Category HIGHWAY ENGINEERING HANDBOOK

For a typical wall with two or more rows of anchors constructed from the top down, the general procedure is to (1) design for the final condition with multiple rows of anchors and (2) check the design for the various stages of construction. The required horizontal component of each anchor force can be calculated using apparent earth pressure distribu­tions such as given in Fig. 8.50. Any other applicable forces such as horizontal water pressure, surcharge, or seismic forces must be included where applicable. The anchor inclination must be considered in calculating the anchor force. The horizontal anchor spac­ing and anchor capacity must provide the required total anchor force.

Vertical wall elements must be designed to resist all applicable forces such as hori­zontal earth pressure, surcharge, water pressure, and anchor and seismic loadings, as well as the vertical component of earth pressure due to wall friction and the vertical component of anchor loads and any other vertical loads. In the analysis, supports may be assumed at each anchor location and at the bottom if the vertical element extends below the bottom of the wall.

All components should be checked for the various earth pressure distributions and other loading conditions that may exist during construction.

The design of anchored walls involves a determination of several factors. Included are the size, spacing, and depth of embedment of vertical wall elements and facing; the type, capacity, spacing, depth, inclination, and corrosion protection of anchors; and the struc­tural capacity and stability of the wall, wall foundation, and surrounding soil mass for all intermediate and final stages of construction. The bearing capacity and settlement of vertical wall elements under the action of the vertical component of the anchor forces and other vertical loads must also be evaluated.

AASHTO provides the following guidance:

For walls supported in or through soft clays with Su < 0.3y’H, continuous vertical ele­ments extending well below the exposed base of the wall may be required to prevent heave in front of the wall. Otherwise, the vertical elements are embedded several feet as required for stability or end bearing. (Where significant embedment of the wall is required to prevent bottom heave, the lowest section of wall below the lowest row of anchors must be designed to resist the moment induced by the pressure acting between the lowest row of anchors and the base of the exposed wall, and the force Pb = 0.7(yHBe — 1.4cH — ^cBe) acting at the mid-height of the embedded depth of the wall.)

In the above, the following definitions apply:

Be = width of excavation perpendicular to wall c = cohesion of soil H = design wall height

Su = undrained shear strength of cohesive soil у = soil unit weight y’ = effective unit weight of soil

The choice of lateral earth pressures used for design should take into account the method and sequence of construction, rigidity of the wall-anchor system, physical characteris­tics and stability of the ground mass to be supported, allowable wall deflections, space between anchors, anchor prestress, and potential for anchor yield. For stable ground masses, the final lateral earth pressures on a completed wall with two or more levels of anchors constructed from the top down can be calculated using the apparent earth pres­sure distributions shown in Fig. 8.50. For unstable or marginally stable ground masses, design earth pressures will be greater than those shown in Fig. 8.50. Therefore, loads

APPARENT EARTH

SOIL TYPE PRESSURE DISTRIBUTION

H = final wall height Ka = active earth pressure coefficient

Y = effective soil unit weight

Y = total soil unit weight m = reduction factor

qu = unconfined compressive strength

NOTES

(1) Ka = tan2 (45 – 2 )

(2) Ka = 1 – m (2qu/yH) but not

less than 0.25

m = 1 for overconsolidated clays

m = 0.4 for normally consolidated clay

(3) Value of 0.4 should be used for long-term excavations; values between 0.4 and 0.2 may be used for short-term conditions.

should be estimated using methods of slope stability analysis that include the effects of anchors, or that consider “interslice” forces.

In developing design earth pressures, consideration should be given to wall displace­ments that may affect adjacent structures or underground utilities. Rough estimates of set­tlement adjacent to braced or anchored flexible walls can be made using Fig. 8.51. If wall deflections estimated using Fig. 8.51 are excessive, a more detailed analysis can be made using beam-on-elastic-foundation, finite element, or other methods of analysis that con­sider soil-structure interaction effects. Where a structure or utility particularly sensitive to settlement is located close to a wall, wall deflections should be calculated on the basis of the loading, soil properties, anchor spacing, and wall element stiffness.

The distribution of earth pressure loading for anchored walls with one level of anchors can be assumed to be triangular and to be based on a lateral earth pressure coefficient (i. e., Ka, K0, or Kp) consistent with the expected wall deflection. To consider the case where excavation has advanced down to the first anchor level but the anchors have not yet been installed, the wall can be treated as a nongravity cantilevered wall and the earth pressure distribution assumed triangular. Overstressing of anchors

CURVE I

CURVE E = Stiff to very hard clay

CURVE Ш = Soft to medium day, factor of

safety against basal heave (5-1 equal to 2.0 ”У ” 4

CURVE Ш. = Soft to medium clay, factor of

safety agoinst basal heave (= 5-’ su ^ equol to 1.2 yH + q у

FIGURE 8.51 Settlement profiles behind braced or anchored walls. (From Standard Specifications for Highway Bridges, 2002, American Association of State Highway Officials, Washington, D. C., with permission)

should be avoided, because excessive anchor loads, relative to the capacity of the retained ground mass, can cause undesirable deflections, or passive failure of the wall into the retained soil. As with other walls, design lateral pressures for walls constructed from the top down must include the lateral pressure due to traffic or other surcharge loading.

Where there is no anchor level or only one, the magnitude and distribution of lateral resisting forces for embedded vertical elements in soil or rock can be determined as described in Art. 8.6.1. When two or more levels of anchors have been installed, the lateral resistance provided by embedded vertical elements will depend on the element stiffness and deflection under load.

Earth pressures on anchored walls constructed from the bottom up (fill construction) are affected by the construction method and sequence. These must be well specified, and the basis for lateral earth pressures fully documented. For walls with a single anchor level, consider a triangular distribution, defined by Kay per unit length of wall height, plus surcharge loads. For walls with multiple anchor levels, consider a rectangular pressure dis­tribution, derived by increasing the total force from the triangular pressure distribution just described by one-third and applying the force as a uniform pressure distribution.

Drainage considerations for anchored walls are similar to those discussed in Art. 8.6.2.

Anchored walls are made up of the same elements as cantilevered walls but are fur­nished with one or more tiers of anchors for additional lateral support. Anchors may be either prestressed or dead-man type. Tendons or bars extend from the wall face to a region beyond the active zone where they are grouted in place or mechanically anchored. Such walls are typically constructed from the top down in cut situations rather than fill conditions. Figure 8.49 illustrates an anchored wall and defines terminology.

The overall stability of slopes in the vicinity of walls is considered part of the design of retaining walls. The overall stability of the retaining wall, retained slope, and foun­dation soil or rock can be evaluated for all walls using limiting equilibrium methods of analysis. AASHTO gives the following requirements:

A minimum factor of safety of 1.3 shall be used for walls designed for static loads, except the factor of safety shall be 1.5 for walls that support abutments, buildings, critical utilities, or other installations with a low tolerance for failure. A minimum factor of safety of 1.1 shall be used when designing walls for seismic loads. In all cases, the subsurface condi­tions and soil/rock properties of the wall site shall be adequately characterized through in – situ exploration and testing and/or laboratory testing…

8.6.3 Corrosion Protection

Prestressed anchors and anchor heads must be protected against corrosion that would result from ground and groundwater conditions at the site. The level of corrosion protec­tion depends on both the ground environment and the potential consequences of an anchor failure. Also, anchors for permanent walls require a higher level of corrosion protection than those for temporary walls.

Flexible cantilevered walls should be dimensioned to ensure stability against passive fail­ure of embedded vertical elements using a factor of safety of 1.5 based on unfactored loads. Vertical elements must be designed to support the full design earth, surcharge, and water pressures between the elements. In determining the depth of embedment to mobi­lize passive resistance, consideration should be given to planes of weakness (such as “slickensides,” bedding planes, and joint sets) that could reduce the strength of the soil or rock from that determined by field or laboratory tests. AASHTO recommends that for embedment in intact rock, including massive to appreciably jointed rock, which should not be allowed to fail through a joint surface, design should be based on an allowable shear strength of 0.10 to 0.15 times the uniaxial compressive strength of the intact rock.

8.6.2 Structure Design

Structural design of individual wall elements may be performed by service load or load factor design methods.

The maximum spacing L between vertical supporting elements depends on the rela­tive stiffness of the vertical elements and facing, the design pressure P, and the type and condition of soil to be supported. Design the facing for the bending moment Mmx at any level, as determined by the following equations:

Simple span (no soil arching):

PL2

M = —— (8.22)

max 8

Simple span (soil arching):

PaL2

M = —— (8.23)

max 12

Continuous:

PaL2

M = —— (8.24)

max 10

Equation (8.22) is applicable for simply supported facings where the soil will not arch between vertical supports (e. g., in soft cohesive soils or for rigid concrete facing placed tightly against the in-place soil). Equation (8.23) is applicable for simply sup­ported facings where the soil will arch between vertical supports (e. g., in granular or stiff cohesive soils with flexible facing, or rigid facing behind which there is sufficient space to permit the in-place soil to arch). Equation (8.24) is applicable for facings that are continuous over several vertical supports (e. g., reinforced shotcrete).

Flexible cantilevered walls must be designed to resist the maximum anticipated water pressure. For a horizontal static groundwater table, the total hydrostatic water pressure can be determined from the hydrostatic head by the traditional method. For differing groundwater levels on opposite sides of the wall, the water pressure and seepage forces can be determined by net flow procedures or other methods. Seepage can be controlled by installation of a drainage medium. Preformed drainage panels, sand or gravel drains, or wick drains can be placed behind the facing with outlets at the base of the wall. It is important that drainage panels maintain their function under design earth pressures and surcharge loadings. AASHTO requires that they extend from the base of the wall to a level 1 ft (300 mm) below the top of the wall.

Where thin drainage panels are used behind walls, saturated or moist soil behind the panels may be subject to freezing and expansion. In such cases, insulation can be provided on the walls to prevent soil freezing or the wall can be designed for the pres­sures that may be exerted on it by frozen soil.

Nongravity cantilevered walls are those that provide lateral resistance through vertical elements embedded in soil, with the retained soil between the vertical elements usually supported by facing elements. Such walls may be constructed of concrete, steel, or timber. Their height is usually limited to about 15 ft (4.6 m), unless provided with additional support anchors.

8.6.1 Earth Pressure and Surcharge Loads

Lateral earth pressure can be estimated assuming wedge theory using a planar surface of sliding as defined by Coulomb’s theory. For permanent walls, effective stress meth­ods of analysis and drained shear strength parameters for soils can be used for deter­mining lateral earth pressures. Alternatively, the simplified earth pressure distributions shown in Figs. 8.45 and 8.46 can be used. Nomenclature and notes for Fig. 8.45 are given in Table 8.8.

1. Determine the active earth pressure on the wall due to surchage loads, the retained soil, and differential water pressure above the dredge line.

2. Determine the magnitude of active pressure at the dredge line (P*) due to surcharge loads, retained soil, and differential water pressure, using the earth pressure coefficient Ka2.

3. Determine the value of x = P*/[(Kp2 – Ka2)y2] for the distribution of net passive pressure

in front of the wall below the dredge line.

4. Sum moments about the point of action of F to determine the embedment (D0) for which the net passive pressure is sufficient to provide equilibrium.

5. Determine the depth (point a) at which the shear in the wall is zero (i. e., the point at which the areas of the driving and resisting pressure diagrams are equivalent).

6. Calculate the maximum bending moment at the point of zero shear.

7. Calculate the design depth, D = 1.2 D0 to 1.4 D0, for a safety factor of 1.5 to 2.0.

(a) Pressure distribution (b) Simplified design procedure

N°tes: (1) Surcharge and water pressures must be added to the above earth pressures.

(2) Forces shown are per horizontal foot of vertical wall element.

FIGURE 8.46 Simplified earth pressure distributions and design procedures for permanent flexible cantilevered walls with continuous vertical wall elements. (From Standard Specifications for Highway Bridges, 2002, American Association of State Highway and Transportation Officials, Washington, D. C., with permission)

For temporary applications in cohesive soils, total stress methods of analysis and undrained shear strength parameters apply. The simplified earth pressure distributions shown in Figs. 8.46 and 8.47 can alternatively be used with the following limitations:

1. The ratio of overburden pressure to undrained shear strength must be less than 3. This ratio is referred to as the stability number N = yH/c.

2. The active earth pressure must not be less than 0.25 times the effective overburden pressure at any depth.

Nomenclature and notes for Fig. 8.47 are given in Table 8.8.

Where discrete vertical wall elements are used for support, the width of each vertical element should be assumed to equal the width of the flange or diameter of the element for driven sections, and to equal the diameter of the concrete-filled hole for sections encased in concrete.

For permanent walls, Figs. 8.45 and 8.46 show the magnitude and location of resultant loads and resisting forces for discrete vertical elements embedded in soil and rock. The procedure for determining the resultant passive resistance of a vertical element assumes that net passive resistance is mobilized across a maximum of 3 times the element width or diameter (reduced, if necessary, to account for soft clay or discontinuities in the embedded depth of soil or rock). Also, a depth of 1.5 times the width of an element in soil, and 1 ft (300 mm) for an element in rock, is ineffective in providing passive lateral support.

Legend:

y’ = effective unit weight of soil b = vertical element width

l = spacing between vertical wall elements, center to center S = undrained shear strength of cohesive soil s = shear strength of rock mass Pp = passive resistance per vertical wall element P = active earth pressure per vertical wall element p = ground surface slope behind wall 1 + for slope up from wall

p’ = ground surface slope in front of wall J — for slope down from wall Ka = active earth pressure coefficient; refer to Art. 8.2.3

K = passive earth pressure coefficient; refer to Standard Specifications for Highway Bridges,

P AASHTO, 2002. ф’ = effective angle of soil friction

Notes:

1. For temporary walls embedded in granular soil or rock, refer to Fig. 8.45 to determine passive resis­tance and use diagrams on Fig. 8.47 to determine active earth pressure of retained soil.

2. Surcharge and water pressures must be added to the indicated earth pressures.

3. Forces shown are per vertical wall element.

4. Pressure distributions below the exposed portion of the wall are based on an effective element width of 3b, which is valid for l > 5b. For l < 5b, refer to Figs. 8.46 and 8.48 for continuous wall elements to determine pressure distributions on embedded portions of the wall.

Source: From Standard Specifications for Highway Bridges, 2002, American Association of State Highway

and Transportation Officials, Washington, D. C., with permission.

(a) Embedment in cohesive soil (b) Embedment in cohesive soil

retaining granular soil retaining cohesive soil

Notes: (1) For walls embedded in granular soil, refer to Fig. 8.46 and use above diagram for retained cohesive soil when appropriate.

(2) Surface and water pressures must be added to the above earth pressures.

(3) Forces shown are per horizontal foot of vertical wall element.

FIGURE 8.48 Simplified earth pressure distributions for temporary flexible cantilevered walls with continuous vertical wall elements. (From Standard Specifications for Highway Bridges, 2002, American Association of State Highway and Transportation Officials, Washington, D. C., with permission)

The design lateral pressure must include lateral pressure due to traffic, permanent point and line surcharge loads, backfill compaction, or other types of surcharge loads, as well as the lateral earth pressure.

According to the K0-Stiffness Method, with reference to Dt from Fig. 8.44a and b, the peak load, Tmax (lb/ft), in each reinforcement layer can be calculated with the procedure summarized below (Allen and Bathurst, 2001):

Ф(ь = facing batter factor Ф(8 = facing stiffness (actor

Pa = atmospheric pressure (a constant to preserve dimensional consistency equal to 2110 lb/ft2 for the indicated units)

^global- ^ocal> Ф(Ь Ф(8> and are further defined bel°W.

K0 can be determined from the coefficient of lateral at-rest earth pressure for nor­mally consolidated soil:

K0 = 1 – sin Ф’ (8.17)

where Ф’ (degrees) is the peak angle of internal soil friction for the wall backfill. For steel reinforced systems, K0 for design should be 0.3 or greater. This equation for K0 has been shown to work reasonably well for normally consolidated sands, and can be modified by using the overconsolidation ratio (OCR) for sand that has been preloaded or compacted. However, because the OCR is very difficult to estimate for compacted sands, especially at the time of wall design, the K0-Stiffness Method was calibrated using only Eq. (8.17) to determine K0. Because the K0-Stiffness Method is empirically based, it can be argued that the method implicitly includes compaction effects, and therefore modification of Eq. (8.17) to account for compaction is not necessary. Note also that the method was calibrated using measured peak shear strength data corrected to peak plane strain shear strength values.

Global stiffness 5global considers the stiffness of the entire wall section, and is calcu­lated as follows:

= Hve = sumof Jj

global = H/n = H

where Jave (lb/ft) is the average modulus of all reinforcement layers within the entire wall section, Jt (lb/ft) is the modulus of an individual reinforcement layer, H is the total wall height, and n is the number of reinforcement layers within the entire wall section.

Local stiffness Slocal (lb/ft2) considers the stiffness and reinforcement density at a given layer, and is calculated as follows:

Slocal = H (8Л9)

where J is the modulus of an individual reinforcement layer, and Sv is the vertical spacing of the reinforcement layers near a specific layer.

The local stiffness factor Ф^^ is defined as

Ф^ = ( Hh ) (8.20)

global

where a is a coefficient that is also a function of stiffness. Observations from available data suggest that setting a = 1.0 for geosynthetic-reinforced walls and a = 0.0 for steel-reinforced soil walls is sufficiently accurate.

The wall face batter factor Ф(Ь which accounts for the influence of the reduced soil weight on reinforcement loads, is determined as follows:

Ф(ь = ( Hh ) (8.21)

Kavh /

where Kabh is the horizontal component of the active earth pressure coefficient accounting for wall face batter, Kavh is the horizontal component of the active earth pressure coefficient, and d is a constant coefficient (recommended to be 0.5 to provide the best fit to the empirical data). The wall is assumed to be vertical.

The facing stiffness factor Фй was empirically derived to account for the signifi­cantly reduced reinforcement stresses observed for geosynthetic walls with segmental concrete block and propped panel wall facings. It is not yet known whether this facing stiffness correction is fully applicable to steel-reinforced wall systems. On the basis of data available, Allen and Bathurst (2001) recommend that this value be set equal to the following:

0. 5 for segmental concrete block and propped panel faced walls

1. for all other types of wall facings (e. g., wrapped face, welded wire or gabion faced, and incremental precast concrete facings)

1.0 for all steel-reinforced soil walls

Note that the facings defined above as flexible still have some stiffness and some ability to take a portion of the load applied to the wall system internally. It is possible to have facings that are more flexible than the types listed above, and consequently walls with very flexible facings may require a facing stiffness factor greater than 1.0.

The maximum wall heights available where the facing stiffness effect could be observed were approximately 20 ft (6 m). Data from taller walls were not available. It is possible that this facing stiffness effect may not be as strong for much taller walls. Therefore, caution should be exercised when using those preliminary Фй values for walls taller than 20 ft (6 m). Detailed background information as well as several numerical examples for both steel and geosynthetic reinforced soil walls are provided by Allen and Bathurst (2001).

The following is a numerical example of applying the preceding equations for the evaluation of Tmax at reinforcing layers 4 ft (1.2 m), 10 ft (3 m), and 18 ft (5.5 m) from the top of the wall.

• Design assumptions

A 20-ft-high (6-m) segmental concrete block MSE wall has a vertical facing and 10 layers (2-ft or 0.6 m uniform spacing) of the same grade polyester (PET) geogrid reinforcements. Thus, H = 20 ft (6 m), Фй = 0.5, n = 10, Sv = 2 ft (0.6 m), and Jave = 28,780 lb/ft (420 kN/m) for PET. Since the wall is vertical, Kabh/Kavh = 1.0. The wall has a 2-ft earth surcharge, soil with 125 lb/ft3 unit weight, and 34° peak soil friction angle. Thus, S = 2 ft, у = 125 lb/ft3, Ф = 34°, and Pa = 101 kPa = 101 kN/m2 = 2110 lb/ft2.

• Computations

From Eq. (8.17), K0 = 1 – sin 34° = 0.441.

From Eq. (8.18), Sglobal = (28,780)/(20/10) = 14,390 lb/ft2.

From Eq. (8.19), Slocal = 28,780/2 = 14,390 lb/ft2.

From Eq. (8.20), Ф^ = (14,390/14,390)’ = 1.0.

From Eq. (8.21), Фл = (1.0)05 = 1.0.

From Eq. 8.16, for the K0-Stiffness Method, Tmax = 0.5 (Sv)(0.441)(125)(20 + 2)(DtmJ(1.0) (1.0)(0.5)(0.27)(14,390/2110)°’24 = (129.8)(Sv)(D^).

Next, evaluate Tmax at distances Z from the top of the wall, obtaining the distribution factor Dtmax from Fig. 8.44 for each Z/H ratio: At 4 ft, Z/H = 0.2, Dtmx = 0.733, Tmax =

95.1 (Sv) “lb/ft2 = 190.2 lb/ft; at 10 ft, Z/H = 0.5, Dtmax = 1.00, Tmax =129.8 (Sv) lb/ft2 = 259.6 lb/ft; and at 18 ft, Z/H = 0.9, D, = 0.60, T = 83.8 (S ) lb/ft2 = 167.6 lb/ft.

tmax ‘ max x V’

If the results for this example are compared with those obtained by the AASHTO method (Art. 8.5.11), it will be seen that the total required reinforcement forces for the ^-Stiffness Method are only about one-quarter of those for the AASHTO method.

With the assumption that all the 10 reinforcement layers have the same stiffness, the calculation of reinforcement forces demonstrated above is a first trial. The global stiffness factor (Sglobal) should be revised according to the actual reinforcing stiffness distribution. To avoid the iterative nature of the ^-Stiffness Method, Allen and Bathurst (2001) also provide a simplified methodology with different combined global stiffness curves according to the type of reinforcing material as well as the height of wall.

Allen and Bathurst (2001) developed a new methodology for estimating reinforcement loads in both steel and geosynthetic reinforced soil walls known as the K0-Stiffness Method. Figure 8.44a and b, for polymeric and metal reinforcements, respectively, are provided for estimating the reinforcement load distribution with respect to the magnitude of maximum reinforcement tension from the top to the bottom of the wall. The soil reinforcement load distribution factor (D, max) in these two figures was determined empirically from all of the available field wall case histories. There were empirical databases consisting of measured reinforcement strains and loads from nine full-scale field geosynthetic wall cases (13 different wall sections and surcharge conditions, and 58 individual data points) and 19 full-scale field steel reinforced soil wall cases

(24 different wall sections and surcharge conditions, and 102 individual data points). The resulting factor is shown in Fig. 8.44a for geosynthetic-reinforced soil walls and in Fig. 8.44b for steel-reinforced soil walls. This factor, D, , is the ratio of the

‘max

maximum tension force Tmax in a reinforcement layer to the maximum reinforcement loads in the wall, T (the maximum value of T within the wall). The two parts of Fig. 8.44 provide the distributions of load, but the magnitude of Tmax is evaluated by the equations of the ^-Stiffness Method in Art. 8.5.13. Empirical reinforcement load distributions provided in Fig. 8.44a and b apply only to walls constructed on a firm soil foundation. The distributions that would result for a rock or soft-soil foundation may differ from those shown. The two parts of the figure demonstrate the differences in reinforcement load distributions between geosynthetic – and steel-reinforced soil walls. The long recognized fact of nontriangular load distribution is clarified, espe­cially for the geosynthetic-reinforced soil wall. Though two different drawings have been used to determine the reinforcement load distribution, this new method provides an improved load estimation for both steel – and geosynthetic-reinforced soil walls and a unified approach.

This new method was developed empirically through analyses of many full-scale wall case histories. In most cases, reinforcement loads had to be estimated from measured reinforcement strain converted to load through a properly estimated reinforcement modulus. For metal-reinforced soil walls, the use of Young’s modulus to convert strain to stress and load is relatively straightforward. However, to accurately determine the
reinforcement loads for geosynthetic-reinforced soil walls, the correct modulus, con­sidering time and temperature effects, had to be estimated accurately. The creep modulus generated from long-term laboratory creep data through regular product analysis was considered accurate enough for estimating reinforcement loads from measured strains.

Once the correct load levels in the reinforcement layers were established, the rein­forcement loads obtained from the full-scale walls were compared to what would be predicted with the new method and the current methodologies found in design guidelines and design codes, including the simplified coherent gravity approach in article 5.8.4.1 of AASHTO. All existing design methodologies were found to provide inaccurate load predictions, especially for geosynthetic-reinforced walls. Considering all available case histories, Allen and Bathurst (2001) reported that the average and coefficient of varia­tion (COV) of the ratio of the predicted to measured Tmax, the peak reinforcement load in each layer, for the simplified method were as follows: 2.9 and 85.9 percent, respectively, for geosynthetic walls, and 0.9 and 50.6 percent, respectively, for steel-reinforced soil walls. The average and COV of the ratio for the K0-Stiffness Method were as follows: 1.12 and 40.8 percent, respectively, for geosynthetic walls, and 1.12 and 35.1 percent, respectively, for steel-reinforced soil walls. This indicates a marked improvement and shows that the calculated loads can be estimated more closely with the D, factors

‘max

and the K0-Stiffness Method.

In the determination of the magnitude of Tmax in the wall, the stiffness of all wall components (facing type, facing batter, reinforcement stiffness, and spacing) relative to soil stiffness is evaluated. By the nature of extensibility of soil reinforcement, the rein­forcement load distributions (D, max) are differentiated by two unique figures. From working load to ultimate load up to incipient soil failure, this methodology covers the full range of strain and load predictions. The method is workable to estimate reinforce­ment responses for both the serviceability and strength limit state. It also includes the estimate of wall deformation from reinforcement strain prediction, load, and resistance factors that account for the uncertainty in the method and material properties.