Technical Communication Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis K.M. Kouzer a , Jyant Kumar b, * a Department of Civil Engineering, Govt. Engg. College, Thrissur 680 009, Kerala, India b Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, India article info Article history: Received 15 September 2008 Received in revised form 10 February 2009 Accepted 11 February 2009 Available online 20 March 2009 Keywords: Anchors Failure loads Limit analysis Numerical analysis Optimization Uplift capacity abstract The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (n c ) is determined. On account of interference, the magnitude of n c is found to reduce continuously with a decrease in the spac- ing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction A number of theories are available to determine the ultimate uplift capacity of isolated horizontal strip anchors [1–6]. However, only limited information is available in the literature to find the interference effect on the ultimate vertical uplift capacity of a group of closely spaced anchors. The effect of interference on the uplift capacity of a group of anchors was theoretically studied by Meyerhof and Adams [1] on the basis of the limit equilibrium ap- proach in which the vertical equilibrium of a rectangular soil wedge encompassing the outer edges of the extreme anchors in the group was considered. Small scale model tests were later per- formed by Hanna et al. [7] on circular anchors and by Geddes and Murray [8] on square anchors to study the interference effect on the uplift capacity of a group of anchors. Kumar and Kouzer [9] have theoretically examined the effect of anchors’ spacing on the magnitude of the vertical uplift resistance for a group of strip an- chors placed horizontally in a cohesionless medium; the analysis was carried out by using an upper bound limit analysis with the employment of a simple rigid block mechanism bounded by planar rupture surfaces. Further, by using the finite elements limit analy- sis approach, Kouzer and Kumar [10] have computed the vertical uplift resistance for a group of an infinite number of strip anchors embedded in sand. It is understood from the existing theoretical and experimental observations that the vertical uplift capacity of the anchors reduces quite significantly with a decrease in the spac- ing between the anchors. In the present study, it is intended to per- form a rigorous computational analysis to find the vertical uplift resistance of a group of two strip anchors placed horizontally in a cohesionless medium. The analysis is carried out by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. The effect of the spacing be- tween the anchors (S) was studied in detail for different embed- ment ratios of anchors. The nodal velocity patterns were also studied. The results from the computational analysis were com- pared with the available theoretical and experimental results from the literature. 2. Definition of the problem A group of two closely spaced strip anchor plates, each of width B, are spaced at a clear distance S as shown in Fig. 1a. The anchor plates are embedded at a depth d from the ground surface; the embedment ratio (k) of the anchor is d/B. The anchors are perfectly rigid and are placed in a cohesionless soil medium. The thickness of the anchor plate is assumed to be negligible as compared to its width. The angle of interface friction between the anchor plate, both upper and lower surface, and the adjoining soil mass was as- sumed to be equal to /; it is, however, known that for an isolated anchor the roughness of the anchor plate hardly affects the vertical uplift resistance of the horizontal anchors [2,5] and it was also 0266-352X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.compgeo.2009.02.003 * Corresponding author. Tel.: +91 80 22933119; fax: +91 80 23600404. E-mail address: jkumar@civil.iisc.ernet.in (J. Kumar). Computers and Geotechnics 36 (2009) 1084–1089 Contents lists available at ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo