NCMA TEK 15-9A 1

A n i n f o r m a t i o n s e r i e s f r o m t h e n a t i o n a l a u t h o r i t y o n c o n c r e t e m a s o n r y t e c h n o l o g y

SEISMIC DESIGN OF SEGMENTAL RETAINING WALLS

TEK 15-9AStructural (2010)

INTRODUCTION

This TEK describes a method of analysis and design for conventional and geosynthetic-reinforced segmental retain-ing walls (SRWs) under seismic loading. The methodology extends the approach for structures under static loading to simple structures that may be required to resist additional dynamic loads due to earthquakes. The seismic design

NCMA Design Manual for Segmental Retaining Walls and SRWallv4 design software approach and uses the Mononobe-Okabe (M-O) method to calculate dynamic earth forces. The methodology adopts many of the recommendations contained in AASHTO/

mechanically stabilized earth (MSE) structures subjected Design Manual

for Segmental Retaining Walls goes beyond the AASHTO/FHWA publications by addressing the unique stability re-quirements of SRWs that are constructed with a dry-stacked column of modular block units. Properly designed reinforced SRWs subjected to seis-mic and/or dynamic loading will in general perform well

be performed in addition to the static analysis to satisfy all Design

Manual for Segmental Retaining Walls. The project's geo-technical engineer should select the ground acceleration

of practice and site conditions. NCMA’s methodology uses a displacement approach that explicitly incorporates

Ground Acceleration (PGA) following FHWA’s approach. It should be noted that outward displacements caused by "near" maximum probable magnitude earthquakes may

of the seismic design is to prevent catastrophic failure (a

to be evaluated after a near design event.

Guide to Segmental Retaining Walls (ref. Inspection Guide for Segmental Retaining

Walls Design Manual for Segmental Retaining Walls.

DESIGN ASSUMPTIONS

The NCMA seismic design and analysis methodology applies when the following conditions are met:

horizontally at the base and yield laterally through the height of the wall. This assumption is based on installa-tion recommendations of a system that is placed on soils

unreinforced weak concrete that can crack if necessary.

and homogeneous. Soil strength is described by the Mohr-Coulomb failure criterion. The apparent cohesive strength component reported under Mohr-Coulomb failure criterion is ignored for conservatism. Adequate drainage details should also accompany the design to ensure the soils re-main unsaturated and that the assumed design conditions are reached and maintained.

kv ground acceleration is ignored based on the presumption that horizontal and vertical accelerations associated with a seismic event do not coincide.

constant horizontal foreslope angle.

Related TEK: Keywords: -

tural design

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the facing column given their transient nature.-

ing to the full height of the SRW facing units (i.e. wall design H).

be securely attached such that they cannot be dislodged during ground shaking.

with the exception of bearing capacity analyses.-

tive failure wedge.

base of the SRW unit column and/or geosynthetic reinforced

sources of instability.

numerical procedures using the same principles of M-O formulation be used. These include the

-

slope stability programs that are outside of the scope of the NCMA Design Manual. A limitation of the pseudo-static seismic design method presented here is that it can only provide an estimate of the margins of safety against

provide any direct estimate of anticipated wall deformations. This is a limitation common to all limit-equilibrium design methods in geotechnical engineering.

GEOSYNTHETIC REINFORCED SEGMENTAL RETAINING WALLS—MODES OF FAILURE

Stability analyses for geosynthetic reinforced SRW systems under static and seismic loading conditions involve separate calculations to es-

facing and internal compound modes of failure (Figure 1). External stability calculations consider the reinforced soil zone and the facing column as a monolithic gravity structure. The evaluation of

similar to that used for conventional reinforced concrete masonry gravity structures. Internal stability analyses for geosynthetic reinforced soil walls are carried out to ensure that the structural integrity of the reinforced zone is pre-served with respect to reinforcement over-stressing

internal sliding along a reinforcement layer. Facing stability analyses are carried out to ensure that the facing column is stable at all el-

2 NCMA TEK 15-9A

Table 1—Recommended Minimum Factors of Safety and Design Criteria for

Conventional/Reinforced SRWsFailure Modes: Wall Design Static Seismic

FSsl 1.5 1.1FSot 1.1/1.5

FSsc/FSsl(i) 1.5 1.1FSto 1.5 1.1

FSpo 1.5 1.1FScs 1.5 1.1

Fcom 1.3 1.1Failure Modes: Geotechnical Concerns Static Seismic

FSbc 1.5FSgl 1.3—1.5 1.1

Figure 1—SRW Failure Modes for Stability Analysis

Horizontal Movement Rotation

Rotation

Moment

SettlementTilt

Base Sliding Overturning

Excessive Settlement

A. External Stability

Horizontal Movement Horizontal Movement

Movement between courses

Pullout Tensile Overstress Internal Sliding

Facing Connection

B. Internal Stability

C. Local Stability of SRW Units

E. Geotechnical Concerns

Crest Toppling

Global/Slope Stability

D. Internal Compound Stability

Rotation

Tilt

Bearing Capacity

evations and connections between the facing units and reinforcement layers are not over-stressed. Internal compound stability analyzes the coherence of the block-geogrid system through potential compound slip circles that originate behind the soil-reinforced SRW and exit at the face of the wall. Minimum recommended factors of safety (FS) of static and seismic design of geosynthetic reinforced SRW structures are

seismic design are taken as 75% of the values recommended for stati-cally loaded structures following AASHTO/FHWA practice. Potential concerns such as settlement of reinforced SRW

foundation soils is not considered here. Separate calculations for foundation-induced deformations may be required by the designer.

involving volumes of soil beyond and below the base of the

computer programs are available that consider the effects of both

EXTERNAL STABILITY

External stability calculations are similar to those for conven-

to wall weight and the dynamic earth increment. Dynamic earth

forces in otherwise conventional expressions for the factor of

applied when calculating external seismic forces on conventional

INTERNAL STABILITY

the static stability analysis of SRWs is extended to the dynamic

are modeled as tie-backs with the tensile force Fi in layer n equal to the earth pressure integrated over the contributory area Ac(n) at the back of the facing column plus the corresponding wall inertial force increment. Hence:Fi(n) = khint w(n) + Fgsta(n) + Fdyn(n)where: khint w(n) = wall inertial force increment

NCMA TEK 15-9A 3

Fgsta(n) = static component of reinforcement loadFdyn(n) = dynamic component of reinforcement load. Internal stability calculations are also similar to those car-ried out for conventional static conditions with the inclusion of

is applied to internal stability with the exception of internal sliding Pdyn. Figure 3 shows the static and dynamic

earth pressure distribution for internal stability calculations. The calculations for internal stability are presented in detail in Reference 1.

Figure 2—External Stability Calculation Variables, Reinforced SRW Structures

K (H )

0.5[0.5 K (H )]0.5HL < Hmin

Lmin

B'f

ext

extext

a dyn

L

h

H

uH

Wu

arP = K (H )s2

2

PsH (H )/2

e

DYNAMIC INCREMENTQ applied

foundation pressure

a

Rs

2e

rW hs

dynH

r(s)W e

aq2

IRh ext

H

L"0.5H

extext

qdP

STATIC COMPONENT

qdP = (q )K (H )ad

e

(H )/2ext

dynV

dyn0.5 P

qdHPqdVP

e

(H )/3ext

PsV

Ps

0.5 P0.5 P

W'

Static earth forcedue to soil

Static earth forcedue to dead load

Dynamic earth forceincrement

wW rsWIRP

W'

W'i

WrWwPIR

Wrs

L'

Figure 3—Geometry & Forces Used to Calculate Reinforcement Loads for

Reinforced SRW Structures

K(H )

0.5 K(H )

dyn (n) i

a dyn

H

DYNAMICINCREMENT

c(n)A

( - )i

(n)D

w(n) gstat(n)

Soil + Dead SurchargeSTATIC

COMPONENT

( - )i ( - )i

k W + F + F = Fhint

FACING STABILITY

Facing stability calculations are similar to those used for the static analysis with the addition of the dynamic load. To

each reinforcement elevation is compared to the tensile force Fi

Pdyn is used to mirror the external overturning analysis.

INTERNAL COMPOUND STABILITY

The consideration of seismic load for internal compound stability calculations is based on the addition of an inertial force (khW The incorporation of an additional dynamic load or inertial force is calculated as follows:

where: di = vertical distance from the gravity center of the soil mass

to the center of the slip surfaceR = radius of the slip surface

REFERENCES1. Design Manual for Segmental Retaining Walls

SRWallv43. Mechanically Stabilized Earth Walls and Reinforced Soil Slopes Design and Construction Guidelines

5. Guide to Segmental Retaining Walls6. Inspection Guide for Segmental Retaining Walls,

8. Field Observations of Reinforced Soil Structures Under Seismic Loading

Retaining Walls Stand Up to the Northridge Earthquake

4 NCMA TEK 15-9A

NCMA and the companies disseminating this technical information disclaim any and all responsibility and liability for the accuracy and the application of the information contained in this publication.

NATIONAL CONCRETE MASONRY ASSOCIATION

www.ncma.org

Tavailable = available reinforcement force at the location of the intersection of the failure plane

Favailable = available facing force at failure plane exit.

FIELD PERFORMANCE

SRW performance during earth-quakes is generally considered to be

SRWs within 31 miles (50 km) of the

Northridge earthquakes have shown that this type of retaining wall system can withstand considerable horizontal and vertical accelerations without experiencing unacceptable defor-mations. Similar to other structures

designer should be aware that SRWs may need to be evaluated if

The design procedures presented in Design Manual for Segmental Retaining Walls

take advantage of SRW technology to build safe and economical retaining walls to withstand seismic forces.

FS

W PFS

T Favailable available

=

++

+ +( ) tan

cos (sin tan ) /( cos )

!" " !

"!!!

!! + +( )sinW P k W dRhi"

Figure 4—Soil Slice Showing Dynamic

Load

Soil slice

NS

ö, ,c = 0

P

Wk Wh

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