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US Army Corps

of Engineers®

ENGINEERING AND DESIGN

31 Oct 2003

Slope Stability

ENGINEER MANUAL

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i

DEPARTMENT OF THE ARMY EM 1110-2-

U.S. Army Corps of Engineers

CECW-EW Washington, DC 20314-

Manual No. 1110-2-1902 31 October 2003

Engineering and Design

SLOPE STABILITY

Subject Paragraph Page

Chapter 1 Introduction Purpose and Scope ..........................................................................................................1-1 1- Applicability ...................................................................................................................1-2 1- References.......................................................................................................................1-3 1- Notation and Glossary.....................................................................................................1-4 1- Basic Design Considerations ..........................................................................................1-5 1- Stability Analysis and Design Procedure........................................................................1-6 1- Unsatisfactory Slope Performance..................................................................................1-7 1-

Chapter 2 Design Considerations Introduction.....................................................................................................................2-1 2- Aspects Applicable to all Load Conditions.....................................................................2-2 2- Analyses of Stability during Construction and at the End of Construction ....................2-3 2- Analyses of Steady-State Seepage Conditions................................................................2-4 2- Analyses of Sudden Drawdown Stability .......................................................................2-5 2- Analyses of Stability during Earthquakes .......................................................................2-6 2-

Chapter 3 Design Criteria General............................................................................................................................3-1 3- New Embankment Dams ................................................................................................3-2 3- Existing Embankment Dams...........................................................................................3-3 3- Other Slopes....................................................................................................................3-4 3-

Chapter 4 Calculations and Presentations Analysis Methods............................................................................................................4-1 4- Verification of Computer Analyses and Results.............................................................4-2 4- Presentation of the Analysis and Results ........................................................................4-3 4-

Appendix A References

Appendix B Notation

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Subject Paragraph Page

Appendix C Stability Analysis Procedures – Theory and Limitations

Appendix D Shear Strength Characterization

Appendix E Chart Solutions for Embankment Slopes

Appendix F Example Problems and Calculations

Appendix G Procedures and Examples for Rapid Drawdown

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(6) Joints and joint systems.

(7) Weathering.

(8) Cementation.

(9) Slickensides.

(10) Field evidence relating to slides, earthquake activity, movement along existing faults, and tension jointing.

c. Material characterization. In evaluating engineering properties of soil and rock materials for use in design, consideration must be given to: (1) possible variation in natural deposits or borrow materials, (2) natural water contents of the materials, (3) climatic conditions, (4) possible variations in rate and methods of fill placement, and (5) variations in placement water contents and compacted densities that must be expected with normal control of fill construction. Other factors that must be considered in selecting values of design parameters, which can be evaluated only through exercise of engineering judgment, include: (1) the effect of differential settlements where embankments are located on compressible foundations or in narrow, deep valleys, and (2) stress-strain compatibility of zones of different materials within an embankment, or of the embankment and its foundation. The stability analyses presented in this manual assume that design strengths can be mobilized simultaneously in all materials along assumed sliding surfaces.

d. Conventional analysis procedures (limit equilibrium). The conventional limit equilibrium methods of slope stability analysis used in geotechnical practice investigate the equilibrium of a soil mass tending to move downslope under the influence of gravity. A comparison is made between forces, moments, or stresses tending to cause instability of the mass, and those that resist instability. Two-dimensional (2-D) sections are analyzed and plane strain conditions are assumed. These methods assume that the shear strengths of the materials along the potential failure surface are governed by linear (Mohr-Coulomb) or nonlinear relationships between shear strength and the normal stress on the failure surface.

(1) A free body of the soil mass bounded below by an assumed or known surface of sliding (potential slip surface), and above by the surface of the slope, is considered in these analyses. The requirements for static equilibrium of the soil mass are used to compute a factor of safety with respect to shear strength. The factor of safety is defined as the ratio of the available shear resistance (the capacity) to that required for equilibrium (the demand). Limit equilibrium analyses assume the factor of safety is the same along the entire slip surface. A value of factor of safety greater than 1.0 indicates that capacity exceeds demand and that the slope will be stable with respect to sliding along the assumed particular slip surface analyzed. A value of factor of safety less than 1.0 indicates that the slope will be unstable.

(2) The most common methods for limit equilibrium analyses are methods of slices. In these methods, the soil mass above the assumed slip surface is divided into vertical slices for purposes of convenience in analysis. Several different methods of slices have been developed. These methods may result in different values of factor of safety because: (a) the various methods employ different assumptions to make the problem statically determinate, and (b) some of the methods do not satisfy all conditions of equilibrium. These issues are discussed in Appendix C.

e. Special analysis procedures (finite element, three-dimensional (3-D), and probabilistic methods).

(1) The finite element method can be used to compute stresses and displacements in earth structures. The method is particularly useful for soil-structure interaction problems, in which structural members interact with a soil mass. The stability of a slope cannot be determined directly from finite element analyses, but the

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computed stresses in a slope can be used to compute a factor of safety. Use of the finite element method for stability problems is a complex and time-consuming process. Finite element analyses are discussed briefly in Appendix C.

(2) Three-dimensional limit equilibrium analysis methods consider the 3-D shapes of slip surfaces. These methods, like 2-D methods, require assumptions to achieve a statically determinate definition of the problem. Most do not satisfy all conditions of static equilibrium in three dimensions and lack general methodologies for locating the most critical 3-D slip surface. The errors associated with these limitations may be of the same magnitude as the 3-D effects that are being modeled. These methods may be useful for estimating potential 3-D effects for a particular slip surface. However, 3-D methods are not recommended for general use in design because of their limitations. The factors of safety presented in this manual are based on 2-D analyses. Three-dimensional analysis methods are not included within the scope of this manual.

(3) Probabilistic approaches to analysis and design of slopes consider the magnitudes of uncertainties regarding shear strengths and the other parameters involved in computing factors of safety. In the traditional (deterministic) approach to slope stability analysis and design, the shear strength, slope geometry, external loads, and pore water pressures are assigned specific unvarying values. Appendix D discusses shear strength value selection. The value of the calculated factor of safety depends on the judgments made in selecting the values of the various design parameters. In probabilistic methods, the possibility that values of shear strength and other parameters may vary is considered, providing a means of evaluating the degree of uncertainty associated with the computed factor of safety. Although probabilistic techniques are not required for slope analysis or design, these methods allow the designer to address issues beyond those that can be addressed by deterministic methods, and their use is encouraged. Probabilistic methods can be utilized to supplement conventional deterministic analyses with little additional effort. Engineering Technical Letter (ETL) 1110-2- 556 (1999) describes techniques for probabilistic analyses and their application to slope stability studies.

f. Computer programs and design charts. Computer programs provide a means for detailed analysis of slope stability. Design charts provide a rapid method of analysis but usually require simplifying approxima- tions for application to actual slope conditions. The choice to use computer programs or slope stability charts should be made based on the complexity of the conditions to be analyzed and the objective of the analysis. Even when computer programs are used for final analyses, charts are often useful for providing preliminary results quickly, and for providing an independent check on the results of the computer analyses. These issues are discussed in Appendix E.

g. Use and value of results. Slope stability analyses provide a means of comparing relative merits of trial cross sections during design and for evaluating the effects of changes in assumed embankment and foundation properties. The value of stability analyses depends on the validity of assumed conditions, and the value of the results is increased where they can be compared with analyses for similar structures where construction and operating experiences are known.

h. Strain softening and progressive failure. “Progressive failure” occurs under conditions where shearing resistance first increases and then decreases with increasing strain, and, as a result, the peak shear strengths of the materials at all points along a slip surface cannot be mobilized simultaneously. When progressive failure occurs, a critical assumption of limit equilibrium methods – that peak strength can be mobilized at all points along the shear surface -- is not valid. “Strain softening” is the term used to describe stress-strain response in which shear resistance falls from its peak value to a lower value with increasing shear strain. There are several fundamental causes and forms of strain softening behavior, including:

(1) Undrained strength loss caused by contraction-induced increase in pore water pressure. Liquefaction of cohesionless soils is an extreme example of undrained strength loss as the result of contraction-induced pore pressure, but cohesive soils are also subject to undrained strength loss from the same cause.

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d. Establish the seepage and groundwater conditions in the cross section as measured or as predicted for the design load conditions. EM 1110-2-1901 describes methods to establishing seepage conditions through analysis and field measurements.

e. Select loading conditions for analysis (see Chapter 2).

f. Select trial slip surfaces and compute factors of safety using Spencer's method. In some cases it may be adequate to compute factors of safety using the Simplified Bishop Method or the force equilibrium method (including the Modified Swedish Method) with a constant side force (Appendix C). Appendix F provides example problems and calculations for the simplified Bishop and Modified Swedish Procedures.

g. Repeat step f above until the “critical” slip surface has been located. The critical slip surface is the one that has the lowest factor of safety and which, therefore, represents the most likely failure mechanism.

Steps f and g are automated in most slope stability computer programs, but several different starting points and search criteria should be used to ensure that the critical slip surface has been located accurately.

h. Compare the computed factor of safety with experienced-based criteria (see Chapter 3).

Return to any of the items above, and repeat the process through step h , until a satisfactory design has been achieved. When the analysis has been completed, the following steps (not part of this manual) complete the design process:

i. The specifications should be written consistent with the design assumptions.

j. The design assumptions should be verified during construction. This may require repeating steps b, c, d, f, g, and h and modifying the design if conditions are found that do not match the design assumptions.

k. Following construction, the performance of the completed structure should be monitored. Actual piezometric surfaces based on pore water pressure measurements should be compared with those assumed during design (part d above) to determine if the embankment meets safe stability standards.

1-7. Unsatisfactory Slope Performance

a. Shear failure. A shear failure involves sliding of a portion of an embankment, or an embankment and its foundation, relative to the adjacent mass. A shear failure is conventionally considered to occur along a discrete surface and is so assumed in stability analyses, although the shear movements may in fact occur across a zone of appreciable thickness. Failure surfaces are frequently approximately circular in shape. Where zoned embankments or thin foundation layers overlying bedrock are involved, or where weak strata exist within a deposit, the failure surface may consist of interconnected arcs and planes.

b. Surface sloughing. A shear failure in which a surficial portion of the embankment moves downslope is termed a surface slough. Surface sloughing is considered a maintenance problem, because it usually does not affect the structural capability of the embankment. However, repair of surficial failures can entail considerable cost. If such failures are not repaired, they can become progressively larger, and may then represent a threat to embankment safety.

c. Excessive deformation. Some cohesive soils require large strains to develop peak shear resistance. As a consequence, these soils may deform excessively when loaded. To avoid excessive deformations, particular attention should be given to the stress-strain response of cohesive embankment and foundation soils during design. When strains larger than 15 percent are required to mobilize peak strengths, deformations in

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the embankment or foundation may be excessive. It may be necessary in such cases to use the shearing resistance mobilized at 10 or 15 percent strain, rather than peak strengths, or to limit placement water contents to the dry side of optimum to reduce the magnitudes of failure strains. However, if cohesive soils are compacted too dry, and they later become wetter while under load, excessive settlement may occur. Also, compaction of cohesive soils dry of optimum water content may result in brittle stress-strain behavior and cracking of the embankment. Cracks can have adverse effects on stability and seepage. When large strains are required to develop shear strengths, surface movement measurement points and piezometers should be installed to monitor movements and pore water pressures during construction, in case it becomes necessary to modify the cross section or the rate of fill placement.

d. Liquefaction. The phenomenon of soil liquefaction, or significant reduction in soil strength and stiffness as a result of shear-induced increase in pore water pressure, is a major cause of earthquake damage to embankments and slopes. Most instances of liquefaction have been associated with saturated loose sandy or silty soils. Loose gravelly soil deposits are also vulnerable to liquefaction (e.g., Coulter and Migliaccio 1966; Chang 1978; Youd et al. 1984; and Harder 1988). Cohesive soils with more than 20 percent of particles finer than 0.005 mm, or with liquid limit (LL) of 34 or greater, or with the plasticity index (PI) of 14 or greater are generally considered not susceptible to liquefaction. The methodology to evaluate liquefaction susceptibility will be presented in an Engineer Circular, “Dynamic Analysis of Embankment Dams,” which is still in draft form.

e. Piping. Erosion and piping can occur when hydraulic gradients at the downstream end of a hydraulic structure are large enough to move soil particles. Analyses to compute hydraulic gradients and procedures to control piping are contained in EM 1110-2-1901.

f. Other types of slope movements. Several types of slope movements, including rockfalls, topples, lateral spreading, flows, and combinations of these, are not controlled by shear strength (Huang 1983). These types of mass movements are not discussed in this manual, but the possibility of their occurrence should not be ignored.

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Table 2- Shear Strengths and Pore Pressures for Static Design Conditions Design Condition Shear Strength Pore Water Pressure During Construction and End-of- Construction

Free draining soils – use drained shear strengths related to effective stresses 1

Free draining soils – Pore water pressures can be estimated using analytical techniques such as hydrostatic pressure computations if there is no flow, or using steady seepage analysis techniques (flow nets or finite element analyses). Low-permeability soils – use undrained strengths related to total stresses 2

Low-permeability soils – Total stresses are used; pore water pressures are set to zero in the slope stability computations. Steady-State Seepage Conditions Use drained shear strengths related to effective stresses.

Pore water pressures from field measurements, hydrostatic pressure computations for no-flow conditions, or steady seepage analysis techniques (flow nets, finite element analyses, or finite difference analyses). Sudden Drawdown Conditions Free draining soils – use drained shear strengths related to effective stresses.

Free draining soils – First-stage computations (before drawdown) – steady seepage pore pressures as for steady seepage condition. Second- and third-stage computations (after drawdown) – pore water pressures estimated using same techniques as for steady seepage, except with lowered water level. Low-permeability soils – Three-stage computations: First stage--use drained shear strength related to effective stresses; second stage--use undrained shear strengths related to consolidation pressures from the first stage; third stage--use drained strengths related to effective stresses, or undrained strengths related to consolidation pressures from the first stage, depending on which strength is lower – this will vary along the assumed shear surface.

Low-permeability soils – First-stage computations--steady-state seepage pore pressures as described for steady seepage condition. Second-stage computations – total stresses are used; pore water pressures are set to zero. Third-stage computations -- same pore pressures as free draining soils if drained strengths are used; pore water pressures are set to zero where undrained strengths are used.

(^1) Effective stress shear strength parameters can be obtained from consolidated-drained (CD, S) tests (direct shear or triaxial) or

consolidated-undrained (CU, R ) triaxial tests on saturated specimens with pore water pressure measurements. Repeated direct shear or Bromhead ring shear tests should be used to measure residual strengths. Undrained strengths can be obtained from unconsolidated-undrained (UU, Q) tests. Undrained shear strengths can also be estimated using consolidated-undrained (CU, R) tests on specimens consolidated to appropriate stress conditions representative of field conditions; however, the “R” or “total stress” envelope and associated c and 2 φ, from CU, R tests should not be used. For saturated soils use φ = 0. Total stress envelopes with φ > 0 are only applicable to partially saturated soils.

where

s = maximum possible value of shear stress = shear strength

c = cohesion intercept

σ = normal stress

φ = total stress friction angle.

(b) For effective stresses, the Mohr-Coulomb failure criterion is expressed as

s = c' + σ' tan φ ' (2-2)

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Figure 2-1. Strength envelopes for soils

where

s = maximum possible value of shear stress = shear strength

c' = effective stress cohesion intercept

σ' = effective normal stress

φ' = effective stress friction angle.

(c) Nonlinear strength envelopes are represented by pairs of values of s and σ, or s and σ'.

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Figure 2-2. Representation of shear strength parameters for anisotropic soil

d. Unit weights. The methods of analysis described in this manual use total unit weights for both total stress analyses and effective stress analyses. This applies for soils regardless of whether they are above or below water. Use of buoyant unit weights is not recommended, because experience has shown that confusion often arises as to when buoyant unit weights can be used and when they cannot. When computations are performed with computer software, there is no computational advantage in the use of buoyant unit weights. Therefore, to avoid possible confusion and computational errors, total unit weights should be used for all soils in all conditions. Total unit weights are used for all formulations and examples presented in this manual.

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e. External loads. All external loads imposed on the slope or ground surface should be represented in slope stability analyses, including loads imposed by water pressures, structures, surcharge loads, anchor forces, hawser forces, or other causes. Slope stability analyses must satisfy equilibrium in terms of total stresses and forces, regardless of whether total or effective stresses are used to specify the shear strength.

f. Tensile stresses and vertical cracks. Use of Mohr-Coulomb failure envelopes with an intercept, c or c', implies that the soil has some tensile strength (Figure 2-3). Although a cohesion intercept is convenient for representing the best-fit linear failure envelope over a range of positive normal stresses, the implied tensile strength is usually not reasonable. Unless tension tests are actually performed, which is rarely done, the implied tensile strength should be neglected. In most cases actual tensile strengths are very small and contribute little to slope stability.

(1) One exception, where the tensile strengths should be considered, is in back-analyses of slope failures to estimate the shear strength of natural deposits. In many cases, the existence of steep natural slopes can only be explained by tensile strength of the natural deposits. The near vertical slopes found in loess deposits are an example. It may be necessary to include significant tensile strength in back-analyses of such slopes to obtain realistic strength parameters. If strengths are back-calculated assuming no tensile strength, the shear strength parameters may be significantly overestimated.

(2) Significant tensile strengths in uncemented soils can often be attributed to partially saturated conditions. Later saturation of the soil mass can lead to loss of strength and slope failure. Thus, it may be most appropriate to assume significant tensile strength in back-analyses and then ignore the tensile strength (cohesion) in subsequent forward analysis of the slope. Guidelines to estimate shear strength in partially saturated soils are given in Appendix D, Section D-11.

(3) When a strength envelope with a significant cohesion intercept is used in slope stability computations, tensile stresses appear in the form of negative forces on the sides of slices and sometimes on the bases of slices. Such tensile stresses are almost always located along the upper portion of the shear surface, near the crest of the slope, and should be eliminated unless the soil possesses significant tensile strength because of cementing which will not diminish over time. The tensile stresses are easily eliminated by introducing a vertical crack of an appropriate depth (Figure 2-4). The soil upslope from the crack (to the right of the crack in Figure 2-4) is then ignored in the stability computations. This is accomplished in the analyses by terminating the slices near the crest of the slope with a slice having a vertical boundary, rather than the usual triangular shape, at the upper end of the shear surface. If the vertical crack is likely to become filled with water, an appropriate force resulting from water in the crack should be computed and applied to the boundary of the slice adjacent to the crack.

(4) The depth of the crack should be selected to eliminate tensile stresses, but not compressive stresses. As the crack depth is gradually increased, the factor of safety will decrease at first (as tensile stresses are eliminated), and then increase (as compressive stresses are eliminated) (Figure 2-5). The appropriate depth for a crack is the one producing the minimum factor of safety, which corresponds to the depth where tensile, but not compressive, stresses are eliminated.

(5) The depth of a vertical crack often can be estimated with suitable accuracy from the Rankine earth pressure theory for active earth pressures beneath a horizontal ground surface. The stresses in the tensile stress zone of the slope can be approximated by active Rankine earth pressures as shown in Figure 2-6. In the case where shear strengths are expressed using total stresses, the depth of tensile stress zone, zt , is given by:

D D t

2c z tan 45 2

⎛ φ ⎞ = (^) ⎜ ° + ⎟ γ (^) ⎝ ⎠

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Figure 2-5. Variation in the factor of safety with the assumed depth of vertical crack

where cD and φD represent the “developed” cohesion value and friction angle, respectively.

The developed shear strength parameters are expressed by:

D

c c = F

and

D

tan arctan F

⎛ φ⎞ φ = (^) ⎜ ⎟ ⎝ ⎠

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Figure 2-6. Horizontal stresses near the crest of the slope according to Rankine active earth pressure theory

where c, φ, and F are cohesion, angle of internal friction, and factor of safety.

In most practical problems, the factor of safety can be estimated with sufficient accuracy to estimate the developed shear strength parameters (cD and φD) and the appropriate depth of the tension crack.

(6) For effective stress analyses the depth of the tension crack can also be estimated from Rankine active earth pressure theory. In this case effective stress shear strength parameters, c' and φ' are used, with appropriate pore water pressure conditions.

2-3. Analyses of Stability during Construction and at the End of Construction

a. General. Computations of stability during construction and at the end of construction are performed using drained strengths in free-draining materials and undrained strengths in materials that drain slowly. Consolidation analyses can be used to determine what degree of drainage may develop during the