The stability of soil slopes stabilised with vegetation V. OPERSTEIN  and S. FRYDMAN   Faculty of Civil Engineering, Technion, Israel Institute of Technology This is the third and ﬁnal paper describing a research project, carried out at the Technion in Israel, to study the inﬂuence of plant roots on the stability of slopes. The two previous papers described earlier stages of the research, in which root and soil properties were established, and the reliability of the numerical scheme, based on the use of the ﬁnite difference code FLAC, was checked. The present paper uses the previous results as a basis for analysing the stability of root-reinforced chalky slopes under various conditions. It is demonstrated that the stability analysis of root-reinforced slopes must consider the roots as indivi- dual elements, and take account of their properties, as well as their interaction with the surrounding soil. Use of the ‘equivalent layer ’ approach, in which the reinforced soil is replaced by an equivalent soil with strength properties obtained from laboratory shear tests, is likely to be signiﬁcantly non-conservative. The inﬂuence of root incli- nation is studied, and it is shown that vertical roots do not contribute signiﬁcantly to slope stability, whereas a con- siderable contribution is provided by roots that are perpendicular to the slope face. The numerical scheme may be used for the analysis of more complex soil–root interaction problems. Keywords : Numerical analysis; shear strength; slopes; soil stabilisation; vegetation Cet expose ´ est le troisie `me et le dernier d’une se ´rie de ´crivant un projet de recherche re ´alise ´ au Technion en Israe ¨l, aﬁn d’e ´tudier l’inﬂuence des racines de plantes sur la stabilite ´ des pentes. Les deux pre ´ce ´dents expose ´s de ´crivent les premie `res phases de la recherche, phases au cours desquelles les proprie ´te ´s des racines et du sol ont e ´te ´ e ´tablies et la ﬁabilite ´ de la formule nume ´rique, base ´e sur l’utilisation du code de diffe ´rence ﬁnie FLAC, a e ´te ´ ve ´riﬁe ´e. Cet expose ´ utilise les pre ´ce ´dents re ´sultats comme base pour analyser la stabilite ´, dans diverses conditions, des pentes crayeuses renforce ´es par des racines. Nous de ´montrons que l’analyse de stabilite ´ des pentes renfor- ce ´es par des racines doit conside ´rer les racines en tant qu’e ´le ´ments individuels et tenir compte de leurs pro- prie ´te ´s ainsi que de leur interaction avec le sol environ- nant. L’utilisation de la me ´thode ‘couche e ´quivalente’ dans laquelle le sol renforce ´ est remplace ´ par un sol e ´quivalent, dont les proprie ´te ´s de re ´sistance ont e ´te ´ de ´termine ´es a ` partir d’essais de cisaillement en laboratoire, sera proba- blement non conventionnelle. Nous e ´tudions l’inﬂuence de l’inclinaison des racines et nous montrons que les racines verticales ne contribuent pas de manie `re signiﬁca- tive a ` la stabilite ´ des pentes alors que les racines perpendi- culaires a ` la face de la pente ont une action conside ´rable. La formule nume ´rique pourra e ˆtre utilise ´ pour l’analyse de proble `mes d’interaction sol-racines plus complexes. Introduction This paper presents the ﬁnal stage of a three-part research project aimed at developing a methodology for the design and analysis of stabilisation of ﬁll slopes by vegetation. The ﬁrst stage of the research (Operstein and Frydman, 2000) studied the inﬂuence of plant roots on the shear strength of a chalky ﬁll and of a heavy clay. That stage included a study of the tensile deformation and strength properties of roots of several plants, the pull-out resistance of the plants from the chalky soil, and the inﬂuence of the roots on the shear strength and shear stress–deformation relations of the soils. Shearing tests on soil columns of 200 mm diameter, with and without roots, were performed in a large direct shear apparatus, and expressions were developed for the root contribution to strength. In the second stage (Frydman and Operstein, 2001), parameters required for the numerical analysis of reinforced, chalky ﬁll slopes were determined, and a scheme was developed for the analysis of a root- reinforced soil system, using the ﬁnite difference computer code FLAC (Itasca, 1993); the reasons for the choice of that particular numerical code were discussed by Frydman and Operstein. The scheme involves the use of the hyperbolic constitutive model to represent the soil, and the roots are modelled by cable elements. The applicability of the scheme to root-reinforced soil was veriﬁed by analysing the large direct shear tests, while incorporating parameters obtained independently, in the ﬁrst stage of the research. A compari- son between the results of analyses and of tests showed good agreement, indicating that the analysis scheme should be suitable for the analysis of root-reinforced slopes. This last stage of the research was aimed at applying the above numerical scheme to the design and analysis of slopes reinforced with plant roots. Analysis of soil slopes without vegetation Before attempting to apply FLAC to the analysis of root- reinforced slopes, a series of analyses was carried out for non-reinforced slopes. Numerical schemes such as ﬁnite elements and ﬁnite differences do not calculate stability Ground Improvement (2002) 6, No. 4, 163–168 163 1365-781X # 2002 Thomas Telford Ltd (GI 135) Paper received 10 August 2001; last revised 27 February 2002; accepted 21 March 2002