NAJIA SAEED MOHAMMED. ELHAZZAR1
Civil engineering Department ,AL Gubba, University of Derna ,Libya
Email: gegesaeedsaeed@gmail .com
HNSJ, 2023, 4(10); https://doi.org/10.53796/hnsj4109
Published at 01/10/2023 Accepted at 19/09/2023
Abstract
There are two stages of analysis of reinforced earth walls, namely external stability and internal stability. External stability checks assumes that the failure surface lies completely outside the reinforced soil mass and analysis of internal stability consists of evaluating the surfaces of the sliding potential within reinforced soil mass. In this paper we are going to shows potential external and internal failure mechanisms are usually considered when we design retaining walls by using Load and Resistance Factor Design (LRFD) to evaluate external and internal stability for retaining walls by an excel spreadsheet and the excel program are applied for different example by changing the propriety with the FHWA manual solutions. Also as we all know the design codes varies from country to country, In this paper we are going to be applied American Association of State Highway and Transportation Official (AASHTO) retaining Walls Design Code(ASSHTO) included the retaining walls section in their Bridge Design Manual .
The retaining structures are composed of three components: reinforcement, soil and wall element all three parts are working together to stabilize the soil mass. We can save money, time and space by using these kinds of structure. Retaining walls applications have been used in transportation construction industrial, waterway, commercial and public structures. The most important thing when planning to design retaining walls to choose a design approach to use, selection depends on some factors such as: safety, material availability, construction difficulty, time and money. There is several design and analysis methods, in this paper we are going to use Load and Resistance Factor Design method and an excel spreadsheet used to perform analyses according to LRFD was prepared.
An example problem that was selected from (FHWA) manual is solved by using an excel spread sheet, it can be able to check internal and external stabilities for MSW very easy. All the details about the MSE wall, such as dimensions, properties of backfill and reinforcement etc are listed below.
Project requirements:
Exposed wall height ,He = 28 ft, Length of wall =850 ft, Design life =75 years, Precast panel unit: 5 ft wide 5 ft tall 0.5 ft thick, Type of reinforcement: grade 65 (FY = 65ksi, 1.969 in0.157 in) [1].
Project parameters:
Reinforced backfill, =, =125 pcf, coefficient of uniformity, = 7Retained backfill, = , =125 pcf, Foundation soil,=, =125 pcf [1] .
Depth of embedment and length of reinforcement:
Base on AASHTO (2007), the minimum embedment depth: d = 28/20 =1.4 ft so it is assumed that, d =2 ft. So design height of the wall H = He + d = 28+2 =30 ft, Length of reinforcement assumed to be L =0.8 H=24 ft [1].
Factored Bearing resistance of foundation soil:
For service limit consideration, qnf-ser =7.5 ksf, for strength limit consideration, qnf-str = 10.5ksf.
Estimation of unfactored loads:
1- Coefficient of active earth pressure:
= (1)
= 1.563, So =0.537.
2-Vertical force:
Table (1) :Unfactored vertical forces and moment [1] .
force | Val(k/ft) | Moment arm(ft) | Moment (k-ft/ft) |
V1= (γr)(H)(L) | 90.0 | L/2=12 | 1080.0 |
V2 =0.5(L) (Ltanβ) ( γf) | 18.0 | 2/3(L) | 288.0 |
FTV=0.5(γr) (h^2) (Kaf ) (sinβ) | 26.48 | L | 635.44 |
3-Horizontal forces:
Table (2) :Unfactored Horizontal Forces and Moment [1].
force | Valu(k/ft) | Moment ar(ft) | Moment |
FTH =0.5(γr)(h^2)(Kaf ) (cosβ) | 52.95 | h/3=14.0 | 741.35 |
Tanβ = 0.5, and h=30+24(0.5) =42 ft, the forces and moments should be multiplied by appropriate load factor and resistance factor, the figure (1) shows unfactored vertical and horizontal force [1].
The figure (1); unfactored vertical and horizontal force
- Evaluate external stability of MSE walls
The potential external failure mechanisms that are usually considered in the design of MSE walls are following.
1-Sliding Stability
The sliding may occur along the base of the wall of the MSE wall. Sliding force is the horizontal component of the thrust on the vertical plane at the back of the wall. In the sliding stability calculations, driving force general consist of the live load above the retained backfill, factored horizontal, loads due to earth, water, seismic and surcharge [2].
2- Eccentricity at base of MSE walls
In limit eccentricity calculations, the MSE wall is checked with respect to overturning. Eccentricity is defined as the ratio of summation of overturning and the resisting moments about the bottom center of the base length, to the total vertical load [2].
3- Bearing resistance
Bearing capacity in another external stability check that is performed for both strength and service limit state .The bearing capacity with respect to general shear failure can be assessed by the comparison of the factored vertical pressure at the base of the wall and the factored bearing resistance of the foundation soil. The vertical pressure due to the MSE walls is calculated as [2].
- Evaluation of internal stability
Internal failure can occur in two ways: the tensile forces in the inclusions become so large, namely failure by elongation or breakage of the reinforcement. And the tensile forces in the reinforcements become larger than the pullout resistance (failure by pullout) .For internal stability calculations; it is assumed that a failure surface divides the reinforced zone in active and resistance zones [2].
1. Estimation the location of the Critical Failure Surface, Variation of (Kr) and pullout resistance stress coefficients (F*):
The critical failure surface and variation of Kr and F* must be estimated depending on the type of reinforcement. For the case of inextensible steel ribbed strips, these factors are can be calculated from figure (2).
Figure (2); Location of Potential Failure Surface for Internal Stability Design of retaining Walls (a) Inextensible Reinforcements and (b) Extensible Reinforcements.
2- Establish vertical layout of soil reinforcement:
Depending on the depth Z the Svt can be estimate at each level; for example at Z=9.2ft
Svt = Z+– Z–
= 9.2+ 0.5(12.1-9.2) = 10.65ft and =9.2-0.5(9.2-6.3) = 7.75 ft. so Svt = 10.65-7.75 = 2.9ft
3-Calculate horizontal stress (σ H) and Maximum tension T max at each reinforcement:
The horizontal stress at any given depth within the reinforced soil zone is expressed as follows: σH = Kr [σv] +∆σH (2)
Where:
Kr = coefficient of lateral earth pressure in the reinforced soil zone
σv = factored vertical pressure at the depth of interest,
∆σH = Supplemental factored horizontal stress due to external surcharges [2].
4-Estimation Nominal and Factored Long –Term Tensile Resistance of Soil Reinforcement:
For steel reinforcement, the corrosion affect must be considered in the design like calculation .The corrosion losses over the design life period is calculated as:
Ec = En – ER (3)
Where:
Ec = the thickness of the reinforcement at the end of the design life.
En = the nominal thickness at construction,
ER = the thickness of metal expected to be lost by uniform corrosion during the service life of the structure.
The nominal long-term tensile strength of the reinforcement Tal can be estimate by following equation:
Tal =Fy Ac / b (4)
Ptal = Fy Ac (5)
Where:
b = the gross width of the strip, sheet or grid,
Fy = yield stress of steel,
Ac = design cross section area of the steel (= b) [1].
5-Estimation of Nominal and Factored Pullout Resistance of Soil: Reinforcement The pullout resistance soil reinforcement is depended on various parameters of soil reinforcement; these parameters are explained in the following equation:
Pr = α (F*) (2b) (Le) (σv) (γp-EV) (6)
Le = the length of embedment in the resisting zone
F* = Pullout resistance factor
α = Scale correction factor, (1.0 for metallic reinforcements and 0.6 to 1.0 for geosynthetic reinforcements)
σv = Nominal vertical stress at the reinforcement level in the resistant zone,
The factored pullout resistance as follows: Prr = ø Pr [2].
6- Number of Soil Reinforcing Strips at Each level of Reinforcement:
The number of strip reinforcement at any level related with Tmax and Prr .For tensile resistance, the number of strips is determined as follows [2]:
Nt =Tmax /Tr (7)
For pullout resistance, the number of strips is determined as follows:
Nt = Tmax /Prr (8)
Discussion
By using this spreadsheet we can evaluate external and internal analyses for MSE very easy and very faster, when we planning to design new retaining walls or when we check stability for MSE such example problem that was selected from (FHWA) as we know we can checked external and internal analyses with hand calculations but when we use this spreadsheet we can save time and effort.
CONCLUSION
The common design method of MSE wall depending on LRFD was used to evaluate external and internal analyses of MSE. Then, an excel spreadsheet that used to check internal and external stabilities for a given MSE wall with simple geometry was prepared. This spreadsheet is run for the example that is given in FHWA manual (2009) also evaluate external and internal analyses. And by using this spreadsheet the program run for deferent projects by changing the property such as exposed wall height. The appendix contain the calculations for evaluate external and internal analyses by excel spreadsheet.
REFERENCES
1-Berg, R.R., Christopher, B.R., Samtani. N.C. (2009). Design of Mechanically Stabilized Earth Walls and Reinforced Soil Slopes-Volume II. (FHWA-NHI-10-025).
2- Sun, C., & Graves, C. (2013). Mechanically Stabilized Earth (MSE) Walls Design Guidance. University of Kentucky Transportation Center.
APPENDIX
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