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    Soil Dynamics and Earthquake Engineering 29 (2009) 428 437

    Contents lists available at ScienceDirect

    Soil Dynamics and Earthquake Engineering





    journal homepage:

    Earthquake-induced displacements of gravity retaining wallsand anchor-reinforced slopes

    Aurelian C. Trandafir a,, Toshitaka Kamai b, Roy C. Sidle c

    a Department of Geology and Geophysics, University of Utah, 135 South 1460 East Rm 717, Salt Lake City, UT 84112-0111, USAb Research Centre on Landslides, Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, 611-0011 Kyoto, Japanc Slope Conservation Section, Geohazards Division, Disaster Prevention Research Institute, Kyoto University, Gokasho, Uji, 611-0011 Kyoto, Japan

    a r t i c l e i n f o

    Article history:

    Received 20 October 2005

    Received in revised form

    17 April 2008

    Accepted 21 April 2008




    Gravity retaining walls


    Seismic displacements

    61/$ - see front matter & 2008 Elsevier Ltd. A


    esponding author. Tel.: +18015850491; fax:

    ail addresses:, a.tranda (A.C. Trandafir).

    a b s t r a c t

    This paper examines in terms of seismic performance, the effectiveness of anchor reinforcement against

    gravity retaining walls used to stabilize a dry homogenous fill slope in earthquake-prone environment.

    Both analyzed stabilizing measures have the same design yield acceleration estimated from a limit

    equilibrium approach. The earthquake-induced displacements are calculated using a sliding block

    formulation of the equation of motion. Sliding failure along the base of the gravity retaining wall and

    rotational failure of the soil active wedge behind the wall, as well as rotational failure of the slide mass

    of the anchor-reinforced slope were considered in the present formulation. For the specific

    characteristics of the analyzed fill slope and input horizontal ground motion, the slope reinforced

    with anchors appears to experience vertical and horizontal seismic displacements at slope crest smaller

    by 12% and respectively, 32% than the vertical and horizontal earthquake-induced deformations

    estimated at the top of the active wedge behind the gravity retaining wall.

    & 2008 Elsevier Ltd. All rights reserved.

    1. Introduction

    Gravity walls are widely used as earth retaining systemssupporting fill slopes adjacent to roads and residential areas builton reclaimed land. The October 23, 2004 Chuetsu earthquake, oneof the largest recent seismic events in Japan, triggered numerouslandslides across Niigata Prefecture; several residential develop-ments constructed on reclaimed land in Nagaoka city incurredsubstantial damage to houses and roads due to earthquake-induced failure of artificial fill slopes [1,2]. Fig. 1 is a map of thedamage in Takamachi-danchi residential area of Nagaoka cityshowing the zones affected by earthquake-induced fill slopefailures. The tension cracks behind the gravity retaining wallssupporting the fill material, and the zones of deformed andcompletely destroyed retaining walls (Fig. 1) were mapped duringa post-earthquake field reconnaissance survey a few days after theChuetsu earthquake, undertaken by an investigation team led byProf. Toshitaka Kamai of the Disaster Prevention ResearchInstitute, Kyoto University. The survey revealed that fill slopefailures were caused by the excessive seismic displacements ofthe gravity retaining walls supporting the fill material (Fig. 2). Thestructural damage to houses and roads associated with earth-

    ll rights reserved.


    quake-induced ground failure in Takamachi-danchi covered onlythose areas developed on fill slopes, whereas the structureslocated on natural slopes did not experience any visible damageduring the Chuetsu earthquake.

    During post-disaster investigations and discussions on poten-tial mitigation measures related to the landslide damage in urbanareas prone to earthquakes, the potential effectiveness of groundanchors to reinforce artificial fill slopes has been raised as analternative to the existing gravity retaining walls. With theavailability of modern execution technologies, reinforcementsystems involving permanent grouted anchors may provide bettertechnical and economical advantages compared to gravity retain-ing walls. This paper addresses the technical aspect of thisproblem by providing a comparative study on the seismicbehavior of the two stabilization techniques (i.e., gravity retainingwalls versus anchor reinforcements) applied to a dry homoge-neous fill slope subjected to horizontal earthquake shaking. Bothstabilizing measures are assumed to be designed at the samehorizontal yield acceleration, which serves as basis of comparisonfor the calculated earthquake-induced displacements.

    The dynamic displacement analysis presented in this study isbased on the sliding block model originally developed by New-mark [3] to investigate the seismic behavior of earth structures.The sliding block approach has been extensively used in analysesof the seismic performance of slopes along rotational or planarfailure surfaces in dry or saturated soils with or without,,



    Takamachi-danchi, Nagaoka City

    Nagaoka City

    400 km

    Cracks behind walls

    Collapse (fully destoried walls)

    Damaged area (deformed walls)

    Fig. 1. Map of Takamachi-danchi residential area showing the ground failure and gravity retaining wall damage during the October 23, 2004 Chuetsu earthquake, Niigata,Japan.

    A.C. Trandafir et al. / Soil Dynamics and Earthquake Engineering 29 (2009) 428437 429

    degradation of yield strength along the sliding surface [414].Richards and Elms [15] and Whitman and Liao [16] employed theNewmark procedure in evaluations of earthquake-induced dis-placements of gravity retaining walls, and Kim et al. [17]introduced a displacement approach for the seismic design ofquay walls based on the sliding block concept. Applications of theNewmark model to the development of performance-baseddesign charts for geosynthetic-reinforced slopes subjected toearthquake shaking have also been reported [18].

    The Newmark model is basically a one-block translational orrotational mechanism along a rigid-plastic sliding surface,activated when the ground shaking acceleration exceeds a criticallevel. Therefore, this rigid block approach lacks the ability ofmodeling the seismic compliance of a soil slope or the dynamicresponse of backfill behind a retaining wall and, consequently, theassociated effects on earthquake-induced displacements anddynamic wall thrust [2,1923]. However, despite this deficiency,the Newmark sliding block concept is still widely used in

    engineering practice even though finite-element commercialsoftware is currently available for the analysis of the seismicbehavior of earth retaining systems. One of the major short-comings of a finite-element analysis when applied to rigorouspredictions of permanent deformations is the requirement forsophisticated nonlinear elasto-plastic models that should be ableto account for the nonlinear inelastic behavior of the soil and ofthe interfaces between the soil and the wall elements. Theparameters characterizing these constitutive models are derivedfrom specialized laboratory tests that are not readily available tothe practitioners. Furthermore, numerical instabilities may easilyoccur in finite-element computations due to significant distor-tions of the finite-element mesh in order to achieve relativelymoderate to large permanent deformations. Dynamic finite-element meshes that would regenerate with progressive deforma-tion to avoid excessive distortions are still in a development stageand have not yet been implemented in commercial software. Forsuch reasons, the sliding block model still represents an attractive


    A.C. Trandafir et al. / Soil Dynamics and Earthquake Engineering 29 (2009) 428437430

    option when performing quantitative preliminary assessments ofearthquake-induced permanent displacements, since it requiresonly fundamental design information (e.g., geometry of theproblem), a minimum number of material properties (i.e., unitweight and shear strength parameters), and involves a robustcomputational process.

    2. Sliding block formulation for fill slope supported by gravitywall

    The geometry of the analyzed fill slope and gravity retainingwall is presented in Fig. 3 as a typical cross section fromTakamachi-danchi residential area of Nagaoka city, NiigataPrefecture, Japan, which was severely damaged by the October23, 2004 Chuetsu earthquake (Figs. 1 and 2). A retaining wall ofheight Hw 5.4 m is used to hold back the earth and maintain a

    Fig. 2. Gravity retaining wall in Takamachi-danchi residential area damagedduring the October 23, 2004 Chuetsu earthquake, Niigata, Japan.







    n (m


    Natural ground

    Gravity wall








    Fig. 3. Forces considered in the seismic sliding block analy

    difference in the elevation of the ground surface which has aheight H 7.6 m from the wall base. The case of a dryhomogeneous fill is considered herein with a unit weight g 17kN/m3, an internal angle of friction f 271 and a cohesion