They will evaluate the data from the investigation which show high values and if they are not fully aware about the behavior of stiff fissured clays they will push for a more optimistic design in order to reduce excavation volumes. The situation becomes even more difficult in design – built projects where during excavation the contractor may need to use hydraulic hammers to break up the material and steep slopes are  stable (pic. 4). In such situation everybody “blames” the designer for a very conservative design if fully softened shear strength has been used.
  5. The evaluation of existing stable slopes not designed with fully softened shear strength is another difficult situation. If the fully softened shear strength is used the FS may be found to be even below unity FS<1.0 but the slope is stable for a couple of years after excavation. It is difficult to persuade the Owner of such slopes (usually highway or railway) that in the future stability problems may occur.
  6. Finally it is very difficult to evaluate in what part of the slope and how deep you will use fully softened values especially for high slopes.
  7. Another critical issue is the evaluation of the long term pore pressures to be used in the analysis. In my opinion this is the most difficult issue but I will get back on this in another entry because much could be said.

As a closing remark I would like to state the final conclusion of the Vanderberge et al, 2013 paper: “Consideration of local experience with regard to slope performance, recognition of the possible consequence of slope failures, and application of sound engineering judgment are all essential elements of a comprehensive approach to geotechnical engineering of slopes.”

Visual observations and field experience versus mathematical formulations and office work

Geotechnical information, , ,

Geotechnical Engineers, Engineering Geologists and Geoprofessionals in general are involved in evaluating and quantifying earth processes, earth materials, and human intervention on or in the earth in a way that can be used to manage geological risk and to produce safe and economical structures such as tunnels, dams, cuts etc.

In order to produce such evaluation the geoprofessional needs to understand the geology of the area, to evaluate the material properties and to analyze the problem at hand based on sound engineering principals.

Unfortunately this does not happen all of the time, either because many are focused in desk studies and numerical models without proper understanding of the actual conditions and others because they oversimplify and base their estimates solely on visual observations of the area.

The problem is that in order to effectively manage and work with models one needs to spend increased amount of time in the office studying the method and learning how to implement in a computer (not much time left for field work!). On the other hand the field is time consuming and usually far away from the office… (not much time to spent in front of a computer!).

Can we combine these two? Many people and consulting offices do, but there are others that don’t.

I will present an example where the lack of field work and understanding scree coreof the situation can produce significant errors. In figure 1 the drilling core of cemented talus is presented. The material is classified as (GP) per ASTM 2487, SPT blow counts produce refusal of penetration and anyone evaluatingscree slope this material from the office would assign the following material properties c’=0kPa and φ’>37ο, and they would design a slope with maximum inclination of about 28o in order to have a FS of about FS>1.4. The reality is that this slope is standing vertical without any stability problems as can be observed in figure 2.

It is very important for geotechnical engineers to have a real understanding of field conditions.