Category HIGHWAY ENGINEERING HANDBOOK

The following design example is provided with the permission of the Reinforced Earth Company. Typical calculations are shown, including the determination of allowable
reinforcement tension for galvanized steel reinforcing strips. Figure 8.40 shows a cut­away view of a typical Reinforced Earth retaining wall. Refer to Fig. 8.41 for illustration of calculation steps.

Geometry

Height of wall H = 20 ft

Strip length B = 20 ft (AASHTO minimum = 0.7H = 14 ft) Soil Properties

	ф	Cohesion, c	Unit weight, у
R. E. material	34.00°	—	0.125 kip/ft3
Random fill	25.00°	0.100 kip/ft2	0.120 kip/ft3
Foundation	25.00°	0.300 kip/ft2	—

Other Properties

• Equivalent fill height for traffic surcharge of 0.25 kip/ft2 =

0.25 kip/ft2 0.120 kip/ft3

• Maximum value of apparent coefficient of friction (bond) = 1.50.

• Coefficient of friction at foundation level (sliding) = 0.47.

• Surface area of one “A” panel = 24.2 ft2.

• Maximum reinforcement tension = 7.20 kips per strip.

• Stress at connection = 100 percent of maximum tie tension.

General Calculations. Random fill is used outside the zone filled with R. E.

(Reinforced Earth) material.

Pressure Coefficient for Random Fill. For the case of level ground at the top of the wall, a vertical backface, and neglecting the effect of wall friction, the pressure coefficient for the fill is given by

Ka = tan2(45° – ф)

Substituting ф = 25° gives

/ 25°

Ka = tan2l 45°———- —) = 0.4059

To allow for the effects of cohesion in the fill (see Fig. 8.41b), define an equivalent pressure K such that

eq

yHK = yHK – 2cVk

eq a a

Thus

, / 2c VK

ф = 21 45° – arctan / K _ —————————- –

eq a 7H

_ 2 X 0,10kip/ft2 X VO.4059
0.12kip/ft3 X 20 1t

= 28.58°

The calculation of the equivalent pressure coefficient follows as Keq = tan2^45° _ —— j = 0.3528

This coefficient is subsequently used to calculate F1, the horizontal force on the wall caused by the surcharge, and F2, the horizontal force on the wall caused by the fill.

Vertical Loads and Resisting Moment. The vertical loads to be considered are the weight of the reinforced fill, V1, and of the surcharge, Vsurch. These loads are calculated and multiplied by their horizontal moment arm from the base (point A in Fig. 8.41b), and the results are summed to determine the resisting moment M. The sum of the vertical loads is designated Rv.

Load, kips/ft	Moment arm, ft	Resisting moment Mr, kips • ft/ft
V1 = 0.125 kip/ft3 X 20 ft X 20 ft = 50.0 kips/ft	10 ft	500 kips • ft/ft
V h = 0.25 kip/ft2 X 20 ft = 5.0 kips/ft	10 ft	50 kips • ft/ft
R = V, + V h = 50 + 5 = 55 kips/ft v 1 surch		Total Mr = 550 kips • ft/ft

Horizontal Forces and Overturning Moment. The horizontal force due to the sur­charge, F1, and that due to the random fill, F2, are illustrated in Fig. 8.41b. They are calculated using the value of Keq determined previously and multiplied by their vertical moment arm from the base, and the results are summed to determine the overturning moment M.

o

Load, kips/ft	Moment arm, ft	Overturning moment Mo, kips • ft/ft
F1 = 0.3528 X 0.250 kip/ft2 X	10 ft	17.64 kips • ft/ft
20 ft = 1.764 kips/ft
F2 = 0.3528 X 0.120 kip/ft3 X	20 ft/3 = 6.67 ft	56.44 kips • ft/ft
(20 ft)2 X (K) = 8.47 kips/ft
F1 + F2 = 10.23 kips/ft		Mo = 74.08 kips • ft/ft

Eccentricity e ((without Surcharge). The eccentricity without surcharge must be calculated to make sure it is less than one-sixth of the base dimension B, which is the length of the reinforcing strip.

e=	B	M – M ro	2—	500 – 74.08
2	V1	2	55
B	2—
		= 3.33 ft	OK
6	6

e <

1.4816 ft

Safety Factors. The safety factor against overturning is the ratio of the resisting moment to the overturning moment. The safety factor against sliding is the ratio of the horizontal resisting forces (weight of reinforced fill times friction factor plus foundation cohesion force) to the horizontal active forces. These safety factors must be calculated to make sure they are within limits.

M 500

SF (overturning) = —- =——————– = 6.75 > 2.0 OK

Mo 74.08

V1 tan 25° + c X B
F—

334.75

Safety factor for overturning = ———————– = 20 > 2.0 OK

e	2	—————– 0.482 It 33.475
81^ VI <0	= 3.33 ft	OK
a V	—	33.475 kip
B – 2e	20 ft – 2 X 0.482 ft

20

334.75 – 16.15

= 1.759 kips/ft2

The pressure coefficient K is assumed to vary linearly between K0 (the coefficient of earth pressure at rest) at the top of the wall and Ka (the coefficient of active earth pressure) at a depth of 20 ft. Below a 20-ft depth, K = Ka. The distance below the top of the wall is d.

Maximum horizontal pressure a = Ka

K„ = 1 – sin 34° = 0.4408

0.4408 – 0.2827

= 0.4408 —————- 20————— X 11.39 ft

K = 0.3508

ah = 0.3508 X 1.759 kips/ft2 = 0.617 kip/ft2

The area of a standard “A” panel is 24 ft2. Use four strips per panel.

Reinforcing strip tension = 0,617 X 24 = 3.73 kips per strip

4

3.73 kips/strip < 7.2 maximum tension for 75-yr design life OK

(See subsequent calculations for maximum tension allowable for strip and connections.) Check length of strip:

V = 0.125 kip/ft2 X 11.39 ft X 20 ft = 28.475 kips (without surcharge)

Resisting moment = 28.475 kips X 10 ft = 284.75 kips • ft/ft Overturning moment SMo = 16.15 kips • ft

e=	20	284.75 – 16.15
2	28.475
20/6 =	3.33 ft	OK

e <

0.567 ft

V

ah = 0.3508 X 1.509 kips/ft2 = 0.5295 kip/ft2 T = tension on an “A” panel = ah X A = 0.5295 kip/ft2 X 24.2 ft2

= 12.81 kips

R = frictional resistance of reinforcing strips = 2b X leff X H X 8 X f* X N

2 X 197

where 2b = ———- ——– = 0.328 ft = width of top and bottom surface of one strip

H = 11.39 ft = overburden leff = 14.834 ft = effective strip length *8 = 0.125 kip/ft3

f* = 1.5 – [(1.5 – tan 34° X 11.39 ft)/20 ft] = 1.03 = coefficient of apparent friction N = 4 = number of strips per panel

R = 0.328 ft X 14.834 ft X 11.39 X 0.125 kip/ft3 X 1.03 X 4 = 28.54 kips

Effective length safety factor = — = 28,54 = 2.23 > 1.5 OK 6 3 T 12.81

Design Summary at Intermediate Levels Level, ft Maximum horizontal stress, Stress at facing, kips/ft2 Straps per panel Reinforcing strip tension, kips Horizontal stress (bond), kips/ft2 Effective length safety factor Strip length, ft 2.00 0.21 0.21 4 1.29 0.11 2.52 20.00 4.01 0.31 0.31 3 2.50 0.21 1.84 20.00 6.47 0.42 0.42 3 3.39 0.32 1.76 20.00 8.93 0.52 0.52 3 4.21 0.43 1.67 20.00 11.39 0.62 0.62 4 3.73 0.53 2.23 20.00 13.85 0.70 0.70 4 4.26 0.62 2.28 20.00 16.31 0.79 0.79 4 4.76 0.71 2.29 20.00 18.77 0.86 0.86 4 5.22 0.79 2.25 20.00

Calculation of Allowable Reinforcement Tension. The following calculations show the determination of the allowable reinforcement tension for galvanized reinforcing strips in permanent mechanically stabilized earth structures. Allowable stresses in strips and components are based on the AASHTO Bridge Specifications. The allowable rein­forcement tension is based on maintaining allowable hardware stresses to the end of a 75-year service life. After 75 years, the structure will continue to perform with reinforce­ment stresses that may or may not exceed allowable levels, depending on the soil environment and the applied reinforcement loads. The calculations are based on the following mechanical properties of the reinforcement components.

• Reinforcing strips

50- X 4-mm ribbed (1.97- X 0.16-in)

ASTM A572 grade 65

Fu = 80 kips/in2 ( minimum tensile strength)

Fy = 65 kips/in2 (minimum yield point)

• Tie strips

50- X 3.0-mm (1.97- X 0.12-in)

ASTM A570 grade 50 Fu = 65 kips/in2 Fy = 50 kips/in2

• Bolts

/2-in-diameter X 1/4 inch long ASTM A325

To begin, consider the tie strips at a section where there are no bolt holes (Section A-A, Fig. 8.42). There are two 50- X 3-mm tie strip plates with 2 oz/ft2 (86 ^m) of zinc. Calculate the life of the zinc coating (see Art. 8.5.7):

T = 2 yr + 86 fun – 2yr(15 ixm/yr) = 16 yr 4 ^m/yr

No carbon steel is lost until after depletion of the zinc.

Next, calculate the carbon steel loss in the subsequent 59 years. (See Art. 8.5.7.) The thickness of the carbon steel loss on one side is determined as follows:

Дє = 59 yr X 12 ^m/yr = 708 ^m on each exposed side

The outside surfaces of the tie strip plates are in contact with soil; the inside surfaces are not in contact with soil. Therefore, use one-half the carbon steel loss rate for the inside surfaces. The sacrificial thickness of reinforcement during service life is deter­mined from:

ES = 708 ^m + 354 ^m = 1062 ^m per plate

The thickness of the reinforcement at end of service life is the nominal thickness minus the sacrificial thickness:

EC = En — ES = 3000 ^m — 1062 ^m = 1938 ^m per plate

50 x 4 mm A-572 Gr. 65 reinforcing strip (galvanized)

Section @ – @: gross section of tie strip Section © – ©: net section of tie strip and reinforcing strip at bolt

Section © – ©: gross section of reinforcing strip

FIGURE 8.42 Structural connection of reinforcing strip to facing panel. (From the Reinforced Earth Co., with permission)

The cross-sectional area at end of service life is found from:

The allowable tensile stress is found from:

FT = 0.55Fy = 0.55(50 kips/in2) = 27 kips/in2

The allowable tension on reinforcement is:

Tal = FTAS = 27 kips/in2 X 0.300 in2 = 8.10 kips per connection

Now, consider the tie strips at a section through the bolt holes (Section B-B, Fig. 8.42). There are two 50- X 3-mm tie strip plates with 2 oz/ft2 (86 [m) of zinc. The diameter of each bolt hole is %s in (14.3 mm). The life of the zinc is 16 years, as found in the calculation for Section A-A.

Calculate the thickness of carbon steel loss over the subsequent 59 years:

Дє = 708 [m per exposed side

(See the preceding calculation for Section A-A.) Corrosion does not occur on the inside surfaces of the plates, because of protection provided by sandwiching the reinforcing strip. Thus,

ES = 708 ^m per plate

Proceed with calculations for thickness at end of service life, cross-sectional area, allowable tensile stress, and allowable tension force:

Now, consider the reinforcing strip at a section through the bolt holes (Section B-B, Fig. 8.42). The reinforcing strip is 50 X 4 mm with 2 oz/ft2 (86 ^m) of zinc. The diam­eter of each bolt hole is %s in (14.3 mm). No carbon steel is lost from reinforcing strip surfaces at the net section, because of the sandwiching protection by the tie strip. Thus,

Es = 0

EC = E = 4000 ^m or 4 mm

50 mm — 14.3 mm

(25.4 mm/in)2 FT = 0.50Fu = 0.50(80 kips/in2) = 40 kips/in2 T, = FTAS = 40 kips/in2 X 0.221 in2 = 8.84 kips per connection

The shear strength of each bolt is found as follows. Each bolt is /2 in X 1/4 in, ASTM A325, galvanized. It is assumed that no carbon steel is lost from the bolt shank, because of sandwiching protection by the strips. The bolt head, nut, and washer have more than adequate metal for loss to corrosion.

The allowable shear stress on the bolt (with threads excluded from the shear plane) is

FV = 1.4 X 19 kips/in2 = 27 kips/in2 allowable

The nominal cross-sectional area of the /2-in-diameter bolt is 0.196 in2. The allowable force on each bolt, considering two shear planes, is

Tal = FVAS = 27 kips/in2 X 0.196 in2 X 2 = 10.60 kips per connection

A check shows that bearing strength does not control for this case.

Next, consider the reinforcing strip at a section where there are no bolt holes (Section C-C, Fig. 8.42). The reinforcing strip is 50 X 4 mm, with 2 oz/ft2 (86 ^m) of zinc. The life of the zinc is 16 years, from previous calculations.

Calculate the thickness of carbon steel loss over the subsequent 59 years.

Де = 708 ^m per exposed side (see previous calculations) ES = 2 sides X 708 ^m/side = 1416 ^m

Design Summary for Allowable Reinforcement Tension

Component	Section	Allowable force, kips
Tie strip	Main	8.10
Tie strip	Through bolt holes	8.13
Reinforcing strip	Main	7.20
Reinforcing strip	Through bolt holes	8.84
Bolt	Shear planes	10.60

The least value controls the design. In this case, the allowable reinforcement tension (7.20 kips) is governed by the strength of the reinforcing strip at a section where there are no bolt holes.

8.5.10 Material Properties of Polymeric Reinforcement

The tensile properties of polymeric reinforcement are subject to creep under load because properties of the materials are both time- and temperature-dependent. Also, the materials are subject to damage during the construction process and are affected by durability con­siderations such as aging. Furthermore, characteristics of geosynthetic products made from the same base polymer exhibit the normal variation of most manufactured products.

The allowable long-term reinforcement strength (tension capacity) based on limit state criteria is

Values of RFid, RFcr, and RFD must be determined from the results of prescribed product specific tests, and RFID and RFD should be no less than 1.1 each. Alternatively, in lieu of product-specific tests, a default reduction factor RF for certain geosynthetic products that meet AASHTO minimum requirements may be used. The default reduc­tion factor for “applications not having severe consequences should poor perfor­mance or failure occur” is 4.0 for permanent applications and 2.5 for certain temporary applications.

The allowable connection strength (T’ac) between the wall facing and the reinforcement on a load per unit reinforcement width basis is

where RFc = RFcr X RFd (as defined previously); product-specific long-term degra­dation data at the environment shall be considered CRa = reduction factor to account for reduced ultimate strength resulting from the connection

CRS = reduction factor to account for reduced strength due to connection pullout

FS = 1.5 (minimum) overall factor of safety as defined previously

ASTM designation D4595, “Standard Test Method for Tensile Properties of Geotextiles by the Wide-Width Strip Method,” serves as a quality control test from which a “minimum average roll value (MARV)” is determined and certified by the manufacturer to the user of the product. The MARV value is a measure of the ultimate tensile strength of the polymeric material under the stated test conditions.

As noted, the manufacturing process is subject to variation. The minimum value the manufacturer certifies must therefore meet or exceed the design minimum value. The man­ufacturer must also be able to meet this minimum value at a specific confidence level. The ASTM and the industry have adopted a 95 percent confidence level. A normal distribution of the test results is assumed.

ASTM Designation D4595. Test method ASTM 4595, which is prescribed by AASHTO, covers the measurement of tensile properties of geotextiles using a wide – width strip specimen. The test is also applied to geogrids. A relatively wide specimen is gripped across its entire width in the clamps of a constant-rate-of-extension (CRE) type tensile testing machine operated at a prescribed rate of extension, applying a longi­tudinal force to the specimen until the specimen ruptures. The distinctive feature of this test is that the width of the specimen is greater than the length, and this tends to minimize the contraction (neck-down) effect that is present with other test methods for measuring strip tensile properties of geotextiles. It is believed that the test will provide a closer relationship to expected geotextile behavior in the field. Tensile strength, elongation, initial and secant modulus, and breaking toughness of the test specimen can be calculated from the results.

The determination of the wide-width strip force-elongation properties of geotex­tiles provides design parameters for reinforcement applications such as reinforced MSE walls. D4595 may be used for acceptance testing of commercial shipments of geotextiles, although an individual owner may specify other acceptance criteria.

This test method is generally used by manufacturers, but when it is not, it should be required by owners in order to provide supporting data for the manufacturer’s stated MARV. To the end user, MARV is a minimum value that exceeds design requirements.

To account for testing variation, the manufacturer is required to take a sufficient num­ber of specimens per fabric swatch that the user may expect, at the 95 percent proba­bility level, that the test result will not be more than 5.0 percent of the average above or below the true average of the swatch for both the machine and the cross-machine direction.

The number of tests required to establish a MARV depends upon whether a reliable estimate of the coefficient of variation v of individual observation exists, in the laboratories of either the manufacturer or the end user. Specifically, when there is a reliable estimate of v based upon extensive past records for similar materials tested as directed in the method, the required number of specimens is calculated using the equation:

where n = number of specimens (rounded upward to a whole number)

v = reliable estimate of coefficient of variation of individual observations on similar materials in user’s laboratory under conditions of single-operator precision, %

t = value of Student’s t for one-sided limits (see Table 8.6), a 95% probability level, and degrees of freedom associated with the estimate of v A = 5.0 percent of average, the value of allowable variation

When there is no reliable estimate of v for the manufacturer’s or user’s laboratory, the equation should not be used directly. Instead, specify the fixed number of six specimens each for the machine direction and the cross-machine direction tests. The number of spec­imens is calculated using v = 7.4 percent of the average. This value for v is somewhat larger than usually found in practice. When a reliable estimate of v for the user’s labora­tory becomes available, the above equation will usually require fewer than the fixed number of specimens.

D4595 specifically includes formulas for determining the initial tensile modulus and the offset tensile modulus. Additionally, the formula for breaking toughness is included. The appendix to the designation contains graphical representations for the determination of the modulus values.

TABLE 8.6 Values of Student’s t for One-Sided Limits and 95% Probability df One-sided df One-sided df One-sided 1 6.314 11 1.796 22 1.717 2 2.920 12 1.782 24 1.711 3 2.353 13 1.771 26 1.706 4 2.132 14 1.761 28 1.701 5 2.015 15 1.753 30 1.697 6 1.943 16 1.746 40 1.684 7 1.895 17 1.740 50 1.676 8 1.860 18 1.734 60 1.671 9 1.833 19 1.729 120 1.658 10 1.812 20 1.725 1.645 df = degrees of freedom = number of samples — 1. Source: From Geotextiles magazine, with permission.

8.5.11 Design Example of MSE Retaining Wall with Geogrid Reinforcement

The following design example (provided courtesy of Tensar Earth Technologies) illus­trates an application of AASHTO specifications and the tieback wedge method of analysis.

Step 1: Qualify Design Assumptions. Review plans, specifications, and available infor­mation to confirm feasibility, to determine if the information is adequate to continue with design, and to ascertain that the wall layout is clearly understood.

Step 2: Define Parameters for Soil, Reinforcement, Geometry, and Loading. On the

basis of the information provided, clearly state the design parameters and factors of safety that will be used for design. Provide a diagram for the geometry of the wall that will be designed indicating slopes above and below the wall, any surcharge loadings and their locations, magnitude and direction of application, and hydrostatic and seismic loading conditions.

For this example, refer to Fig. 8.43 for geometry. Design parameters are as follows: 1. Soil

Zone	Ф’, °	c	y, lb/ft3
Reinforced fill	34	0	120
Retained fill	30	0	120
Foundation	30	0	120

Allowable foundation bearing stress is 6000 lb/ft2.

2. Groundwater: none

3. Surcharge: 250 lb/ft2 uniform

4. Seismic loading: none

Step 3: Calculate External Stability. First calculate the coefficient of active earth pres­sure, Ka. The slope angle p is zero above the wall because the slope levels before reaching the end of the reinforcement. Had the slope extended beyond the tail of the reinforcement, a trial wedge solution or infinite slope calculation would be required, depending on the distance of the slope extension.

For the following calculation, refer to Art. 8.2.3 for equation and nomenclature:

For ф’ = 30°, p = 0, 0 = 93.6° (face has 3.6° batter), S = 0: Ka = 0.31.

Minimum embedment length L ~ 0.7H = 0.7(29) = 20.3 ft. Use 20 ft.

Sum moments and forces about the toe of the wall and solve for external safety factors (SF) as follows:

Item, Fig. 8.43	Force, lb	Moment arm, ft	Moment, ft • lb
W1	69,600	10.91	759,336
W2	3,750	14.15	53,075
W3	2,099	20.07	42,127
W4	875	20.07	17,661
Pa	21,502	11.33	243,613
Pq	2,635	17.00	44,795

Rv = W + W2 + W3 = 76,325 lb Rh = Pa + Pq = 24,137 lb

Resisting moment = M1 + M2 + M3 = 854,538 ft • lb Overturning moment = 243,613 + 44,795 = 288,408 ft • lb SF overturning = 854,538/288,408 = 2.96 > 2 .0 OK SF sliding = RCt tan 30°/Rh = 76,325 X 0.5774/24,137 = 1.82 > 1.5 ‘ OK

The safety factor for sliding should be calculated in at least two locations: at the inter­face of the foundation and the reinforced fill, and at the lowest geogrid. In this case, C,, the coefficient of interaction between the geogrid and the reinforced fill, is 1.0 according to test data supplied by the geogrid manufacturer. Because the reinforced fill is stronger than the foundation soils, the lowest safety factor for sliding is at the foundation interface.

Next check bearing. The eccentricity of the vertical reaction is

The maximum bearing stress is then

All external safety factors are satisfied. Next, calculate internal safety factors for geogrid tension, pullout at face, and pullout past the Rankine failure plane.

No.	Height, ft	Depth, ft	Wv lb	W2. lb	Wv lb	W4.lb	P, lb/ft2 a	P, lb/ft2 tl	a,, lb/ft2	v, A2	T, lb/ft	Grid, UX-
13	26.67	2.33	6,692	3750	2099	875	999	568	492	3.99	509	1500
12	23.35	5.65	13,560	3750	2099	875	2,108	826	895	3.34	774	1500
11	20.00	9.00	21,600	3750	2099	875	3,643	1084	1326	3.34	1148	1500
10	16.67	12.33	29,592	3750	2099	875	5,582	1342	1782	3.00	1387	1600
9	14.00	15.00	36,000	3750	2099	875	7,434	1549	2175	2.67	1504	1600
8	11.34	17.66	42,384	3750	2099	875	9,543	1755	2598	2.33	1570	1600
7	9.34	19.66	47,184	3750	2099	875	11,302	1910	2940	2.00	1525	1600
6	7.34	21.66	51,984	3750	2099	875	13,210	2065	3309	1.67	1433	1600
5	6.00	23.00	55,200	3750	2099	875	14,571	2168	3573	1.34	1237	1600
4	4.67	24.33	58,392	3750	2099	875	15,988	2271	3851	1.33	1328	1600
3	3.34	25.66	61,584	3750	2099	875	17,471	2374	4146	1.34	1436	1600
2	2.00	27.00	64,800	3750	2099	875	19,032	2478	4463	1.34	1545	1600
1	0.67	28.33	67,992	3750	2099	875	20,647	2581	4801	1.34	1662	1600
0		29.00	69,600	3750	2099	875	21,502	2635	4989

732

TABLE 8.7 Calculations for Tension in Geogrid Reinforcement of MSE Retaining Wall

Step 4: Calculate Internal Stability. The calculation of Ka for this check is similar to the external calculation, except that the slope angle above the wall (if any) is always assumed to be zero. Thus, Ka = 0.31 in this example. The additional forces contributed by the sloping surface are accounted for in the summation of forces and moments in determining bearing stress. Calculation of internal stability and tension in reinforcements is similar to the preceding calculations. At each level of reinforcement, the vertical stress m is calculated on the basis of the resultant of the forces and moments of both the reinforced fill and the external forces. This stress is then multiplied by Ka and the vertical tributary area vi to calculate the tension in the reinforcement. If the calculated tension T exceeds the allowable tension Tal, either a stronger reinforcement or a reduced vertical spacing must be adopted.

The allowable design stress for the geogrids is determined from AASHTO criteria, considering both ultimate strength and serviceability. Both the geogrid and the connec­tion of the grid to the face must be considered. In this case the following allowable ten­sion values have been determined for two geogrids:

Geogrid UX1500: Tal = 1267 lb/ft

Geogrid UX1600: Tal = 1731 lb/ft

The calculations for tension in Table 8.7 can now be made; the last column indicates the reinforcement selected.

Check pullout in the top geogrid layer. Geogrids must extend beyond the failure plane (45° — ф/2) by at least 3 ft.

Le = 20 — [26.67 tan (45° — ^ + 26.67 tan (3.6°)]

= 7.50 ft > 3.0 OK

Calculate pullout resistance by friction (two grid sides) based on weight acting beyond the failure plane:

Minimum pullout capacity = 2[7.5 ft X 2.33 ft X 120 lb/ft3 + W3]C tan ф = 2(2097 + 2099)1.00 tan 34°

= 5660 lb/ft

FS = 5660/508 = 11.1 > 2.0 OK

The durability of polymeric reinforcements is influenced by time, temperature, mechanical damage, stress levels, microbiological attack, and changes in the molecular structure due to radiation or chemical exposure. The effects of aging and of chemical and biological exposure are highly dependent on material composition, including resin type, grade, and additives; manufacturing process; and final product physical structure.

Polymeric reinforcement, although not susceptible to corrosion, may degrade as a result of physicochemical activity in the soil, such as hydrolysis, oxidation, and environ­mental stress cracking. In addition, it is susceptible to construction damage, and some forms may be adversely affected by prolonged exposure to ultraviolet light. The durability of geosynthetics is a complex subject, and research is ongoing to develop reliable procedures for quantification of degradation effects. Moderate-strength geosynthetics have tensile strengths of about 100 lb/in (17.5 N/mm); some are now available that have strengths well over an order of magnitude higher. Current procedure to account for strength loss due to construction damage, and as a result of aging and chemical and biological attack, is to decrease the initial strength of the intact, unaged material for design.

Where metallic reinforcement is used, the life of the structure will depend on the corro­sion resistance of the reinforcement. Practically all the metallic reinforcements used in construction of embankments and walls, whether they are strips, bar mats, or wire mesh, are made of galvanized steel. Epoxy coating can be used for additional corrosion protection, but it is susceptible to construction damage, which can significantly reduce its effectiveness. PVC coatings on wire mesh also provide corrosion protection, provided again that the coating is not significantly damaged during construction. When PVC or epoxy coatings are used, the maximum particle size of the backfill should be restricted to /4 in (19 mm) or less to reduce the potential for construction damage.

For the purpose of determining the sacrificial metal required (corrosion allowance), the following design life is provided, pursuant to recommendations of Task Force 27 of AASHTO-AGC-ARTBA:

Structure classification Design life, yr

Permanent structure 75

Abutments 100

Rail supporting structures 100

Marine structures 75

The required cross-sectional area of steel reinforcement is calculated using the rela­tionships given in Fig. 8.38 for the selected type of reinforcement (strips or grids). The corrosion loss assumed is based on the following.

In 1985, an FHWA study was initiated to develop practical design and construction guidelines from a technical review of extensive laboratory and field tests on buried

FIGURE 8.38 Metallic reinforcement for MSE walls showing correction for corrosion loss.

(From the Reinforced Earth Co., with permission)

metals. The results of this research were published in December 1990 in the Federal Highway Administration report FHWA-RD-89-186, “Durability/Corrosion of Soil Reinforced Structures”:

For structures constructed with carefully selected and tested backfills to ensure full compli­ance with the electrochemical requirements, the maximum mass presumed to be lost per side due to corrosion at the end of the required service life may be computed by assuming a uniform loss model which considers the following loss rates:

1. Zinc corrosion rate for first 2 years: 15 ^m/yr

2. Zinc corrosion to depletion: 4 |xm/yr

3. Carbon steel rate: 12 ^m/yr

The resulting sacrificial thickness for a 75-year life based on initial galvanization of 2 oz/ft2 (86 |xm) is approximately 1.5 mm of total sacrificial thicknesses. Since this is a maximum loss rate, it is presently assumed that the reduced minimum thickness remains proportional to tensile strength and therefore no further reduction is necessary. (See Fig. 8.39.)

The select backfill materials shall meet the following requirements:

Internal friction angle. The material shall exhibit an internal friction angle of not less than 34 degrees as determined by the standard direct shear test, AASHTO T-236, utilizing a sample of the material compacted to 95 percent of AASHTO T-99, Methods C or D (with oversize correction), at optimum moisture content. Internal friction angle testing is not required for

TABLE 8.5 Backfill Requirements Related to Durability of Steel Reinforcement Property Requirement Test method Resistivity Minimum 3000 D • cm, at 100% saturation California DOT 643 pH Acceptable range 5-10 California DOT 643 Chlorides Maximum 100 ppm California DOT 422 Sulfates Maximum 200 ppm California DOT 417 Source: From the Reinforced Earth Co., with permission.

backfill materials that have at least 80 percent of the material greater than or equal to the /4-in (19-mm) size.

Soundness. The material shall be substantially free of shale or other soft, poor durability particles. The material shall have a magnesium sulfate soundness loss of less than /0 percent after four (4) cycles, as determined by AASHTO T-104.

Electrochemical requirements. The material shall conform to the electrochemical requirements as described in Table 8.5.

The Contractor shall furnish to the Engineer a Certificate of Compliance certifying that the select granular backfill material complies with this section of the specification. A copy of all test results performed by the Contractor, which are necessary to assure compliance with the specifications shall also be furnished to the Engineer.

Backfill not conforming to this specification shall not be used without the written consent of the Engineer.

The frequency of sampling of select granular backfill material, necessary to assure gradation control throughout construction, shall be as directed by the Engineer.

There are instances when one MSE wall is built on top of another. In certain instances, these walls can be considered to be two independent structures, each requiring its own internal design and external stability. The global stability of the slope must be suffi­ciently stable so as not to undermine the stability of the entire embankment.

Figure 8.36 shows a superimposed structure. The walls are such that the load of the upper wall level serves as a surcharge load on the lower wall. Each wall is independently designed.

FIGURE 8.35 Foundation pressure for MSE wall calculated by the AASHTO method based on Meyerhof. (From the Reinforced Earth Co., with permission)

FIGURE 8.36 Superimposed MSE walls. (From the Reinforced Earth Co., with permission)

This design approach does not hold when the MSE structures are directly superimposed, one on another, as shown in Fig. 8.37. Such terraced arrangements are sometimes used for high walls. These offset structures are obviously similar to a single embankment with a sloping face. They exhibit essentially the same overall behavior, and are designed as sloping faced walls.

FIGURE 8.37 Terraced MSE wall. (From the Reinforced Earth Co., with permission)

Figure 8.32 shows the general design equations given by AASHTO for MSE walls with a horizontal backslope and a traffic surcharge. Included is the calculation of safety factors for overturning and sliding, and the maximum base pressure. Inclusion of a traffic sur­charge is required only in those instances where traffic loadings will actually surcharge the wall. Separate surcharge diagrams are applied for the two conditions shown. For sta­bility of the mass, the traffic surcharge should act at the end of the reinforced zone so as to eliminate the “stabilizing” effect of this loading. However, for purposes of determining horizontal stresses, which are increased as a result of this surcharge, the loading is

Assumed for bearing capacity and overall (global) stability comps.

Assumed for overturning and sliding resistance comps.

FACTOR OF SAFETY AGAINST OVERTURNING (MOMENTS ABOUT POINT 0):

= S moments resisting (Mr) = V1 (L/2) 2 0

OT moments overturning (Mo) F1 (H/3) + F2 (H/2) _ .

FACTOR OF SAFETY AGAINST SLIDING:

Fs = S horizontal resisting force(s) = V1 (tan p or tan ф)* ___ 15 SL horizontal driving force(s) F1 + F2 _ ‘

ф = friction angle of reinforced backfill or foundation, whichever is lowest

where q = traffic live load

*tan p is for continuous soil reinforcement (e. g., grids and sheets).

For discontinuous soil reinforcements (e. g., strips) use tan ф. p is the soil/ reinforcement interface friction angle. Use the lower of tan at the base of the wall or tan p at the lowest reinforcement layer for continuous reinforcements.

Note: For relatively thick facing elements (e. g., segmental concrete facing blocks), it may be desirable to include the facing dimensions and weight in sliding and overturning calculations (i. e., use B in lieu of L).

FIGURE 8.32 General design requirements for MSE walls with horizontal backfill and traffic surcharge. (From Standard Specifications for Highway Bridges, American Association of State Highway and Transportation Officials, Washington, D. C., 2002, with permission)

deemed to apply over the entire surface of the wall backfill. Figure 8.33a and b shows the AASHTO equations for the sloping backfill case and the broken backfill case.

While the conventional analysis of a mechanically stabilized earth wall assumes a rigid body, field evaluation has shown that the variation and magnitude of the foundation loading exerted by the wall on the underlying soil differ from the traditional trapezoidal

FACTOR OF SAFETY AGAINST OVERTURNING (MOMENTS ABOUT POINT 0):

Fg = X moments resisting (Mr) = V1 (L/2) + V2 (2L/3) + Fv (L) ^ ^

OT moments overturning (Mo) FH (h/3)

FACTOR OF SAFETY AGAINST SLIDING:

Fs = X horizontal resisting force(s) (V1 + V2 + Fv) (tan p or tan ф)*^

SL horizontal driving force(s) FH _ ‘

ф = friction angle of reinforced backfill or foundation, whichever is lowest

*tan p is for continuous soil reinforcements (e. g., grids and sheets).

For discontinuous soil reinforcements (e. g., strips) use tan ф. p is the soil/ reinforcement interface friction angle. Use the lower of tan at the base of the wall or tan p at the lowest reinforcement layer for continuous reinforcements.

Note: For relatively thick facing elements (e. g., segmental concrete facing blocks), it may be desirable to include the facing dimensions and weight in sliding and overturning calculations (i. e., use B in lieu of L).

FIGURE 8.33a General design requirements for MSE walls with sloping backfill.

(From Standard Specifications for Highway Bridges, 2002, American Association of State Highway and Transportation Officials, Washington, D. C., with permission)

Fv = Ft cos ( I )

For infinite slope I = p Ka for retained fill using 8 = p = I: sin2 (0 + ф’)

FACTOR OF SAFETY AGAINST OVERTURNING (MOMENTS ABOUT POINT 0): Fg 2 moments resisting (Mr) = V1 (L/2) + V2 (2L/3) + Fv (L) ^ 20

OT moments overturning (Mo) Fh (h/3)

FACTOR OF SAFETY AGAINST SLIDING:

Fs £ horizontal resisting force(s) = (V1 + V2 + Fv) (tan p or tan Ф)*^ 1 5 SL horizontal driving force(s) Fh _ ‘

ф = friction angle of reinforced backfill or foundation, whichever is lowest

*tan p is for continuous soil reinforcements (e. g., grids and sheets).

For discontinuous soil reinforcements (e. g., strips) use tan ф. p is the soil/ reinforcement interface friction angle. Use the lower of tan ф at the base of the wall or tan p at the lowest reinforcement layer for continuous reinforcements.

Note: For relatively thick facing elements (e. g., segmental concrete facing blocks), it may be desirable to include the facing dimensions and weight in sliding and overturning calculations (i. e., use B in lieu of L).

FIGURE 8.33b General requirements for MSE walls with broken backfill.

(From Standard Specifications for Highway Bridges, 2002, American Association of State Highway Officials, Washington, D. C., with permission)

pressure distribution assumed under reinforced-concrete cantilever walls. Tests were per­formed by placing pressure cells under the base of an MSE wall. The wall was the Fremersdorf wall constructed in Germany, which is depicted in Fig. 8.34 along with the bearing pressure recorded from the pressure cells. Tests on that structure demonstrated that loading is greater toward the front of the structure because of earth pressure imposed

FIGURE 8.34 Fremersdorf MSE wall with foundation pressures from pressure cell readings. (From the Reinforced Earth Co., with permission)

by the retained fill behind the wall. In addition, the total load was slightly greater than the total weight of the wall, indicating that the thrust behind the structure was inclined. The difference between total loading and weight, and the location of the resultant, made it possible to compute the thrust angle p.

The bearing pressure distribution from the Fremersdorf wall is idealized in the AASHTO equation for soil pressure (cv) shown in Fig. 8.35. A uniform pressure (Meyerhof distribution) is calculated over a width equal to the length of the soil rein­forcement elements minus 2 times the eccentricity of the vertical force.

Well-graded, free-draining granular material is usually specified for permanent-placed soil reinforced walls. Lower-quality materials are sometimes used in reinforced embank­ment slopes. Experience with cohesive backfills is limited. However, low strength, creep properties, and poor drainage characteristics make their use undesirable. Some current research is focused on the use of cohesive soil backfills.

The following gradation and plasticity limits have been established by the AASHTO-AGC-ARTBA* Joint Committee Task Force 27 for mechanically stabilized embankments:

U. S. sieve size	Percent passing
4 in (100 mm)	100
No. 40	0-60
No. 200	0-15
Plasticity index (PI) less than 6 percent

It it recommended that the maximum particle size be limited to /4 in (19 mm) for geosynthetics and epoxy-coated reinforcements unless tests show that there is minimal construction damage if larger particle sizes are used.

Metallurgical slag or cinders should not be used except as specifically allowed by the designer. Material should be furnished that exhibits an angle of internal friction of 34° or more, as determined by AASHTO T-236, on the portion finer than the No. 10 sieve. The backfill material should be compacted to 95 percent of AASHTO T-99, method C or D, at optimum moisture content. See Art. 8.5.7 for backfill requirements that are important in relation to the durability of the steel reinforcement.

On-site or local material of marginal quality can be used only with the discretion and approval of the designer.

MSE walls should be dimensioned as required by AASHTO. The soil reinforcement length must be at least 70 percent of the wall height, as measured from the leveling pad, but not less than 8 ft (2.4 m) for both strip and grid type reinforcement. AASHTO requires the reinforcement length to be uniform throughout the entire height of the wall. The specification does allow deviation from this uniform length requirement, subject to the availability of substantiating evidence.

MSE walls must be designed for both external stability and internal stability. The recommended minimum factors of safety in various areas of external stability are noted in AASHTO as follows:

External stability	Factor of safety
Overturning	2.0 for footings on soil, >1.5 for
	footings on rock
Ultimate bearing capacity	>2.5 for Group 1 loadings, >2.0 if justified by geotechnical analysis
Sliding	1.5
Overall stability (deep-seated failure)	>1.5 for bridge abutment walls; >1.3 for walls with static loads; >1.1 for seismic loads
Seismic (overturning and sliding)	>75% static safety factor

In lieu of the overturning check, the eccentricity e of the force resultant R must be located such that e < L/6 where L is the base length (see Fig. 8.33). In calculating bearing

In regard to internal stability, AASHTO notes the following:

Factor of safety

>1.5

Allowable tension [see Eqs. (8.14a) and (8.14b)]

According to design life [see Eqs. (8.14a) and (8.14b)

>75% static safety factor

Figures 8.29 and 8.30 indicate the two basic failure modes for internal stability analysis— specifically, rupture or creep failure of the reinforcement and a pullout failure mode. These failure modes suggest the use of the tied-back wedge analysis approach depicted in Fig. 8.31, which represents the basic method of analysis included in the AASHTO specifications.

FIGURE 8.31 Parameters for tied-back wedge analysis.

The types of facing elements used in the different reinforced soil systems control their aesthetics, since they are the only visible parts of the completed structure. A wide range of finishes and colors can be provided in the facing. In addition, the facing provides protection against backfill sloughing and erosion, and provides drainage paths. The type of facing influences settlement tolerances. In multianchored structures, the facing is a major structural element. Major facing types include the following:

1. Segmental precast-concrete panels. Examples of these are found in Reinforced Earth, the Georgia stabilized embankment system, the California mechani­cally stabilized embankment system, the VSL Retained Earth system, the Hilfiker

TYPE TYPICAL MECHANICAL PROPERTIES

J represents the modulus in terms of force per unit width of the reinforcement.

* J = E(Ac/b) where: Ac = total cross section of reinforcement material

b = width of reinforcement E = modulus of material

* Allowable values with no reduction for durability considerations

* Confined

FIGURE 8.26 Types of reinforcement and mechanical properties. (From J. K. Mitchell and B. R. Christopher, “North American Practice in Reinforced Soil Systems," Proceedings, Specialty Conference on Design and Performance of Earth Retaining Structures, Geotechnical Division, American Society of Civil Engineers, 1990, with permission)

Reinforced Soil Embankment, Tensar GeoWall, the American Geo-Tech system, the Stress Wall systems, the TRES system, the WEBSOL system, the Tensar system, and the York system of the Department of Environment, United Kingdom. (See Fig. 8.27.)

2. Cast-in-place concrete, shotcrete, or full-height precast panels. This type of facing is available in the Hilfiker and Tensar systems. Shotcrete is the most frequently used system for permanent soil nailed retaining structures. (See Fig. 8.28.)

3. Metallic facings. The original Reinforced Earth system had facing elements of galvanized steel sheet formed into half cylinders. Although precast concrete panels are now usually used in Reinforced Earth walls, metallic facings are still used in structures where difficult access or difficult handling requires lighter facing elements. Preformed metallic facings are also used in some soil nailing systems.

Г//////////////////////////////77777777

FIGURE 8.27 Sloping or vertical wall with reinforcement attached to precast-concrete facing elements.

FIGURE 8.28 Vertical wall with cast-in-place concrete facing. Reinforcement is wrapped around fill used for drainage.

4. Welded wire grids. Wire grid can be bent up at the front of the wall to form the wall face. This type of facing is used in the Hilfiker and Tensar retaining wall systems. Welded wire grid facing is also commonly used with soil nailing in fragmented rocks or intermediate soils (chalk, marl, shales).

5. Gabion facing. Gabions (rock-filled wire baskets) can be used as facing with reinforcing strips consisting of welded wire mesh, welded bar mats, polymer geogrids, or the double-twisted woven mesh used for gabions placed between the gabion baskets.

6. Fabric facing. Various types of geotextile reinforcement are looped around at the facing to form the exposed face of the retaining wall. These faces are susceptible to ultraviolet light degradation, vandalism (e. g., target practice), and damage due to fire.

7. Plastic grids. A plastic grid used for the reinforcement of the soil can be looped around to form the face of the completed retaining structure in a similar manner to welded wire mesh and fabric facing. Vegetation can grow through the grid structure and can provide both ultraviolet light protection for the polymer and a pleasing appearance.

8. Postconstruction facing. For wrapped faced walls, whether geotextiles, geogrids, or wire mesh, a facing can be attached after construction of the wall by shot – creting, guniting, or attaching prefabricated facing panels made of concrete, wood, or other materials. Shotcrete is the most frequently used system for permanent soil nailed retaining structures.

Precast elements can be cast in several shapes and provided with facing textures to match environmental requirements and to blend aesthetically into the environment. Retaining structures using precast-concrete elements as the facings can have surface finishes similar to any reinforced concrete structure. In addition, the use of separate panels provides the flexibility to absorb differential movements, both vertically and horizontally, without undesirable cracking, which could occur in a rigid structure.

Retaining structures with metal facings have the disadvantage of shorter life because of corrosion unless provision is made to compensate for it.

Facings using welded wire or gabions have the disadvantages of an uneven surface, exposed backfill materials, more tendency for erosion of the retained soil, possible shorter life from corrosion of the wires, and more susceptibility to vandalism. These can, of course, be countered by providing shotcrete or hanging facing panels on the exposed face and compensating for possible corrosion. The greatest advantages of such facings are low cost; ease of installation; design flexibility; good drainage (depending on the type of backfill), which provides increased stability; and possible treatment of the face for vegetative and other architectural effects. The facing can easily be adapted and well blended with the natural environment in the countryside. These facings, as well as geosynthetic wrapped facings, are especially advantageous for con­struction of temporary or other short-term design life structures.

8.5.1 Types of MSE Walls

Mechanically stabilized earth (MSE) walls are made up of several elements—specifically, the reinforcement of a soil mass through the use of steel strips, steel or polymeric grids, or geotextile sheets, capable of withstanding tensile forces, and a facing material. Figure 8.25 depicts different types of geosynthetic reinforced walls. The walls depicted range from a sloping geotextile wrapped face, usually used for the more temporary

Vertical cast-in-place Vertical masonry facing

concrete/masonry facing

FIGURE 8.25 Facings for geotextile-reinforced walls.

conditions, to stabilized soil masses faced with more long-term cast-in-place concrete or masonry block facings.

The advantages of MSE walls over the more conventional reinforced concrete walls include

1. Inherent flexibility to accommodate reasonable differential settlements

2. Lower total cost

3. Less construction time

4. Inherent capability to provide drainage to avoid buildup of hydrostatic forces

The reinforcement elements are characterized as extensible or inextensible. Extensible reinforcements can deform without rupture to develop deformations greater than can the soil in which they are placed. Such reinforcements include polymeric geotextiles and geogrids. Inextensible reinforcements cannot deform to deformations greater than the soil they reinforce. Metallic-strip or grid reinforcements are included in this category.

A summary of the available MSE systems in terms of the reinforcement and facing panel details is included in Table 8.4. The summary includes the major proprietary systems available. Figure 8.26 includes data regarding the geometries and some mechanical properties of the different reinforcement types available for use in MSE walls with geotextile reinforcements.

Reinforced Earth was invented by Henri Vidal, who first published results of his studies in 1963. After a brief period of skepticism, the first significant projects were constructed in 1967. The use of Reinforced Earth then spread rapidly, and by the early 1970s many significant projects were in place in several countries. These included the 23-m-high Peyronnet wall on the Nice-Menton Highway and the coal and ore loading facility at the port of Dunkirk, in France; the major retaining walls built along California Route 39 and along Interstate 70 through Vail Pass in the Colorado Rocky Mountains, in the United States; the Henri Bourassa Interchange in Quebec City, Canada; the several retaining walls on the Bilbao-Behobia Expressway in Spain; and the 11-km-long wall built on the St. Denis coastal road on Reunion Island in the Indian Ocean. Subsequently, Reinforced Earth has been accepted by civil engineers in all of the world’s industrialized nations, and its uses have been greatly diversified. Predominant applications are high­way and railway retaining walls and bridge abutments.

As indicated in Table 8.4, several other systems have been used since the introduction of Reinforced Earth. The Hilfiker retaining wall, which uses welded wire reinforce­ment and facing, was developed in the mid-1970s, and the first experimental wall was built in 1975 to confirm its feasibility. The first commercial use was on a wall built for the Southern California Edison Power Company in 1977 for repair of roads along a power line in the San Gabriel Mountains. In 1980, the use of welded wire wall expanded to larger projects, and, over the years, numerous walls have been completed in the United States.

Hilfiker also developed the Reinforced Soil Embankment (RSE) system, which uses continuous welded wire reinforcement and a precast-concrete facing system. The first experimental Reinforced Soil Embankment system was constructed in 1982. The first use of RSE on a commercial project was in 1983, on State Highway 475 near the Hyde Park ski area northeast of Santa Fe, New Mexico. At that site, four reinforced soil structures were constructed totaling 17,400 ft2 (1600 m2) of wall face. Many addi­tional RSE systems have been constructed since.

A system using strips of steel grid (or “bar mat”) reinforcement, VSL Retained Earth, was first constructed in the United States in 1981 in Hayward, California. Since then, numerous VSL Retained Earth projects have been built in the United States.

TABLE 8.4 Reinforcement and Face Panel Details for Several Reinforced Soil Systems Used in North America

Reinforcement

System name detail

System name	Reinforcement detail	Typical face panel detail*
Maccaferri Terramesh system (Maccaferri Gabions, Inc., 43A Governor Lane Blvd., Williamsport, MD 21795) Geotextile reinforced system	Continuous sheets of galva­nized double-twisted woven wire mesh with PVC coating. Continuous sheets of geotex­tiles at various vertical spacings.	Rock fill gabion baskets laced to reinforcement. Continuous sheets of geotex­tiles wrapped around (with shotcrete or gunite facing). Others possible.

*Many other facing types are possible with any specific system. Source: From J. K. Mitchell and B. R. Christopher, “North American Practice in Reinforced Soil Systems,” Proceedings, Specialty Conference on Design and Performance of Earth Retaining Structures, Geotechnical Division, American Society of Civil Engineers, 1990, with permission.

The mechanically stabilized embankment, a bar mat system, was developed by the California Department of Transportation on the basis of its research studies starting in 1973 on Reinforced Earth walls. The first wall using this bar mat type of reinforce­ment system was built near Dunsmuir, California, about 2 years later. Here, two walls were built for the realignment and widening of highway I-5. Since then, California has built numerous reinforced soil walls of various types.

Another bar mat reinforcing system, the Georgia stabilized embankment system, was developed more recently by the Georgia Department of Transportation, and the first wall using its technology was built for abutments at the I-85 and I-285 inter­change in southwest Atlanta. Many additional walls have been constructed using this system.

Polymeric geogrids for soil reinforcement were developed after 1980. The first use of geogrid in earth reinforcement started in 1981. Extensive marketing of geogrid products in the United States was started about 1983 by the Tensar Corporation. Since then, many projects have been constructed using this type of reinforcement.

The use of geotextiles in reinforced soil walls started after the beneficial effect of reinforcement with geotextiles was noticed in highway embankments over weak sub­grades. The first geotextile reinforced wall was constructed in France in 1981, and the first structure of this type in the United States was constructed in 1974. Since about 1980, the use of geotextiles in reinforced soil has increased significantly.

A typical cantilever retaining wall is illustrated by the insert sketch in Fig. 8.21. This rigid-type wall can be constructed with or without a base shear key (see Fig. 8.20) depending on an analysis for resistance to sliding, as discussed later.

The specifications of the owner will govern the selection and use of backfill materials behind retaining walls. In most cases, clean backfill materials having an internal friction angle of at least 34° are assumed in the design of retaining walls, subject to the fol­lowing considerations:

1. With a proper drainage system and with backfilling controlled so that no compaction-induced lateral loads are applied to the wall, the above-noted or better material may be used in construction. A minimum lateral earth pressure of 30 (lb/ft[10] [11])/ft (4.7 kN/m[12]) (equivalent fluid weight) for level backfills, or 40 (lb/ft2)/ft (6.3 kN/m3) for 2:1 sloped fills, should be assumed.

2. Backfill is assumed as on-site inorganic material; however, if it is of a lower class designation, the wall must be designed for an equivalent fluid weight lateral pressure suitable for that class. Therefore, should the designer select a backfill material of lower classification, it will be necessary to clearly specify the backfill material by a supple­mental project special provision and to use an appropriate equivalent fluid weight lateral pressure for design.

The design aids provided in Figs. 8.22 and 8.23 may be used for preliminary dimen­sions in the design of a cantilever cast-in-place retaining wall. On the basis of the Rankine theory of earth pressure, final design may proceed with the following steps:

NOTES:

Class I backfill (see Fig. 8.41)

Class D concrete

Coef. of friction (soil to soil = 0.67, soil to concrete = 0.42)

FIGURE 8.22 Aid for preliminary design of cast-in-place concrete retaining walls showing wall and footing dimensions. (From Bridge Design Manual, Section 5, Colorado Department of Transportation, Denver, Colo., with permission)

width b is approximately one-third to one-half of B. The ratio of footing width to overall height should be in the range from 0.4 to 0.8 for T-shaped walls as shown by the design aids in Figs. 8.22 and 8.23. In these preliminaries, wide-base L-shaped walls (footing width to height ratios larger than 0.8) are used for low wall heights (less than 10 ft or 3 m), and the factor of safety with respect to overturning is relaxed from a minimum of 2.0 to 1.5 when considering the case of D + E + RI.

4. Draw a vertical line from the back face of the footing to the top of the fill. This line serves as the boundary of the free body to which the earth pressure is applied. The applied active earth pressure can be estimated by Rankine theory, and the direction assumed parallel to the backfill surface. Compute the resultant P of the applied earth pressure and associated loads. Resolve P into horizontal and vertical components Ph and Pv, and apply at one-third the total height Ht of the imaginary boundary from the bottom of the footing. (See Fig. 8.21.)

5. Take a free body of the stem and compute the loads applied at the top of the stem as well as loads along the stem (height H), and find the moment and shear enve­lope to meet all the design cases at several points along the height. The working stress design method and the concept of shear friction can be used to calculate the shear strength at the joint between footing and stem.

Wall height at stem (ft)

NOTES:

Class I backfill (see Fig. 8.41)

Class D concrete

Coef. of friction (soil to soil = 0.67, soil to concrete = 0.42)

FIGURE 8.23 Aid for preliminary design of cast-in-place concrete retaining walls showing toe pressure and steel and concrete quantities. (From Bridge Design Manual,

Section 5, Colorado Department of Transportation, Denver, Colo., with permission)

6. Calculate the weight W, which is the sum of the weight of concrete and the weight of soil bounded by the back of the concrete wall and the vertical line defined by step 4 above. Find the distance from the extremity of the toe to the line of action of W, which is the stabilizing moment arm a.

7. Calculate the overturning moment Mo applied to the wall free body with respect to the tip of the toe as:

(8.5)

Calculate the resisting moment Mr with respect to the tip of the toe as:

M = Wa + P B

r v

The safety factor SF against overturning is

Mr

SF (overturning) =——-

M

o

Wa + P B

Ph H, /3

h t

The required safety factor (overturning) should be equal to or greater than 2.0 unless otherwise accepted and documented by the engineer (see step 3).

8. Compute the eccentricity e of the applied load with respect to the center of the footing based on the net moment:

The resultant should be within the middle third of the footing width; i. e., the absolute value of e should be less than or equal to B/6 to avoid tensile action at the heel.

9. The toe pressure q can be evaluated and checked by the following equation:

The toe pressure must be equal to or less than the allowable bearing capacity based on the soils report. Toe pressure is most effectively reduced by increasing the toe dimension.

10. The footing, both toe and heel, can be designed by working strength design. Soil reactions act upward and superimposed loads act downward. The heel design loads should include the portion of the vertical component Pv of earth pressure that is applied to the heel. For the toe design loads and stability, the weight of the overburden should not be used if this soil could potentially be displaced at some time during the life of the wall.

11. Check the factor of safety against sliding without using a shear key. The coef­ficient of friction between soil and concrete is approximately tan (/3ф), where ф is the internal friction angle of the soil in radians. Neglect the passive soil resistance in front of the toe. The sliding resistance SR can be evaluated as:

SR = (W + Pv) tan (|ф) (8.10)

The SF (sliding), which is SR/Ph, should be equal to or greater than 1.5. If SF (sliding) is less than 1.5, then either the width of the footing should be increased or a shear key should be installed at the bottom of the footing.

If a shear key is the choice, the depth of the inert block dc is computed by the sum of the key depth KD and the assumed effective wedge depth, which is approximately half the distance between the toe and the front face of the shear key (b/2). Using the inert block concept, knowing the equivalent fluid weight (yp) of passive soil pressure, and neglecting the top 1 ft (300 mm) of the toe overburden T, the toe passive resistance P is

p

Pp = 0.57p[(To + T + dc — 1)2 — (To + T — 1)2] (8.11)

Total sliding resistance F from friction is the sum of the horizontal component of the resistance from toe to shear key and the resistance from shear key to heel. Therefore:

where ф = internal friction angle of base soil

R1 = soil upward reaction between toe and key, lb/ft (kN/m) R2 = soil upward reaction between key and heel, lb/ft (kN/m)

Sliding resistance is

SR = F + Pp (8.13)

The SF (sliding), which is SR/Ph, should be equal to or greater than 1.5.

12. Repeat steps 3 through 11 as appropriate until all design requirements are satisfied.

Figure 8.24 represents typical values for equivalent fluid pressures of soils. These values are suggested for use in the absence of a more detailed determination.

Structural backfill class designation	Type of soil (compaction conforms with AASHTO 90-95% T180)	Typical values for equivalent fluid unit weight of soils, lb/ft3abc (kN/m3)
Condition	Level backfill	2:1 (H: V) backfill
Class Id: borrowed,	Loose sand or gravel	(Active)	40	50 (6.3/7.9)
selected, coarse-		(At rest)	55	65 (8.6/10)
grained soils	Medium dense sand or	(Active)	35	45 (5.5/7.1)
	gravel	(At rest)	50	60 (6.3/9.4)
	Dense6 sand or gravel,	(Active)	30	40 (4.7/6.3)
	95% T180	(At rest)	45	55 (7.1/8.6)
Class IIAf: on-site,	Compacted, clayed,	(Active)	40	50 (6.3/7.9)
inorganic, coarse-	sand gravel	(At rest)	60	70 (9.4/11)
grained soils, low	Compacted, clayed,	(Active)	45	55 (7.1/8.6)
percentage of fines	silty gravel	(At rest)	70	80 (11/13)
Class IIB: on-	Compacted, silty/sandy	Site-specific material, use with
site, inorganic	gravelly, low/medium	special attention;	see geotech-
LL < 50%	plasticity lean clay	nical engineer. Soils report on
		workmanship of compaction,
		drainage design, and waterstop
		membrane is required.
Class IIC: on-	Fat clay, elastic silt that	Not recommended
site, inorganic	can become saturated
LL > 50%
a At rest, pressure should be used for earth that does not deflect or move.
b Active pressure state is defined by movement at the top of wall of 1/240 of the wall height.
c The effect of additional earth pressure that may be induced by compaction or water should
be added to that of earth pressure.
d Class I: 30 percent or more retained on no. 4 sieve and 80 percent or more retained on no.
200 sieve.
6 Dense: No less than 95 percent density per AASHTO T180.
f Class IIA: 50 percent or more retained on no. 200 sieve.

FIGURE 8.24 Typical values for equivalent fluid pressure for soils. (From Bridge Design Manual, Section 5, Colorado Department of Transportation, Denver, Colo., with permission)