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Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012

Using Steel Bars in Optimum Design of Reinforced Earth Walls by Genetic Algorithm E. Eshtehardian1, R.Taheriattar2, S.Mohammadi3, M.Farzanehrafat4 1

Project and Construction Management Dept., Tarbiat Modares University, Tehran, Iran Eshtehardian@iust.ac.ir 2 Civil Engineering Dept., Iran University of Science and Technology, Tehran, Iran Rezataheria@gmail.com 3 Civil Engineering Dept., Iran University of Science and Technology, Tehran, Iran Sina.moham@gmail.com 4 Civil Engineering Dept., Iran University of Science and Technology, Tehran, Iran Morvarid.fr@gmail.com

Abstract - Mechanically Stabilized Earth Wall (MSEW) is a kind of retaining walls promoted for its simplicity and appropriate flexibility. The most important problem in using this type of retaining walls is high operational volume. Employing new optimization methods in such circumstances play an important role for reducing costs and saving resources. So, the application of optimization techniques in large construction projects such as reinforced earth walls subjected to static forces sounds rational and useful. In this paper, Genetic Algorithm (GA) is used to achieve optimized design of reinforced earth walls. The findings demonstrated that using GA makes the construction of MSE walls cost-effective and provides safety and strength as well. Nevertheless, applying steel bars as a construction method did not contribute to cost deduction.

Prevalence of using reinforced earth walls caused to employ new methods for optimization, aiming to reduce the costs of constructing these walls. Smith et al. revealed the need for more collaborative and systematic approach to design and construction of MSE wall systems [18]. Basudhar et al. succeeded to make more than seven percent reduction in costs using optimization in design of earth walls reinforced with geotextiles [11]. Ghiassian et al. used limit equilibrium method for designing mechanically stabilized earth walls with horizontal metal strips [2]. Genetic algorithm optimization was used to find best layout of reinforcements based on the amount of consumed metal and reinforced wall fill. Integrating the simulation and optimization approaches in optimized design of MSEWs was adopted for the first time in its kind. According to the example presented in their research, costs were reduced up to 15% by using the proposed method [2]. Ghiassian et al. used PSO method to represent a model for optimization of reinforced earth walls design, which showed better results in comparison to linear programming method and costs reduced by 16 percent [1]. Despite several studies conducted to optimize MSEW design, there has not been an effort for optimum design of reinforced earth walls with steel bars in static conditions. So, it seems justifiable and necessary to conduct a scrutiny and concentrate on use of steel bars in optimum design of reinforced earth walls in order to save a great amount of financial and natural resources. This paper examined the application of steel bars in optimum design of reinforced earth walls subjected to static forces using Genetic Algorithm.

Key Words: Optimization; Genetic Algorithm; Reinforced Earth Wall; Steel Bars; Design; Construction

I. INTRODUCTION The reinforced earth wall as one of the most applicable flexible retaining walls promoted for its simplicity, appropriateness and low execution costs [1, 2]. The term â&#x20AC;&#x153;reinforced earthâ&#x20AC;? points to the soil reinforced with elements such as steel bars, metal strips or geo-textiles. Reinforcements lead to increase tension and shear strength due to the friction between soil and reinforcing materials along contacting surfaces.Broad studies have been conducted about the application and design of reinforced earth walls [3, 4, 5, 6, 7, 8, 9, and 13]. Kim and Salgado showed the advantages of LRFD over working stress design (WSD) and evaluates load and resistance factors for external stability checks of MSE walls [14]. In 2012, they did the same for MSE wall sliding and overturning checks [15]. Bathurst et al. reported results of LRFD reliability based calibration of resistance factors for pullout and yield limit states of steel grid and ribbed strip reinforced soil walls [16]. SajnaSayed et al. investigated the effects of inputs uncertainty such as soil and reinforcing properties and their interactions on value of minimum reliability index (Parametric sensitivity analysis) [10]. Abdelouhab et al. numerically analyzed the behavior of MSEWs with different types of strips [17]. ÂŠ 2012 ACEE DOI: 02.ADCS.2012.1. 504

II. STABILITY ANALYSIS In this paper, it was assumed that the MSE wall has a horizontal backfill and reinforcing bars with constant length and uniform distribution.The external and internal stabilities are guaranteed by proper dimensions of structure and reinforcements. External failure mechanism consists of sliding, eccentricity, and bearing capacity and internal failure mechanism includes tension failure and pull-out failure.

Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 The Rankin theory was applied for calculation of active earth pressure coefficients in both internal

3- Determining the most critical frictional properties at the base of the wall and choosing minimum soil friction angle according to three conditions below: -Sliding along the foundation soil (when the value of

K abI and

external K abe stabilities. These coefficients for backfill at an

C f  tg  f or Cu for cohesive soils, is lower than tgr ),

angle ², are calculated as following:

-Sliding along the reinforced soil ( r ),

(1) Where:

-Sliding along the soil-reinforcement surface for sheet

= friction angle of retained backfill.

reinforcements( tg ), is determined by direct shear test and

A. External stability controls: A.1. Sliding: The horizontal component of applied force on vertical wall is withstood by shearing force at the base of the wall. Resistance of wall is guaranteed against sliding, if the resistant force always be greater than driving force. Calculation steps are as follows [12]: 1- Calculating the components of sliding forces per unit length of wall (Fig.1):

in absence of this test, considered

2 tgr . 3

4- Calculating resistant force per unit length:

V1   r L H Rr  

 = minimum soil friction angle ( tg  , tgr , tg f )

(2)

r =

unit weight of soil in reinforced zone

 EV = vertical earth load factor L = steel bars length H = height of wall In these equations, the minimum of EV load factor (equal to 1) is used because it results in minimum resistance for sliding. 5- Calculating capacity demand ratio (CDR) for sliding: (6) If is lower than 1, the reinforcements’ length must be increased and calculations be repeated. A.2. Eccentricity: Eccentricity (e) is the horizontal distance between foundation resultant load and center of the reinforced zone (Fig.1). The variable e is calculated by summing up the overturning and resisting moments about the bottom - center of the base width - and dividing by the vertical load:

Figure 1. The Static Forces

F1 and F2 are the forces made by backfill pressure and uniform surcharge respectively, and = active earth pressure coefficient for the retained backfill

e

 b = moist unit weight of the retained backfill soil

M

MR

V

(7)

For the vertical wall with horizontal backfill and uniform live surcharge, the value of e is computed as follow:

H = height of the retaining wall q = uniform live load surcharge 2- Calculating the resultant forces per unit length of wall (Fig.1):

(8)

(3)

According to FHWA manual, eccentricity is acceptable if the location of vertical resultant force is within the middle one-

 EH = Horizontal earth load factor

half of the base width for soil foundations

 LS = live surcharge factor

and

middle three-fourths of the base width for rock foundations

 LS are 1.5 and 1.75 respectively

[12]. So, for each case of loads, the value of e

because in this way the maximum driving force will be imposed on reinforced earth wall.

must be lower than emax . Otherwise, longer reinforcements

The values of

 EH and

Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 = depth of reinforcements Resistant force of reinforcements which must be greater

(9) A.3. Bearing capacity: At first, for checking the bearing capacity of soil lied

than Tmax is calculated as follow:

under the wall, the eccentricity of resultant force ( e B ) must

(17)

be calculated:

(18) (10)

(19)

 b = allowable tension stress of reinforcements

e B varies with different load combinations and factors.

= diameter of steel bars

Therefore, the critical value must be considered by comparison of load combinations. Also, when the calculated value of eccentricity is negative, a value of 0 should be replaced in equations. Imposed vertical stress at the base of the wall is calculated by Meyerhof’s distribution:

 V F

 V   LS qL  EV . max 1 L  2e B

 = resistant factor; that is equal to 0.90 in case of static loads The number of steel bars per unit length of wall

Tal = allowable tension force for n steel bars. Figure 2 - Reinforced Earth Wall Model

(11)

Ti = allowable tension force for a steel bar..

The bearing capacity of foundation soil can be attained by the equation below:

q n  C f N C  0 .5 L '  f N 

B.2. Pull-out failure: Stability of steel bars against pull-out failure requires effective length which is necessary for resisting tension force. So, the following criteria must be satisfied:

(12)

C f = Cohesion of foundation soil CDRP 

 f = unit weight of foundation soil

= vertical stress at the reinforcement level in the resistant zone Le= length of embedded reinforcement in resisting zone F* = pull-out resistant factor C= a constant coefficient; which is equal to 2 for steel bars Coverage ratio

L  2eB (if eB is

negative, L ' is considered equal to L) Finally, for ensuring that bearing capacity of foundation soil is enough, these equations must be established:

q R  q n   V  F

Scale correction factor

q CDR B  R  1  V F

III. MATHEMATICAL DESCRIPTION Input data include strength properties of steel bars, unit costs of compacting backfill and soil reinforcing, soil characteristics such as friction angle, cohesion and unit weight. The costs needed for construction of an MSE wall consist of: 1-Reinforcements 2-Earthwork of reinforced zone 3-Field operations 4-Facing elements of wall 5-Performing tests and engineering calculations Except for first two items, the other costs are unavoidable and invariable. In this paper, fitness function evaluated the solutions by the amount of consumed steel, earthwork volume of reinforced zone and satisfaction of design criteria.

 = resistance factor; which is equal to 0.65 for MSE walls. B. Internal Stability: B.1. Tension Failure: For checking the tension failure of reinforcements, at first, the force due to lateral earth pressure in static conditions should be calculated:

(20)

Resistance factor for soil reinforcement pullout

N C , N  = Dimensionless bearing capacity coefficients L' = Effective foundation width, equal to

 Le F * V CRc  d b Le F * v  1 Tmax Tmax S H

Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 Also, the earthwork volume of reinforced zone was related to reinforcements’ lengths. So, the variables which affected both design specific cost and design criteria were: metal strips length (L), metal strips width (b), metal strips thickness (t), vertical distance between reinforcement layers ( ), and the horizontal spacing of metal strips in each layer (

This way, fitness value which was a number between 0 and 1 would decrease if the cost increased. In order to satisfy all five capacity demand ratios for different failure modes, five penalty functions considered:   CDR ( x )    C ( x )  1  CDR  min ( x )  P(x) = max  0

) (Fig.2) .

(23)

CDRmin is the minimum capacity demand ratio that must be satisfied for each constraint and C(x) was assigned to each capacity demand ratio to increase or decrease the importance of its penalty in fitness function. x could be any of these parameters:     

After calculating each penalty, the final fitness value calculated as below:

Figure 2. Reinforced Earth Wall Model

Solutions which did not provide enough capacity demand ratios were punished by penalties. Of course, based on the unit costs of steel bars and earthwork, the problem resulted in different optimized solutions. Total cost for executing unit length of MSE wall defined by: Cost = (cs n m L d2 γsteel / 4 + 1000 cf  H L/g) r

(24)

IV. RESULTS

(21)

Modeling of reinforced earth wall and employing GA optimization method were conducted by MATLAB™ Software. In order to evaluate the applicability of steel bars as reinforcements, an example considered from Ghiassian’s research [1]. The only difference between two models was the use of steel bars instead of metal strips. The input parameters and values have been shown in Table.1.

Where H is wall height and γsteel is steel density in kg per cubic meter. Also, cs and cf are unit prices of steel mass and filling work, respectively. Optimum solution considered as the solution with minimum total cost, considering below factors [12]: Capacity Demand Ratio (CDR) for external stability:  CDR for sliding  CDR for eccentricity  CDR for bearing capacity Capacity Demand Ratio (CDR) for internal stability:  CDR for tension failure  CDR for pull-out failure

TABLE I. INPUT PARAMETERS

A. Variables Range: In order to model the problem and design the chromosomes, variables must be limited to the logical specifications of MSE walls. Supposed maximum values for steel bars length (L), horizontal and vertical spacing of steel bars considered 20.48m, 2.56m and 2.56m, respectively. In addition, steel bars diameter varied from 5 to 68 mm. B. Fitness Function: At first, the cost for each solution obtained by the values of m, n, d, and L. Then, the fitness calculated using the following equation:

S, which refers to sliding O, which refers to eccentricity B, which refers to bearing capacity T, which refers to tension failure P, which refers to pull-out failure

(22)

AND

VALUES

Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 The results have also been shown and compared to Ghiassian’s outputs in Table.2. TABLE II. O PTIMUM DESIGN OUTPUTS

It could be observed that using metal strips resulted in less design specific cost in comparison to steel bars. The costs were 18, 15, 11, and 5 percent higher for 6.3, 7.8, 9.3, and 10.8 meters high walls, respectively. The lower the wall, the more the use of metal strips is justified. As it can be seen in Table.2, horizontal spacing between steel bars in optimum design is scrimped. Existing operational problems made the use of steel bars even less desirable. The optimum diameter of steel bars for all heights was at its minimum possible, indicating that application of thin and wide metal strips is definitely better solution for MSE walls. By considering the rational value of 15cm for minimum spacing of steel bars, the design specific cost for a 7.8m wall underwent a 45 percent increase. Moreover, the convergence trends for different wall heights depicted in Figure-3.

REINFORCED EARTH WALL

Figure 3. Convergence Trend for Different Heights of Reinforced Earth Wall

[4] R. Bonaparte, RD. Holtz and JP. Giroud, “Soil reinforcement design using geotextiles and geogrids”. Fluent JE Jr (ed) Geotextile testing and the design engineer, STP 952, ASTM, Philadelphia, 69–116, 1987. [5] HR. Schneider and RD. Holtz, “Design of slopes reinforced with geotextiles and geogrids”. Geotextiles and Geomembranes, 3, 29–51, 1986. [6] D. Leshchinsky and EB. Perry, “A design procedure for geotextile-reinforced walls”. Geosynthetics’87, Industrial Fabrics Association International, St. Paul, Minn, 95–107, 1987. [7] JG. Zornberg, N. Sitar and JK. Mitchell, “Limit equilibrium as basis for design of geosynthetic reinforced slopes”. Geotechnical and Geoenvironmental Engineeirng, 124, 684– 98 , 1998. [8] M. Ehrlich, and JK. Mitchell, “Working stress design method for reinforced soil walls”. Geotechnical Engineering, 120, 624– 45, 1994. [9] H. Jie and D. Leshchinsky, “General analytical framework for design of flexible reinforced earth structures”. Geotechnical and Geoenvironmental Engineering, 130, 1427–35 , 2006. [10] SajnaSayed, G. R. Dodagoudar and K. Rajagopal, “Internal Stability Analysis of Reinforced Soil Walls Using Reliability Approach”, Sri Lankan Geotechnical Society’s International

CONCLUSION According to the convergence trends and also little difference between the results of represented model and the outputs of previous research (Table.2), employing GA for optimum design of reinforced earth walls sounds proper and useful. However, using steel bars as reinforcements could not reduce the total cost of reinforced earth walls and developed operational problems such as infeasible values of horizontal spacing and diameters. So, employing steel bars in MSE walls is not at all a cost-effective construction method in real projects. REFERENCES [1]

H. Ghiassian, and K. Aladini, “Optimum design of reinforced earth walls with metal strips, PSO approach.” Sharif Journal, Tehran, Iran, 2010. [2] H. Ghiassian, and K. Aladini, “Optimum design of reinforced earth walls with metal strips, simulation-optimization approach,”Asian Journal of Civil Engineering, 10(6), pp. 641655, 2009. [3] JG. Collin, “Earth wall design”. PhD thesis, University of California, Berkeley, USA, 1986.

Full Paper Proc. of Int. Conf. on Advances in Design and Construction of Structures 2012 Conference on Soil & Rock Engineering, 2007. [11] P. K. Basudhar, A. Vashistha, D. Kousik and A. Dey, “Cost Optimization of Reinforced Earth Walls.” GeotechGeolEng 26:1–12 (2008) [12] R.R. Berg, B.R. Christopher and N.C. Samtani, “Design of Mechanically Stabilized Earth Walls and Reinforced Soil Slopes,” Volume I. Washington, D.C.: U.S. Department of Transportation (FHWA-NHI-10-024), 2010. [13] R.C. Bachus and L.M. Griffin, “A Perspective on Mechanically Stabilized Earth Walls: Pushing the Limits or Pulling Us Down?,” ASCE., Earth Retention Conference 3, ASCE., Bellevue, Washington, United States, 2010. [14]D. Kim and R. Salgado, ”Load and Resistance Factors for External Stability Checks of Mechanically Stabilized Earth

Walls,” J. Geotech. Geoenviron. Eng., 138(3), 241–251. ASCE., 2012.[15] D. Kim and R. Salgado, “Resistance Factors for MSE wall Sliding and Overturning Checks.” ASCE., GeoCongress 2012, 2012. [16] R. J. Bathurst, B. Q. Huang and T.M. Allen. “LRFD Calibration of Steel Reinforced Soil Walls,” ASCE. Geo-Frontiers Congress 2011, Dallas, Texas, United States, 2001. [17] A. Abdelouhab, D. Dias and N. Freitag, “Numerical analysis of the behaviour of mechanically stabilized earth walls reinforced with different types of strips, Geotextiles and Geomembranes,” Volume 29, Issue 2, April 2011. [18] D.L. Smith, Jr., and N.W. Janacek, “The Geotechnical Engineer’s Role in Design/Construction of MSE Retaining Walls,” ASCE., Geo-Frontiers Congress 2011, Dallas, Texas, United States, 2011.