11th INTERNA TIONAL BRlCKlBLOCK MASONRY CONFERENCE

TONGJI UNIVERSITY, SHANGHA1, CHINA, 14 - 16 OCTOBER 1997

LOCAL ST ABILITY ANALYSIS OF SOIL REINFORCED SEGMENT AL RETAINING WALL USING LIMIT S'fATES

A. J. Valsangkar I and J. L. Dawe2

1. ABSTRACT

The current trend in Canada, Europe and United States of America is to perform geotechnical designs using ultimate limit states approach. The National Building Code of Canada and the American National Standards Institute, each recommend use of load factors combined with resistance factors on the ultimate resistance calculated from unfactored soil strength. In contrast, the Canadian Foundation Engineering Manual and Eurocode are based on partial factors of safety on soil strength in combination with load factors. In this paper, the local stability artalysis of reinforced soil segmental block . retaining walls is presented using both approaches. The new design approaches are then compared with the design procedures based on a global factor of safety approach.

2. INTRODUCTION

In recent years, increasing use of geosynthetically reinforced soil behind retaining walls with segmentaI concrete block facing, as shown in Figure 1, has been reported (1). The design manuals for such retaining wall systems commonly used in USA have typically been based on a working stress design approach. [(2), (3), (4)]

The current trend in Canada, Europe and the United States of America is to do such designs using an ultimate limit states design approach. There are two approaches available within the framework of ultimate limit states design in geotechnical engineering. The Canadian Foundation Engineering Manual :'5); Eurocode (6); and the Canadian Standards Association Code for the design ofhighway bridges (7) recommend use of partial factors for both loads and strength properties of soils. This method of analysis is commonly referred to as

Keywords: Codes, Segmental blocks, Retaining walls, Ultimate Limit States

'Professor, Department ofCivil Engineering, University ofNew Brunswick, Fredericton, NB, E3B 5A3, Canada.

2Professor, Depa:1ment ofCivil Engineering, University ofNew Brunswick, Fredericton, NB, E3B 5A3, Canada.

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factored strength approach. In contrast, the National Building Code of Canada, 1995 (8); the American National Standards Institute A58 (9) and the Ontario Highway Bridge Design Code, 1992 (10) advocate use of partial factors on loads and resistance factors on the u1timate resistance computed from the unfactored strength of soil. This method of analysis is known as factored resistance approach.

Figure 1: Modular Wall

The partial factors recommended in most codes have been obtained mainly by calibrating conventional designs with global factors ofsafety. In a recent paper, Meyerhof(ll) has presented the historical development of geotechnical limit states designo The details of factored strength and resistance approaches are presented in this paper and values of partial and resistance factors according to different codes are presented (Table 1).

In earlier papers (12, 13), the authors have presented design criteria for factored strength and resistance approaches for soil reinforced segmental block retaining walls. In these papers the external and internal stability analyses were considered. In this paper, the local stability is considered using ultimate lirnit states approach and compared with the conventional design approach using global factors of safety.

3. DESIGN PROCEDURE

The design of geosynthetically reinforced wall systems is typically carried out using a lirnit equilibrium approach. Main modes offailure considered in the analysis are:

a. Externai Stability b. Internai Stability C. Global / overall Slope Stability d. Local Stability of Segmental Retaining Blocks.

The local stability analysis deals with (i) pull-out of geosynthetics from blocks (connecting failure), and (ii) bulging ofthe segmental face due to shear transfer within blocks (Figure 2). In this paper, only connection failure is considered due to page restrictions.

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Table I. Partial factors [after Meyerhof, (11)]

EC Canada

Eurocode CFEM NBCC (1993) (1992) (1995)

LOADS

Dead loads, soil 1.1 (0.9)* 1.25 (0.8) 1.25 (0.85) weight

Live loads 1.5 (O) 1.5 (O) 1.5 (O)

Enviro~enudloads 1.5 (O) 1.5 (O) 1.5 (O)

Water pressure 1.0 (1.0) 1.25 (0.8) 1.25 (O)

Accidentalloads 1.0 (O)

SHEAR STRENGTH

Friction (tan <1» 1.25 1.25 Resistance factor of 1.25 to 2.0 on

Cohesion (c) 1.25 1.25 ultimate , resistance

Slopes, earth pressure 1.4 to 1.6 1.5 using unfactored strengths

* Note: Values in parentheses apply when their effect is beneficiai

,.AClNG CONNECTION

4. LOCAL STABILITY Working Stress Design

Figure 2. Local Stability

USA

ANSIA58 (1980)

1.2 to 1.4 (0.9)

0.5 to 1.6 (O)

1.3 to 1.6 (O)

Resistance factor of 1.25 to 2.0 on ultimate resistance using unfactored strengths

At each reinforcement placement depth, D(n), as shown in Figure 3, the facing connection must have adequate strength to preclude the possibility of pull-out or rupture at the

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Acm

l~ __ ~~~ ____________ ~ ~-------------L--------------~

Figure 3. Tensile Force Calculation from Internai Stability Analysis

connection assuming that the reinforcement is subjected to maximum tensile force, F,(n), calculated from an internai stability analysis.

The use offorce, F,(n), in the connection analysis is quite conservative as the peak tensile force in the reinforcement occurs at some distance from the back face of the masonry block unit. It is customary to assume the maximum tensile force, Fin), is mobi!ized where the assumed failure plane intersects the reinforcement.

The maximum tensi!e force in the reinforcement is calculated using the average horizontal stresses at the midpoint ofthe contributing area, A,,(n) using the following equation (4):

(1)

in which Yi = moist unit weight of reinforced soil, K. = coefficient of active earth pressure, õi = interface mction angle between reinforced soi! and masonry blocks, l\1 = wall inclination (Figure 3) and

(2)

in which 4>' = angle ofinternal metion ofretained soi!.

The connection strength, Se, is typically determined by performing laboratory testing, and the results are expressed as:

(3)

in which aca = apparent minimum ultimate connection strength between geosynthetic

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reinforcement and block units (kN/m), À .. = apparent angle offriction between segmentaI units for peak shear capacity (deg), and N = normal force applied during pull-out testing (kN/m).

In soil reinforced retaining walls, the connection strength is influenced by the weight of the segmentaI block units above the reinforcing layer. The connecting strength, Sc(n) at each reinforcement location is calculated as:

(4)

in which W .. (n) = the weight of column of segmental block units supported above the reinforcement layer under consideration.

In conventional design using global factor of safety, the adequacy of the connection strength at any depth is determined by comparing it to the estimated maximum tensile force calculated using Equation (1). The factor of safety is then defined as:

FS (n) = Sin

) a F,(n) (5)

A factor of safety of 1.5 is recommended in the conventional working stress design approach. The coefficient of earth pressure, K.. is calculated using peak angle offriction ofthe reinforced soil and the maximum mobilized angle ofwall fiiction between the masonry blocks and the reinforced soil.

Factored Resistance Approach

In the ultimate limit states design approach using resistance factors and unfactored shear strength, Equation (1) is modified to calculate the factored tensile force, [Fg(n)]r as:

(6)

in which t'q is the load modification factor, and is 1.25, according the NBCC (3) and 1.2 to 1.4 according to ANSI (4). The coefficient of active earth pressure is calculated using peak angle offiiction ofthe reinforced soil and maximum mobilized angle ofwall fiiction between the masonry blocks and the reinforced soil.

The factored connection strength, S.(n) at each reinforcement location is calculated as:

1 [Sin)], = -[aa + W,.,(n) tan Àa]

J, (7)

in which ~ is the resistance modification factor and can be assigned values between 1.25 to 2.0 according to NBCC (3) and ANSI (4). Limit states design requires that:

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(8)

Comparing equations (5) and (8) leads to the following relationship ·between the global factor of safety and load and resistance factors :

(9)

Use of~ = Íq = 1.25 as specified in NBCC (3) and ANSI (4) willlead to the same overall faetor of safety as is achieved in working stress designo

Factored Strength Approach

In this approach faetored shear strength parameters have to be used employing partial factors ofsafety. The factored angle ofintemal frietion ofthe the reinforced soil is obtained from:

(10)

in which f4> = partial faetor on the soil strength = 1.25.

The faetored angle ofwall frietion, (õ;)!> is obtained by using the following equation:

(8 .) = tan-1 --' [tanõ.]

''I f. (11)

Using the factored angles, the coefficient of aetive earth pressure, (KJf is calculated using Equation 2.

The factored maximum tensile force in this approach is then calculated using an equation of the same form at Equation (I) as follows:

(12)

in which Íq is the load modification faetor equal to either 1.25 or 1.4 depending on the code used.

As the same load modificarion factor is used in the faetored resistance and faetored strength approach, the magnitude of [F,(n)]f obtained from Equation (12) will be greater than the magnitude evaluated using Equation (6) because of partial faetors used on the strength parameters.

The connection strength, Se, is normally deterrnined by laboratory testing and it is essential

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to use partial faetors similar to those used in evaluating factored strength:

(13)

in which (a.Jc = faetored apparent minimum u1timate connection strength between geosynthetic reinforcement and block units, and (À.,.)c = factored apparent angle of metion between segmental units for peak shear capacity. These faetored values are obtained from:

(14)

and (À ) = tan- I __ C_' [tan À 1

cs'f 14> (15)

in which t: = partial faetor for the apparent minimum ultimate connection strength, and a value of 1.25 is appropriate if one assumes the parameter Ilc. to be similar to the cohesion parameter for the soil.

The factored connection strength, Sç(n) at each reinforcement location is then calculated as:

(16)

Again the magnitude of[Sç(n)]c obtained from Equation (16) will be less than that obtained from Equation (7) in the faetored resistance approach.

Finally the Iimit states design criteria requires that:

[Fg(n)]r s [Sc(n)]r (17)

As the soil and conneetion strength parameters are faetored in this approach, a direct relationship between the partial faetors and the global faetor of safety caMot be explicit1y determined. However, a parametric study for a typical range of soil and connection strength parameters was condueted and the results are presented in Tables 2 and 3.

Parameter, a, in Table 2 is defined as:

a = [Fg(n)]r

F/n) (18)

in which [F.(n)lr is obtained from Equation (12) and F.(n) is calculated using Equation (1). The comenon range of shear strength parameters for typical granular fill material is assumed

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and the angle ofwall friction is taken to be (213)<1>.

Table 2. Maximum Tensile Force Ratio, IX,

<I> ~ ljJ <1>, (ôJ, K. (deg) • (deg) (deg) (deg) (deg)

40 26.7 10 33 .8 21.9 0.14

35 23.3 10 29.3 19.0 0.18

30 20.0 10 24.8 16.2 0.23

Parameter, ~, in Table 3 is defined as:

aa Àa (kN/m) (deg)

3.5 40

3.5 40

5.0 38

5.0 38

~ = [Se (n)]

[Se (n)]t

Table 3. Connection Strength Ratio, ~,

W,,(n) (aa>, (kN/m) (kN/m)

5 2.33

12 2.33

5 4.0

12 4.0

(Àa)' (deg)

33 .8

33.8

32.0

32.0

(K.), IX

0.19 1.41

0.24 1.36

0.36 1.58

(19)

~

1.7

1.7

1.6

1.6

Typical values of a.,., Àca and Ww(n) were obtained from Simac et.aI .(4). The range of Ww(n) values apply to retaining walls, 3 to 5 m in height.

The values of IX and ~ can be used to compare the global factor of safety with the factored strength approach designo

(20)

As a global factor of safety of 1.5 is commonly used in working stress design, the use of a factored strength approach coupled with partialload factors willlead to designs which are considerably more conservative than the factored resistance approach or working stress design method.

5. CONCLUSIONS

A method is presented for carrying out the local stability analysis of soil reinforced segmental block retaining walls. The study shows that the,factored resistance approach is

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comparable to designs based on working stress method. The results of a parametric study performed indicate that the factored strength approach will lead to considerably more conservative designs when compared to either factored strength approach or working stress designo A revision of partial strength and load factors is needed to make factored strength designs comparable with factored resistance approach.

6. ACKNOWLEDGMENTS

The authors thank AtIantic Masonry Research and Advisory Bureau for the support provided to do this work. Thanks are due to Ms. E. Lee in preparation ofthis paper.

7. REFERENCES

1. Simac, M.R, Bathurst, RJ., and Berg, RR, ''New Design Guidelines for Segmental Retaining Walls", Geotechnical Fabrics Report, July/August, 1993, pp. 14-29.

2. AASIITO, "Standard Specifications for Highway Bridges", Washington, D. C., 15th Edition, 1992.

3. Christopher, B.R, et ai, . "Reinforced Soil Structures: Vol.l, Design and Construction Guidelines", Report FHWA-RO-89-043, FHWA, Washington, D.C., November, 1989.

4. Simac, M.R, Bathurst, RJ., Berg, R.R, and Lothspeich, S.E., "Design Manual for SegmentaI Retaining Walls", National Concrete Masonry Association, Herendon, Va, U.S.A, 1993.

5. Canadian Geotechnical Society, "Canadian Foundation Engineering Manual", 3rd Edition, Montreal, Quebec, Canada, 1992.

6. CEN, "Geotechnical Design, General Rules, " European Committee for Standardization (CEN), Eurocode, 1993.

7. CSA, ''Design ofHighway Bridges," Canadian Standards Association, CSAlCan 3-56-88, 1988.

8. National Research Council ofCanada, "National Building Code ofCanada", NRC, Ottawa, Canada, 1995.

9. ANSL "Development of a Probability Based Load Criterion for American National Standards Institute", National Bureau of Standards, Washington, Special Publication 577, 1980.

10. MOT, "Ontario Highway Bridge Design Code," Ontario Ministry ofTransportation and Communications, Highway Engineering Division, Toronto, Ontario, 1992.

11. Meyerhof, G.G., "Development ofGeotechnical Limit States Design", Canadian

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Geotechnica/Jouma/, Vo1.32, No.1, 1995, pp. 128-136.

12. Valsangkar, A.I., Dawe, I.L., and Seah, C.K., "Limit States Design ofModu1ar Concrete B10ck Retaining Walls", Proceedings of the 7th Canadian Masonry Symposium, Hamilton, On, Canada, VoU, June, 1995, pp. 364-374.

13. Valsangkar, A.I., Dawe, I.L., and Seah, C.K., ''Factored Resistance Approach in the Design of SegmentaI Block Retaining Walls," Proceedings ofthe 4th AustraIasian Masonry Conference, Sydney, Australia, November, ·1995, pp.1 03-112.

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