Category HIGHWAY ENGINEERING HANDBOOK

Where retaining walls are underlain by weak soils, the overall stability of the soil mass containing the retaining wall should be checked with respect to the most critical surface of sliding. A minimum safety factor of 2.0 is desirable but may not always be achievable. A technique known as slip circle analysis can be used to check for global stability. Refer to standard texts on soils engineering.

To provide adequate resistance against sliding, the base of the wall should be at least 3 ft below ground surface in front and below the depth of frost action, depth of seasonal volume change, and depth of scour. Sliding stability should be adequate without including passive pressure at the toe. If insufficient sliding resistance is available, the designer may increase base width, provide a pile foundation, or lower the base of the wall and consider passive resistance below frost depth. If the wall is supported on rock or very stiff clay, a key may be installed below the foundation to provide additional resistance to sliding. Considerations of the need for the 3-ft depth when dealing with Reinforced Earth walls should be evaluated in that such walls are not as susceptible to frost action as more rigid concrete walls. In any event, it is recommended that some nominal depth below ground line be provided to accommodate changes in natural terrain over the anticipated life of the structure, often 75 to 100 years. Such changes occur as a result of normal soil erosion caused by wind, rainfall, and other natural processes. Of course, in situations where scour may occur, hydrologic and hydraulic evaluations of scour depth must be made.

8.4.2 Settlement and Overturning

For walls on relatively incompressible foundations, apply the overturning criteria of Fig. 8.21. If the foundation is compressible, compute settlement by available methods pre­viously referred to and estimate tilt of a rigid wall from the settlement. If the consequent tilt is anticipated to exceed acceptable limits, proportion the wall to keep the resultant force at the middle third of the base. If a wall settles so that the resulting movement forces it into the soil it supports, then the lateral pressure on the active side increases sub­stantially. Table 8.3 shows the magnitudes of wall rotation required to mobilize active and passive earth pressures for different types of soil.

8.4.1 General Criteria

Rigid retaining walls are those that develop lateral resistance primarily from their own weight. Figure 8.20 shows the terms used in the design of this type of wall. On the basis of their overall cross-sections, those walls may be referred to as L walls or T walls. (See insets, Fig. 8.3.)

Examples of rigid structures typically include concrete gravity walls, thick concrete slurry walls, and gabion walls. Additionally, some Reinforced Earth walls, if designed to be reinforced in such a way that limited lateral movement will occur, can also be categorized as rigid walls. In fact, a wall may have considerable flexibility in its vertical dimension and nevertheless be classified and designed as a “rigid” wall system. Requirements for resistance of these wall types include sliding stability, overturning, bearing pressure evaluation, and settlement considerations. Design criteria for rigid retaining walls are summarized in Fig. 8.21. Overall, or global, stability is an important consideration in that, while the wall itself may adequately retain a soil mass, the soil mass may be unstable because, for example, of a deep-seated failure plane. This type of consideration is evaluated by slip circle analysis.

The equation for shearing strength S (lb/ft2 or kPa) of a soil may be taken as follows:

S = c + a tan ф (8.3)

where c = cohesion, lb/ft2 (kPa)

a = confining pressure or normal stress, lb/ft2 (kPa) ф = angle of internal friction of the soil, degrees

The shearing strength of the soil should account for the effect of pore water pressure when present. Equation (8.3) can be modified as:

S = c + (a — u) tan ф (8.4)

where u = pore water pressure, lb/ft2 (kPa)

Soil consolidation is produced by load and is associated with changes in soil mois­ture. It is also a function of time. The time required for drainage to occur, which results from the change in soil moisture, is a function of the permeability of the soil and the distance the water must travel in the material to be released. It is clear that consolidation of coarse-grained materials will occur fairly rapidly. This explains the often used assumption that consolidation of such materials under applied load, for example, the load of a retaining wall, generally occurs during the construction of the wall. Thus, long-term settlement is not normally considered to occur. On the contrary, clays and/or silts are relatively impermeable, so that long-term settlement should be anticipated in the design. The designer must consider various options to accommodate this projected long-term settlement. For example, the designer may (1) require preloading to effect the settlement before the wall is constructed, (2) accelerate the consolidation by drilling for and placing sand drains, and (3) decide to build the structure with pile or caisson support systems that are independent of the consolidation.

Bedrock is divided by geologists into three large groups, namely (1) igneous, (2) meta – morphic, and (3) sedimentary. Igneous rocks are those that have resulted from the cooling and crystallization of molten masses of mineral matter and gases either at or below the earth’s surface. Sedimentary rocks consist of the transported and subse­quently indurated products of weathering of previously existing rock types, while metamorphic rocks are frequently defined as those having characteristic textures and mineral compositions that have resulted from high temperatures and pressures and/or hot mineralizing solutions acting on a parent rock. Figures 8.16, 8.17, and 8.18 indi­cate easily recognizable descriptions for field classification of igneous, metamorphic, and sedimentary rock, respectively.

8.3.2 Soils Laboratory Tests

Grain size, shape, and gradation are generally established by sieve analysis. For the finer clays, a hydrometer analysis is necessary. Figure 8.19 depicts a classification of sediment based on grain size.

Atterberg limit tests are performed on fine-grained soils and represent the amount of water present in the voids. The liquid limit (LL), plastic limit (PL), and plasticity index (PI) constitute the Atterberg limits.

The triaxial shear test is used to find the shear strength of a soil for the determina­tion of pile lengths and of bearing capacity for spread footings or drilled shafts. Triaxial shear test results are also needed to give soil parameters for the design of retaining walls. High-quality, undisturbed samples are required for triaxial shear tests. Poor samples should be discarded rather than tested, as they will give misleading results.

The direct shear test is sometimes performed in lieu of other shear tests, and the use of its results is the same as that noted above for the triaxial shear test. It is impor­tant to remember that direct shear test results are usually less reliable than those obtained from the triaxial shear test, since the failure line in the direct shear test is imposed by the method of testing, whereas the triaxial method allows the sample to fail in its weakest plane. On occasion, it is desirable to shear soil or rock along a par­ticular plane. In these cases, a direct shear test may be used. High-quality, undisturbed samples are needed for this test.

The unconfined compression test of a soil is a uniaxial compression test in which the test specimen is provided with no lateral support while undergoing vertical com­pression. The test measures the unconfined, compressive strength of a cylinder of cohesive or semicohesive soil, which, indirectly, may be indicative of the shearing strength. The test is usually performed on an undisturbed sample of soil at its natural moisture content. It may also be performed on a remolded sample to evaluate the effects of disturbance and remolding upon the shearing strength.

Unconfined compression tests are relatively quick to perform and relatively inex­pensive. When used in conjunction with the triaxial test, the unconfined compres­sion test is of value. Also, it is sometimes used as an index test because it is easy to conduct.

(a)

If gravel is present in appreciable amounts, the term “gravelly” may be added to the class name, vis. “gravelly sand”. The terms “coarse”, “medium”, and “fine”, when used to describe gravel, sand, and silt, refer to standard grade size limits.

(b)

FIGURE 8.19 Classification of soil based on (a) grain size of sediment and (b) standard grain size limits. (From C. H. Harned, Some Practical Aspects of Foundation Studies for Highway Bridges, U. S. Bureau of Public Roads, January 1959)

Retaining wall design engineers not fully trained in soil mechanics need to be acquainted with certain basic principles, in order to understand the data developed by the geotechnical engineer or geologist responsible for the subsurface exploration. Soil is a nonhomogeneous earthen material that varies laterally and vertically in mineral context, grain size, density, grain shape, moisture content, strength, consistency, and compressibility. For the design of retaining walls and other structure-type foundations, the engineering properties of the soil must be evaluated. Such an evaluation will

always require consideration of foundation soil classification, bearing capacity, and compressibility.

Soil Classification. Since the types of soils are so numerous and variable, a classifi­cation system is important. The Unified Soil Classification System (USCS) has been generally accepted by engineers. It is based upon the sizes of the particles, the distrib­ution of the particle sizes, and the properties of the fine-grained portion. Only particle sizes of 3 in (75 mm) or less are included in the USCS. Materials greater in size are generally indicated in the log of borings as cobbles or boulders. Figure 8.14 shows the unified soil classification chart. The basic classifications include coarse-grained and fine-grained soils.

Coarse-Grained Soils. Coarse-grained soils are classified as either gravels or sands, dependent upon the fraction of the material retained on a no. 200 sieve. The classification threshold is 50 percent; i. e., if more than 50 percent of the fraction retained on a no. 200 sieve is retained on a no. 4 sieve, the soil is classified a gravel. If more than 50 percent passes the no. 4 sieve, the soil is classified a sand. There are many groupings of these coarse-grained soils, as indicated in the chart.

Fine-Grained Soils. Fine-grained soils are subdivided by plasticity and compress­ibility rather than by grain size. Fine-grained soils are classified as silt or clay, and as lowly or highly compressible. Criteria for classification are based upon the relation­ship between the liquid limit and the plasticity index. The relationship is given in the form of a plasticity chart shown by the inset in Fig. 8.14 and reproduced in Fig. 8.15. The “A” line on the chart divides clays from silts. Soils whose Atterberg limits plot above the line are clays, designated C; limits that plot below the line are silts, designated M.

8.3.1 General Considerations

Since the stability and safety of a structure—more specifically, retaining wall structures— depend upon the proper performance of the foundation, it is important that an adequate foundation investigation be made. The purpose of the investigation is to provide the designer with information concerning the engineering properties of the subsurface condi­tions. Generally, a retaining wall extends for a considerable length. Accordingly, the amount and type of foundation investigation that should be made and/or which the owner can afford must be considered. The owner must understand that once an exploration crew is dispatched to the site of a proposed wall, the investigation should be sufficiently complete to allow for the selection of an appropriate wall type.

When a rigid concrete retaining wall is to be used, the designer must consider that such a wall can tolerate only minimal differential settlement. If differential settlement is predicted, the designer may have to accommodate this situation by vertical joints in the wall and other systems of articulation in the wall. In many instances, this type of wall, under situations where differential or excessive settlement is anticipated, will require deep foundations such as caissons or piling driven to firm supporting material. Alternatively, subexcavation and replacement of poor material at the base of the wall may be appropriate. When a mechanically stabilized wall is selected under conditions of poor foundation soils, the wall is more tolerant to such a foundation condition. It is important for the owner to realize that while the wall is more tolerant to this condition, the end result as viewed from the finished top surface of the wall may be decidedly different. Therefore, it is important for the owner to set out the requirements of, and acceptance criteria for, the wall prior to the selection process. All alternative wall types evaluated should meet those criteria. Otherwise, the owner is not evaluating equal alternatives.

Subsurface Exploration Plan. Retaining walls are often viewed as subsidiary structures not worthy of any substantial expenditure for subsurface exploration. To the contrary, retaining walls can be costly structures. Further, the ultimate cost of most walls is quite sensitive to the foundation material.

The subsurface exploration plan can include obtaining subsurface data through the use of geophysical methods, such as seismic and electrical resistivity methods. More often the subsurface exploration effort is a simple and traditional boring program.

The boring program can be a simple auger drilling program with an experienced geologist classifying the soil on the basis of the auger cuttings. Clearly, if a physical examination of the type, nature, and characteristics of the subsurface materials is
desired, samples will be necessary. The samples can be disturbed or undisturbed. The disturbed sample is generally taken in cohesionless soils and is used for classification and for moisture determination and compaction tests. More commonly, such samples may be taken by driving a heavy walled sampler into a clean hole. The size of the sampler or spoon varies from 2 in (50 mm) O. D. to 4/2 in (112 mm) O. D. When a standard penetration test (SPT) is required, the sample is obtained by driving a 2-in (50 mm) O. D. by 138-in (34 mm) I. D. sampler.

Where it is necessary to evaluate the structural properties of the subsurface material in its natural condition, an undisturbed sample is taken. This type of sample will produce a core sample that can be used for such laboratory tests as the triaxial shear, uncon­fined compression, and consolidation tests. This type of sample is more frequently taken in cohesive soils that contain little or no granular materials. It is often taken with thin-walled tube samplers (Shelby type).

The SPT results may be used to describe soil density and clayey soil consistency as shown in the following table:

The blows are for the test procedures given in AASHTO Test Designation T-206.

Whenever rock is encountered, core drilling is done to advance the boring and to sample the rock in order to determine the profile and nature of the underlying rock strata. A general method by which the quality of the rock at a site is related to the amount of fracturing and alteration is known as the rock quality designation (RQD). The procedure consists of summing the total length of core recovered by counting only those pieces of hard and sound core that are 4 in or greater in depth. The ratio of this modified core recovery length to the total core run is the RQD. Rock quality is related to the RQD as follows:

Rock quality

designation (RQD) Rock quality

Very poor

Poor

Fair

Good

Excellent

Soil Properties. Soils include matter in three states: solid, liquid, and gas. Figure 8.13 shows a diagram of a soil block and presents the fundamental weight-volume relation­ships among the terms. The following sample problem illustrates application to a soil sample. Refer to Fig. 8.13 for nomenclature.

• Data:

Clay sample with water content of 31.2 percent by weight.

Specific gravity of soil particles is 2.80.

Sample is 98 percent saturated.

• Determine void ratio e and soil unit weight y; assume 1 cm3 of solids for calculations; V = 1.00 cm3:

S

V /V = 0.98

W

Ws = 2.80 X 1 g/cm3 = 2.80 g

W = 0.312 X 2.80 = 0.874 g

W = W + W = 2.80 + 0.874 = 3.674 g

Vw = Ww/yw = 0.874 g/(1 g/cm3) = 0.874 cm3

V = V /0.98 = 0.874/0.98 = 0.892 cm3

V w

V = V – V = 0.892 – 0.874 = 0.018 cm3

g V w

V = V + V = 1.00 + 0.892 = 1.892 cm3

S V

e = V/V = 0.892/1.00 = 0.892

vs

y = W/V = 3.674/1.892 = 1.94 g/cm3

The active pressure coefficient Ka is given by Coulomb theory as

where 0 = angle of slope of back wall to horizontal, degrees ф’ = effective angle of internal friction, degrees 8 = angle of wall friction, degrees P = angle of back slope, degrees

Refer to Figure 8.12 for the force diagram. The resultant horizontal earth force is to be determined for a design case wherein the following assumptions apply:

Design assumptions

ф’ = 34°

8 = 25°

P = 0°

0 = 90°

Y = 125 lb/ft3 (19.6 kN/m3)

H = height of wall = 20 ft (6.1 m)

Soil type = 1 (see Table 8.1)

Computations

sin (0 + ф’) = sin (90° + 34°) = sin 124° = 0.8290 sin2 (0 + ф’) = sin2 (90° + 34°) = sin2 124° = 0.6873 sin (ф’ + 8) = sin (34° + 25°) = sin 59° = 0.8572 sin (ф’ – P) = sin (34° – 0°) = sin 34° = 0.5592 sin (0-8) = sin (90° – 25°) = sin 65° = 0.9063 sin (0 + P) = sin (90° + 0°) = sin 90° = 1.0000 sin2 (0) = sin2 (90) = 1.0000

ka = horizontal active pressure = Ka8’H = 0.2542(125)20 = 635.5 lb/ft2 (U. S. Customary units)

= 0.2542 (19.6) 6.1 = 30.4 kPa (SI units)

Pa = force resultant due to horizontal active pressure

Alternate calculation. Figure 8.10 gives the horizontal and vertical components of active earth pressure, kh and kv, for the five soil types listed in Table 8.1. The pres­sures are given in terms of the ratio H1/H, when H1 is the surcharge height and H is the height of the fill from the base, both as defined by the sketches in Fig. 8.10.

From Fig. 8.10, soil is type 1, H1/H = 0, kh = 30 lb/ft2/ft. Use 35 lb/ft2/ft (5.50 kN/m2/m), per note 3, Fig. 8.10.

Pa = /2khH2 = /2 X 35(20)2 = 7000 lb/ft (U. S. Customary units)

= /2 X 5.50(6.1)2 = 102 kN/m (SI units)

For yielding walls, lateral earth pressures can be computed assuming active conditions and wedge theory, using a planar surface of sliding defined by the Rankine theory. Table 8.1 provides soil properties for computing active earth pressures for five types of soil. Table 8.2 provides friction factors and adhesion for dissimilar materials. See Figs. 8.10 and 8.11 for the magnitude and location of resultant forces on retaining walls considering various types of soil backfill and backslide geometries. The pressures presented in these figures assume mobilization of the soil shear strength along the entire Rankine active failure plane, extending uninterrupted from the ground surface at the base of the wall or to the location on the wall at which the total earth load is being computed. Figure 8.11 shows the failure surface geometry and associated earth pressure distributions for various design conditions. If the soil behind the wall consists of more than one soil type, the design earth pressure should be determined using the weighted average of the properties of the soil types within and along the theoretical failure plane.

AASHTO provides that, for yielding walls, lateral earth pressures should be computed assuming active stress conditions and wedge theory using a planar surface of sliding defined by Coulomb theory. The computational procedures for active pressures are

2k!H2H

Hi

b

Soil type 1 (see Note 3)

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0

Values of Ratio – H-

FIGURE 8.10 Charts for estimating Rankine active earth pressures against retaining walls support­ing sloped ground of limited height. Notes: (1) Soil types shown on curves correspond to soil types described in Table 8.1. (2) For soil type 5, computations of soil pressure may be based on a value of H 4 ft (1.2 m) less than the actual value. (3) The minimum value of kh for design should be 35 lb/ft2/lin ft (5.50 kN/m2/m). (4) Add pressures due to water and surcharge (including 2 ft minimum soil surcharge) to the active earth pressures from these charts. (From Design Manual, Part 4, Pennsylvania Department of Transportation, Harrisburg, Pa., with permission)

DESIGN FAILURE SURFACE HORIZONTAL EARTH

CONDITION GEOMETRY PRESSURE DISTRIBUTION

LEGEND

kh1 = unit horizontal soil pressure due to backfill kh2 = unit horizontal soil pressure due to in situ soil P = angle between Rankine active failure plane and horizontal ф’ = weighted average effective stress angle of internal friction along failure plane

P = tan-1 tan ф’ + 1 + tan^’———— в

s^’ cosф’

NOTES

(1) Obtain values of kh1, kh2, and vertical component of soil pressure.

(2) The earth pressure resultant for this condition can be more accurately determined by Culmann’s graphical construction.

(3) Add pressures due to water and surcharge (including 2-ft minimum soil surcharge).

FIGURE 8.11 Assumed failure surfaces and horizontal earth pressure distributions. (From Design Manual, Part 4, Pennsylvania Department of Transportation, Harrisburg, Pa., with permission)
given below. An alternative to the computation for active pressures using the Coulomb theory for yielding walls and for cohesionless soils is to define the lateral pressures utilizing the Rankine theory.

The above procedures for developing the design pressures on yielding walls are based on the following assumptions:

1. The backfill soils are compacted with lightweight hand-compaction equipment.

2. The soil within the theoretical failure zone is made up entirely of the backfill soil.

3. No point or line loads act on the backfill surface.

4. The retaining wall deflections are consistent with the deflections required to develop the design active earth pressure.

Lateral earth pressure loadings are applied in various states—specifically, active, at-rest, and passive states. The state of pressure to be considered varies with the wall type.

Yielding Walls. Yielding walls are free to translate or rotate about their top or base. For such walls, the lateral earth pressure may be computed assuming active conditions and wedge theory. In general, the lateral displacement at the top of a rigid wall of height H necessary to develop the active state varies from 0.001H in dense cohesion­less soils to as much as 0.004H in loose cohesionless soils. For clay soils, a greater displacement on the order of 0.01H to 0.02H, for stiff and soft soils, respectively, is necessary to develop an active state. See Figs. 8.7 and 8.8.

Thus, it is noted that the amount of displacement necessary to develop active pres­sure can vary, say, for a 20-ft-high (6 m) wall, from less than И in (6 mm), in a dense cohesionless material, to as much as 5 in (125 mm), in soft clay. Clearly, the backfill material selected at any location plays a major role in the earth pressure for which a wall must be designed.

Restrained Walls. Restrained walls are walls that are fixed or partially restrained against translation or rotation. Lateral earth pressures are computed assuming at-rest conditions using the following relationship:

P =

P° 2

where P0 = resultant of at-rest earth pressure, kips/ft (N/mm)

7 = unit weight of soil or rock, kips/ft3 (kN/m3)

H = wall height, ft (mm)

K0 = at-rest pressure coefficient

This latter condition may occur naturally at walls that are not totally freestanding—for example, at the junction of the wingwall at bridge abutments—or the condition may occur by design. Examples include locations where the lateral deflection cannot be tolerated because it retains a structure, or a heavily reinforced concrete counterfort wall, which is sensitive to settlement, located on material susceptible to settlement, especially differential settlement. In the latter case the designer must evaluate options that may include, depending upon the depth of the material that will settle, (1) removal and replacement, (2) deep foundations to adequate bearing material, or (3) selection of a different wall type, if conditions permit, that will be more tolerant to the potential for the differential settlement.

Should some force be present that tends to push the wall into the earth mass it is intended to retain—which therefore develops a resistance to slip on the failure plane or a resistance to the lateral displacement needed to mobilize the active pressure state—a condition known as passive pressure develops. The lateral earth pressure for which the wall must be designed increases significantly, as much as 10 times, and requires special attention. See Fig. 8.9 for a qualitative depiction of the relative lateral displacement.

Rigid Walls. For the case of rigid walls, which involves wall translation or rotation “into the backfill,” the movement necessary to develop passive earth pressure behind the wall varies from 0.020H to 0.060H for cohesionless soils, dense to loose, respectively. Also, for stiff to soft cohesive soils, the lateral displacement will vary from 0.020H to 0.040H. It is obvious that passive earth pressures can be developed in these defined con­ditions. Certainly, the best way for the designer to account for these pressures is to avoid them wherever possible and practical, alleviating the conditions under which such pressures develop. This brief discussion is intended only to generate an awareness in the designer that such conditions can be created. An example would be dead-man type anchorages tying the wall top into solid materials or outside the failure plane of the wedge, thus pre­venting the movement necessary for development of the active pressure state.