Subgrade Improvement for Paved and Unpaved Surfaces Using …docshare04.docshare.tips/files/12311/123117221.pdf · 2017. 4. 18. · Subgrade Improvement for Paved and Unpaved Surfaces

Subgrade Improvement for Paved and Unpaved Surfaces Using Geogrids By Stephen Archer, P.E.

October 2008

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The use of geogrid reinforce-ment is a common practice for engineers, owners, and contractors for building

structures over soft soil conditions. First introduced in the United States in the early 1980s, the unique char-acteristics and mechanisms specific to geogrids offer significant benefits compared with the following conven-tional construction practices:• excavation and replacement with

select fill material,• thick structural (pavement) sections

to account for weak subgrade soil conditions,

• chemical stabilization or modifica-tion with calcium-based materials (i.e., cement, lime, fly ash), and

• stabilization with woven or non-woven geotextiles.

A geogrid is defined as a geosyn-thetic material consisting of

connected parallel sets of tensile ribs with apertures of sufficient size to allow strike-through of surround-ing soil, stone, or other geotechnical material (Koerner, 1998; see Figure 1 on page PDH 4). Commercial geogrid products marketed and sold today include extruded punched-and-drawn geogrids, woven and coated geogrids, welded geogrids, and geogrid composites. Structural biax-ial geogrids can be used to reinforce earth fill over soft ground and provide a stable subgrade under flexible and rigid pavements, unpaved roads, railroad track beds, industrial yards, equipment work platforms, parking areas, and building foundations.

Many small and full-scale stud-ies have been performed to better understand how geosynthetics inter-act with fill materials to contrast their performance with unreinforced condi-tions in a variety of civil engineering

applications. This historical empirical data is the basis for development of a number of design methods to quan-tify the fill thickness required over a geosynthetic reinforcement element to achieve a minimum level of service-ability. As the use of geosynthetics in soft soil conditions has evolved during the last three decades, so has the number of design methodologies and criteria by which geosynthetics are evaluated. This article addresses the following two current design meth-ods commonly used by engineers within the United States and abroad: The Giroud-Han Design Method (2004) and The U.S. Army Corps of Engineers Design Method (2003).

Geogrid reinforcement mechanisms

A subgrade soil beneath a paved or unpaved surface can fail under load in two ways: localized shear failure

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Learning Objectives• Understand the primary mechanisms by which geogrids

reinforce granular fill over soft soils and how these features translate to quantifiable fill savings relative to conventional practice.

• Develop an understanding of two design methods endorsed by the American Society of Civil Engineers and the U.S. Army Corps of Engineers for designing geogrid-reinforced unpaved surfaces over soft soils.

• Translate the granular fill savings to cost benefits that can be realized relative to a geotextile solution and an unreinforced solution.

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Subgrade Improvement for Paved and Unpaved Surfaces Using Geogrids

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and deeper-seated bearing capacity fail-

ure. Localized shear failure, or base punch-

ing, typically occurs in the form of severe deformation or rutting in soft saturated subgrades when loading exceeds the subgrade shear strength. The subgrade beneath an unrein-forced fill will fail in localized shear failure at about half of the stress level than the ultimate bearing capacity of the subgrade. Premature failure of a paved or unpaved surface due to weak subgrades leads to costly full-depth repairs that can be avoided with good engineering judgment at the time the section is designed. Geogrids offer protection over weak foundation soils because of the ability of the material to act as a “snowshoe” over soft, rut-prone conditions.

Geogrid reinforcement of granu-lar fills over soft ground can prevent localized shear failure of the subgrade and therefore significantly increase the effective bearing capacity of the subgrade. In addition, geogrids reinforce the granular fill through confinement of the particles, stiffen-ing the base layer for improved load distribution.

The net effect of these mechanisms is a reduction in the fill thickness required to provide stable foundation support for a paving operation or for the immediate trafficking of unpaved structures such as haul roads or work-ing platforms (see Figure 2).

In 2003, the U.S. Army Corps of Engineers (Corps) identified and defined the primary applications for biaxial geogrid reinforcement for paved and unpaved structures: mechanical subgrade stabilization and base reinforcement. In an engineer-ing technical letter (ETL), the Corps referenced three primary mechanisms as being relevant to the interaction of geogrid reinforcement and pavement materials: lateral restraint, improved bearing capacity, and tensioned membrane effect (Perkins and Ismeik, 1997a; see Figure 3). The following is summarized from the Corps ETL 1110-1-189 (page 3).

Lateral restraint — Considered the primary reinforcement mecha-nism by the Corps document, lateral restraint describes the ability of the aperture geometry of a grid to confine aggregate particles within the plane of the material. This feature yields a stiffening effect to the reinforced granular material, both above and below the geogrid (in the case of the material being installed at the mid-point of a granular fill), that results in an increase in modulus of the rein-forced layer.

Improved bearing capacity — Typically associated with geogrid use over soft subgrades, improved bear-ing capacity describes a change in the potential failure mechanism of the subgrade from a localized shear — generally characterized as a deep rutting failure — to a general bear-

Figure 1: Biaxial geogrid and aggregate Figure 2: Granular fill thickness reduction achieved through a biaxial geogrid layer

Figure 3: Geogrid reinforcement mecha-nisms of lateral restraint (top), improved bearing capacity (center), and tensioned membrane effect (bottom).


ing capacity failure. The result is an improved effective bearing capacity of the subgrade resulting from pressure dissipation at the geogrid-subgrade interface.

Tensioned membrane effect — Initial research suggested that the tensioned membrane effect was the primary mechanism of geogrid over soft ground. Subsequent stud-ies have proven that geogrid offers discernable structural enhancement without significant rutting of the subgrade layer. This is a key distinc-tion of geogrids when compared with geotextiles as it relates strain accumu-lation within each layer of a paved or unpaved structure. As punched and drawn geogrids are manufactured by “pre-straining” the polymer, yielding an effective stress transfer of vertical and horizontal stress, both woven and non-woven geotextiles require the strain be induced after the product is installed, leading to rut accumulation in the aggregate layer and subgrade layer. The result is a structure that may require frequent rehabilitation or premature replacement, depending on serviceability requirements and life cycle cost valuation of the structure.

These mechanisms, unique to geogrid reinforcement, collectively contribute to the interaction of gran-ular fill with the open structure of the geosynthetic. Research and thou-sands of full-scale applications during the last 30 years have yielded two reliable design methods that now give guidance for the use of geogrids, as well as geotextiles, for constructing unpaved surfaces over soft soils.

Giroud-Han Method (2004)Recognizing a need to advance

geosynthetic design for unpaved surfaces, J.P. Giroud, Ph.D., and Jie Han, Ph.D., published a design method in the August 2004 edition of the American Society of Civil Engineers (ASCE) Journal of Geotechnical and Geoenvironmental Engineering. Their approach combines bearing capac-ity theory with empirical data from full-scale test sections and monitored

unpaved roads. Some distinctions of the Giroud-Han method relative to conventional geosynthetic road design practice include the following:• consideration of the effects of varia-

tion in base course strength,• consideration of the number and

size of load cycles (axle passes) and the desired roadway performance,

• consideration of how the load distri-bution angle within the base course changes with time,

• recognition that geotextiles and geogrids perform differently in roads,

• recognition that not all geogrids perform the same, and

• calibration and validation of the theoretical results with laboratory and full-scale test data.

The method accounts for, in addi-tion to the factors considered by the Giroud and Noiray (1981) methods developed for the then U.S. Forest Service, the strength/modulus of the base material, the variations of the stress distribution angles through the base course, and the aperture stability modulus “strength” property of the geogrid. The theoretical model that was initially developed was calibrated using data from large-scale, cyclic plate load tests directed by Mohammed Gabr, Ph.D., at North Carolina State

University. These tests were run for both rein-forced and unreinforced conditions with 6- and 10-inch-thick base courses placed on a soft subgrade. Two reinforcement geogrids were used for the testing — Tensar BX1100 and BX1200.

The tests yielded data for pressures on the subgrade and deformations at the surface as functions of the number of load cycles for the various combinations of reinforcement and base thickness. The pressure data was used to estimate the load distribu-tion angle and to quantify the effects of base reinforcement and thickness on both the initial angle and on the changes in the angle with continued applications of load. Layer elastic theory was used to assess the effect of the base course modulus on the stress distribution angle. The newly available test data made it possible to develop this more comprehensive and statistically accurate unpaved road design method.

Giroud and Han (2004a) summa-rized the significance of this cali-bration effort: “The design method presented in this paper and the companion paper is theoretically based and experimentally calibrated. Therefore, it more accurately predicts performance for both geogrid- and

Figure 4: Aggregate thickness values using the Giroud-Han method for 2-inch rut depth, 80-psi tire pressure, 20-kip axle, and 1,000-axle-pass loading criteria



geotextile-reinforced unpaved roads and for

unreinforced, unpaved roads than do earlier meth-

ods developed by Giroud and Noiray (1981) and Giroud et al. (1985). As such, the method presented herein supersedes these previous methods.”

In consideration of these principles and the conventional practice of load distribution theory, the follow-ing equation was derived to predict the required thickness of fill (h) to provide the prescribed serviceability for the given loading conditions and soil subgrade support. In using this equation, the designer is required to solve iteratively for fill thickness (h):

where:h = required base course thickness

(m)J = geogrid aperture stability modu-

lus (m-N/degree)N = number of axle passesP = wheel load (kN)r = radius of the equivalent tire

contact area (m)CBRsg = California bearing ratio (CBR)

of the subgrade soilCBRbc = CBR of the base courses = allowable rut depth (mm)fs = factor equal to 75 mmfc = factor equal to 30 kPaNc = bearing capacity factor, in which

Nc = 3.14 and J = 0 for unrein-forced base course; Nc = 5.14 and J = 0 for geotextile-reinforced base course; Nc = 5.71 and J = 0.32 m-N/degree for Tensar BX1100-reinforced base course; and Nc = 5.71 and J = 0.65 m-N/degree for Tensar BX1200-reinforced base course.

The Giroud-Han Method is unique in its approach of combining standard

bearing capacity theory and observed practical performance. As such, it presents the design engineer with the most reliable method currently avail-able for the design of unpaved roads. The method was developed, cali-brated, and validated with data from full-scale, field and laboratory tests considering different geogrids. The formulation can be refined further to consider new geogrid products and new research data as it becomes available.

The Giroud-Han Method can be expected, and it can be shown, to give the most accurate predictions of field performance for similar loading conditions, base and subgrade prop-

erties, and for the specific geogrids used in the various test programs. Figure 4 demonstrates a specific example comparing the output of a design for an unreinforced section and sections reinforced with a geogrid and a geotextile. Once output has been calculated for the available options, a cost-benefit analysis can then be undertaken given the in-place costs for both the aggregate fill and the geosynthetic(s).

U.S. Army Corps of Engineers Method (2003)

In February 2003, the Corps published a design method consider-ing the use of geogrids and geotex-tiles for paved and unpaved roads. Its approach for unpaved surfaces, based on the methodology originally developed by the U.S. Forest Service, distinguishes the performance of geotextiles and geogrids as rein-forcement components in subgrade improvement applications.

The design charts developed by the Corps are based on empirical data

obtained from full-scale test sections undertaken at the Corps Research and Development Center in Vicksburg, Miss. This data was combined with the old bearing-capacity design methodol-ogy developed by Steward, et al., for the U.S. Forest Service (1977). Based upon the Corps’ independent, full-scale testing (Webster, 1992), a mate-rial specification was developed for geotextile and geogrid products. The geogrid specification recommended in this document is shown in Table 1 on page PDH 7.

Geogrid-reinforced aggregate surface design using the Corps method requires the design engi-neer to select an appropriate Bearing Capacity Factor, Nc , for the geosyn-thetic type being considered. The Corps recommended the following Nc values: • Nc = 2.8 without a geosynthetic, • Nc = 3.6 with a geotextile for conser-

vative designs, and • Nc = 5.8 with a geogrid.

The next step in determining an appropriate granular fill thickness is to determine the subgrade shear strength, C (psi). This may be deter-mined through conventional shear testing in situ (shear vane, torvane, pocket penetrometer, et cetera), or by laboratory tests on extruded, undis-turbed samples. The shear strength of the soil can also be correlated from alternative tests (field CBR, dynamic cone penetrometer, et cetera). The relationship recommended by the Corps between the cone index, CBR, and shear strength is presented in Figure 5 on page PDH 7.

The subgrade bearing capacity used to calculate the required aggre-gate thickness is determined in accor-dance with Equation 2:

Subgrade Bearing Capacity =C * Nc (psi) (Equation 2)

Once the subgrade bearing capac-ity has been determined, the designer can reference one of the three relevant design charts (single wheel, dual wheel,

(Equation 1)


and tandem gear wheel weight) in the ETL document to calculate the required aggregate thickness. An example chart for a single wheel load condition is presented in Figure 6 on page PDH 8.

Resulting thickness savings with

the geosynthetic relative to the unre-inforced sections are substantial. A minimum aggregate thickness of 6 inches is recommended by the Corps for aggregate-surfaced pavements. To facilitate a comparison of the design

methods described in this article, an analy-sis has been performed using the same design criteria used in the earlier example describing the Giroud-Han method. The results for the Corps method are presented in Figure 7 on page PDH 8.

Design method comparisonA comparison of the Giroud-Han

and the Corps design input and output reveal both similarities and differences between the two methods (see Table 2 on page PDH 8). A similar sensi-tivity study of the Giroud-Han and the Corps methods was performed to compare the predicted fill thickness outputs for given conditions (Tingle and Jersey, 2007). Figures 4 and 7 plot sample output such that each method for the two types of geosyn-thetic (geogrid and geotextile) can be compared. A direct comparison of required aggregate fill thickness using each method reveals the following:• Generally, the Giroud-Han method

yields thicker aggregate required for both the unreinforced and geotex-tile-reinforced relative to the Corps method.

• Except for extremely soft subgrade conditions (CBR ≤ 0.5), the Giroud-Han method yields thinner aggregate required for the geogrid-reinforced relative to the Corps method.

Figure 5: Relationship between cone index, CBR, and shear strength, C (TM 5-518-8)

Table 1: Minimum biaxial geogrid specification requirements per the Corps method (2003)


• The minimum thick-ness allowed for traffick-

ing allowed by the Corps method is 6 inches, while

the Giroud-Han method allows for a minimum of 4 inches of granular fill.• Both methods suggest that geogrid

reinforcement requires less aggre-gate fill when compared with a geotextile for the same level of serviceability and design criteria

Of the two methods reviewed, only the Giroud-Han method addresses the difference in index properties of geogrids. Engineers, owners, and contractors routinely compare the index properties of commercially available geosynthetics to determine the proper selection of a product for a given appli-cation. However, research has shown that index properties alone do not correlate to in-ground performance. Accordingly, designers are encouraged to seek manufacturer-specific, full-scale empirical evidence that proves that the performance predicted by each of the methods reviewed in this article indeed correlate to the geosynthetic manufac-turer brand in question.

Cost-benefit analysis Essential to any design analy-

sis is the need for the in-place cost of an alternative solution relative to conventional practice. The primary benefit that owners, engineers, and contractors seek in using geosynthet-ics is the potential for front-end cost savings associated with raw material

Figure 7: Aggregate thickness values using the U.S. Army Corps of Engineers method for 2-inch rut depth, 80-psi tire pressure, 10,000-pound wheel load, and 1,000-axle-pass loading criteria

Figure 6: Aggregate-surfaced pavement design curves for single-wheel loads



Table 2: Comparison of required aggregate thickness: Giroud-Han (G-H) and U.S. Army Corps of Engineers (USACOE) methods for 2-inch rut depth, 80-psi tire pressure, 20-kip axle, and 1,000-axle-pass loading criteria


use. In the case of aggregate-surfaced roads, the raw material in question is the aggregate itself. To realize the value of the geosynthetic, a designer is encouraged to explore the in-place cost of both the geosynthetic and the aggregate fill required to provide the designed service life of the structure in question.

This relatively simple analysis can be performed through weighted average price data that is available from most state departments of transportation and other public enti-ties that publish this information on a monthly, quarterly, or annual basis. The steps involved for such an analy-sis include the following:1) Determine the in-place cost of

aggregate per square yard-inch of depth (see Figure 8).

2) Determine the in-place cost of the geosynthetic of choice (geogrid or geotextile).

3) Determine the required aggregate fill thickness for an unreinforced case for the given loading and serviceability using either method reviewed above.

4) Determine the required aggre-gate fill thickness for a reinforced case for the same loading and serviceability using geogrid and/or geotextile.

5) Subtract the required reinforced thickness from the required unre-inforced thickness to determine aggregate fill thickness savings for each reinforced section.

6) Calculate the cost savings by multi-plying the aggregate fill thickness savings in inches (obtained in step 5) by the in-place aggregate cost per square yard-inch of depth, and then subtract the in-place cost of the geosynthetic per square yard.

The output from the Giroud-Han method shown in Figure 4 demon-strates the potential cost savings that can be realized using a layer of geogrid reinforcement over soft soil. For example, if a haul road is to be constructed over a subgrade CBR equal to 1.5 for a 2-inch rut depth,

20-kip axle load, and 80-psi tire infla-tion, the required aggregate thickness necessary is represented below:• unreinforced = 20 inches,• geotextile-reinforced = 14 inches,

and• geogrid-reinforced = 7 inches

If aggregate costs $20/ton in-place, the savings realized for the geosyn-thetic solutions equate to:

Geotextile-reinforced = (20 inches – 14 inches) = 6 inches x ($1/square yard-inch) = $6/square yard minus geotextile cost

Geogrid-reinforced = (20 inches – 7 inches) = 13 inches x ($1/square yard-inch) = $13/square yard minus geogrid cost

SummaryGiven present day challenges asso-

ciated with increasing raw material

pricing and dwin-dling project fund-ing, geosynthetics offer owners and engineers a proven, cost-effective alternative to conventional building practice for constructing unpaved haul roads and working surfaces over soft subgrade soil conditions. Significant initial cost and construction time savings can be realized through the inclusion of a geogrid layer. Much empirical evidence, along with full-scale and small-scale research, has yielded reli-able design methods for quantifying the benefits of geosynthetics relative to expensive alternates such as under-cut-and-replace and chemical stabili-zation or modification.

Current methods developed by Giroud-Han and the U.S. Army Corps of Engineers offer guidance in deter-mining both the proper selection of the geosynthetic type and the neces-sary granular fill thickness to provide

Figure 8: Aggregate in-place cost conversion chart (unit weight = 133 pounds/cubic foot)



• U.S. Army Corps of Engineers, 2003, Use of Geogrids in Pavement Construction, ETL 1110-1-189.

• Giroud, J.P., and L. Noiray, 1981, “Geotextiles-Reinforced Unpaved Road Design,” Journal of Geotechnical Engineering, Vol. 107, No. 9, pages 1233-1253, ASCE.

• Giroud, J.P., and Han, J., 2004a, “Design Method for Geosynthetic-Reinforced Unpaved Roads: Part I – Development of Design Method,” Journal of Geotechnical and Geoenvironmental Engineering, in press, ASCE.

• Koerner, Robert M., 1998, Designing With Geosynthetics, Fourth Edition, Prentice Hall, Upper Saddle River, N.J.

• Perkins, S. W., and Ismeik, M., 1997a, “A Synthesis and Evaluation of Geosynthetic Reinforced Base Layers in Flexible Pavements: Part I,” Geosynthetics International, Vol. 4, No. 6, pages 605-621.

• Tingle, Jeb S., and Jersey, Sarah R., 2007, “Empirical Design Methods for Geosynthetic-Reinforced Low-Volume Roads”, Transportation Research Record: Journal of the Transportation Research Board, No. 1989, Vol. 2, Washington D.C., pages 91-101.

• Webster, S.L., 1992, “Geogrid Reinforced Base Course for Flexible Pavements for Light Aircraft: Test Section Construction, Laboratory Tests and Design Criteria”, U.S. Army Corps of Engineers Report No. DOT/FAA/RD-92-25

References

Professional Development Series Sponsor:9025 Centre Pointe Dr., Suite 400, West Chester, OH 45069Phone: 800-338-1122 • Fax: 513-645-7993 • Email: [email protected] Web: www.contech-cpi.com

CE News Professional Development Series Reporting FormArticle Title: Subgrade Improvement for Paved and Unpaved Surfaces Using Geogrids Publication Date: October 2008 Valid for credit until: October 2010 Sponsors: CONTECH Construction Products Inc., Tensar International Corporation

Instructions: Select one answer for each quiz question and clearly circle the appropriate letter. Provide all of the requested contact infor-mation. Fax this Reporting Form to 513-645-7993. (You do not need to send the Quiz; only this Reporting Form is necessary to be submitted.)1) a b c d 6) a b c d

2) a b c d e 7) a b c d

3) a b c d 8) a b c d

4) a b c d e 9) a b c d

5) a b c d e 10) a b c d

Required contact informationLast Name: First Name: Middle Initial:

Title: Firm Name:

Address:

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Certification of ethical completion: I certify that I read the article, understood the learning objectives, and completed the quiz questions to the best of my ability. Additionally, the contact information provided above is true and accurate.

Signature: Date:

Stephen Archer, P.E., roadway systems marketing director for Tensar International Corporation, has more than 15 years of experience in the geosynthetics industry and geotechni-cal engineering. He can be contacted at [email protected]

optimal performance. Given these methods,

the cost benefits of each method and geosynthetic

solution may be realized.Participants are encouraged to

download the U.S. Army Corps of Engineers method reviewed within this article, available online at www.usace.army.mil/publications/eng-tech-ltrs/etl1110-1-189/entire.pdf.


Professional Development Series Quiz

1. Of the reinforcement mechanisms described in the Corps' ETL, which is considered to be the primary reinforcement mechanism in unpaved structures?

a) Tensile membrane effect b) Lateral restraint

c) Improved bearing capacity d) Separation

2. Which of the following are true statements?

a) The Giroud-Han method considers how the load distribution angle within the base course changes with time.

b) The Giroud-Han method considers the number and size of load cycles (axle passes) and the desired roadway performance.

c) The Giroud-Han method recognizes that not all geogrids perform the same.

d) The Giroud-Han method recognizes that geotextiles and geogrids perform differently in roads.

e) All of the above statements are true.

3. According to the Giroud-Han method, what is the key index property used to model the strength characteristic of the geogrid element within the design equation?

a) Tensile strength at 5 percent strain

b) Tensile strength at ultimate strain

c) Junction strength

d) Aperture stability modulus

4. The Giroud-Han method is considered to have superseded which of the following methods for designing unpaved roads over soft ground conditions?

a) Giroud and Noiray (1981)

b) U.S. Army Corps of Engineers (2003)

c) Giroud et al. (1985)

d) Both a and c

e) All of the above

5. What are the key parameters needed to run a cost-benefit analysis comparing an unreinforced design section with a section reinforced with geogrid?

a) The in-place cost of the geogrid

b) The in-place unit cost of the granular fill ($/ton)

c) The unit weight of the granular fill

d) The thickness savings yielded for a geogrid-reinforced design section

e) All of the above

6. Which of the following statements is false?

a) Both the Giroud-Han method and the U.S. Army Corps of Engineers method recognize that geogrids and geotextiles perform differently in unpaved roads.

b) Both design methods demonstrate that aggregate fill thickness required for geogrid is less than for geotextiles.

c) Both methods account for subgrade strength, wheel load, tire pressure, and the geogrid aperture stability modulus.

d) The Giroud-Han method was calibrated and validated around full-scale testing.

7. Dynamic cone penetration tests reveal a soft subgrade soil strength, CBR = 1.5. Using the U.S. Army Corps of Engineers method, determine the required aggregate thickness (round up to the nearest inch) of an unreinforced, geotextile-reinforced, and geogrid-reinforced unpaved road section for a single-wheel load weighing 10,000 pounds.

a) 15 inches (unreinforced); 13 inches (geotextile); and 9 inches (geogrid)

b) 18 inches (unreinforced); 16 inches (geotextile); and 12 inches (geogrid)

c) 12 inches (unreinforced); 10 inches (geotextile) and 6 inches (geogrid)

d) 16 inches (unreinforced), 10 inches (geotextile) and 9 inches (geogrid)

8. An analysis using the U.S. Army Corps of Engineers method reveals a design for an unpaved road requires 14, 12, and 8 inches of aggregate for unreinforced, geotextile, and geogrid reinforced roads, respectively. What would be the potential cost savings (per square yard) for a geogrid section relative to an unreinforced design, given an in-place cost for aggregate fill of $22/ton?

a) $5.50/square yard minus the in-place cost of the geogrid

b) $6.60/square yard minus the in-place cost of the geogrid

c) $7.70/square yard minus the in-place cost of the geogrid

d) $8.80/square yard minus the in-place cost of the geogrid

9. Dynamic cone penetration tests reveal a soft subgrade soil strength, CBR = 1.0. Using the Giroud-Han method, determine the required aggregate thickness (round up to the nearest inch) of an unreinforced, geotextile-reinforced, and geogrid-reinforced unpaved road section for an axle load weighing 20,000 pounds, 80-psi tire pressure, 2-inch limiting rut depth, and 1,000 axle passes.

a) 21 inches (unreinforced); 14 inches (geotextile); and 10 inches (geogrid)

b) 14 inches (unreinforced); 20 inches (geotextile); and 7 inches (geogrid)

c) 23 inches (unreinforced); 17 inches (geotextile); and 9 inches (geogrid)

d) 26 inches (unreinforced); 19 inches (geotextile); and 11 inches (geogrid)

10. An analysis using the Giroud-Han method reveals a design for an unpaved road requires 23, 14, and 9 inches of aggregate for unreinforced, geotextile, and geogrid reinforced, respectively. Assuming an installed cost for geotextile of $1.25/square yard, what would be the potential cost savings (per square yard) for a geogrid section relative to a geotextile design given an in-place cost for aggregate fill of $23.50/ton?

a) $7.12/square yard minus the in-place cost of geogrid

b) $9.33/square yard minus the in-place cost of geogrid

c) $4.63/square yard minus the in-place cost of geogrid

d) $5.88/square yard minus the in-place cost of geogrid

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