Trench stability in cohesive soil

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1 Trench stability in cohesive soil K. Gorska 1 Wroclaw University of Technology, Poland ABSTRACT Trench is connected to very narrow and deep excavation filled with bentonite suspension. This paper presents estimation of its stability in cohesive soil. The stability is assessed by two calculation methods. The first involves the equilibrium of forces acting on the rigid wedge. The second one includes numerical calculations conducted in Plaxis 3D Foundations. A few examples having different dimensions (length and depth) are analyzed in uniform soil conditions. Graphs defining the dependence of length, depth and factor of safety are presented. It is found that for long trenches (L 6m) the soil kinematics at failure coincides with the literature data. Short trenches are under a large influence of the arching effect and cohesive forces. The limit equilibrium method can be used under the condition of employing a factor, which reduces the value of the earth pressure. Keywords: retaining wall, trench, safety, stability, numerical analysis, arching, failure. 1 INTRODUCTION Trench excavation is widely used in geotechnical works. It is performed as the first stage of construction for diaphragm walls, barrettes or slurry walls [3, ]. A deep vertical cut in the ground is excavated under a slurry suspension. The first application of diaphragm walls was in the early sixties [] and now they are continually used successfully supporting the construction of deep excavations or deep foundations. Walls made from concrete and steel work well against high values of internal forces and permit the transfer of loads from leaning slabs. Another advantage is water resistance that is only provided by a proper execution of panel joints. Van Tol presents four cases of leakage through the diaphragm walls at stop end joints in deep excavations, which led to very serious settlement behind the walls []. Different variations in construction phases result in a huge range of implementation possibilities, e.g. slurry walls in which a suspension is mixed with cement that hardens []. The first stage of construction is critical for the construction process. In the following phases, the stability of the surrounding soil is easier to maintain. During the concreting process pressure inside the trench increases (slurry is being continuously replaced by concrete) as does the exerted force on the faces and the toe of the trench. There is a widespread belief among geoengineers that if the slurry level exceeds the water level by more than 1 m and the slurry unit weight is greater than.5 kn/m 3 trench stability is guaranteed; although in this case the safety margin is unknown. The primary question is in what situations special care or preparations 1 Wroclaw University of Technology, ul. Wybrzeze Wyspianskiego 7, Wroclaw. karolina.gorska@pwr.wroc.pl

2 during the trenching process should be taken. Usually, major problems are not related to the trenching process, but are connected to human error. There are several theories for calculating trench stability that have been implemented in practice. The first group of theories concerns D cases with long trenches. The wedge is triangular and the slip surface is inclined by the angle θ cr = π/4 + φ /, as in the Coulomb criterion, where φ is friction angle. Initially only homogeneous, perfectly cohesive soil conditions without groundwater were analyzed by Nash and Johns [5]. Later, other forces such as groundwater pressure and a varying slurry level were taken into consideration (Morgerstern and Amir Tahmasseb [4]). These solutions can be assumed for shallower rather than longer trenches (trenches with dimensions of L<H). If 3D working conditions are considered, the forces acting on the sides - shear forces and cohesion forces - must be analyzed. This represents the simplest transition from D to 3D analysis and was proposed by Prater [7]. Another modification is the inclination of the sides into the interior of the wedge. The inclination angle α = π/4+φ/ proposed by Washbourne [11] seems to have a too small value according to numerical calculations conducted by the author. This angular wedge shape is easily described, but it differs from the shape observed in the numerical calculations. The first solution with a curved failure surface was presented by Piaskowski & Kowalewski in 1965 [6]. This solution uses a vertical elliptic cylinder cut by a critical plane. The latest 3D solutions by Tsai and Chang employ a more realistic smooth and convex shear surface [9]. This method uses vertical columns as a generalization for standard D slices. This paper presents two further methods of analysis for trench stability. LIMIT EQUILIBRIUM METHOD The first method involves the equilibrium of forces acting on the rigid wedge and comes from the Coulomb method for two-dimensional stability of a slope with an infinite length [1]. The shape of the wedge is a prism with triangular sides (see Figure 1a). Acting forces on the wedge are (see Figure 1b): the bulk weight of the wedge W, the resultant force on the slip surface R, cohesion force on the slip surface C R, the earth pressure P h and the hydrostatic slurry pressure P s. To simulate spatial working conditions, shear forces S s and cohesion forces C on the wedge sides are applied. This method provides a very quick and accurate estimation for engineering purposes. Figure 1 a) 3D-view of the sliding block; b) Polygon of acting forces in the plane of symmetry. In the limit-equilibrium method for this specific case the stability of cohesive soil P h and P s must have equal values. This statement leads to the determination of the failure surface inclination. For the D case it is θ cr = π/4 + φ /. P h is determined from the projection of all acting forces in the horizontal and vertical directions. The equilibrium equations are as follows: where: Fz = 0 Ph + S sz + Cz + CRz = Rz F = W = Ry + CRy + S sy + C y 0 y W 0.5 H ctgθ L z = γ y ( ) R = R tg θ ϕ S = K γ ctgθ H 3 /6 n S = S tgϕ s n S = S cosθ sx S = S sinθ sz s s (1)

3 C = 0.5 ctgθ H c C = C cosθ x C = C sinθ z C = L H c/sinθ R 3 FINITE ELEMENT METHOD The second method includes numerical calculations conducted in Plaxis 3D Foundations. This program uses a finite element method. During numerical calculations, displacements and stress in the surrounding soil are determined. This enables estimating the shape and range of the wedge and to establish if the arching effect occurs. The trench excavation process in a block of soil is taken into consideration and the advantage of two axes of symmetry is used. On vertical surfaces of the resulting solid boundary conditions allowing only vertical movement. On the basis of body movement is blocked in all directions. Surface area remains free. At first the sensitivity of the size of the modeled area in relation to the mesh size was tested. Within three blocks different in size eventually a block sizes m was adopted, as to eliminate the effect of the impact of sides, and at the same time not unduly magnifying the size of the task. Adopted regions of different mesh size reduce computation time without significantly affecting the accuracy of the results. The excavation process is modeled as the removal of m thick layers of soil and the application of slurry pressure. For simplification, the hydrostatic slurry pressure is assumed as external stabilizing load. It increases linearly with depth and is applied to all faces of the trench, including the toe. The slurry level is kept unchanged at the ground surface. To determine the shape of the wedge, the standard procedure of tanφ/c reduction is used. Since no limit state i.e. no failure is observed, the interpretation of the FS/displacement curve is made. The FS/displacement curve indicates a rapid change in the inclination. The factor of safety increases until soil displacements reach values of 3 cm. The exact displacement value depends on which point is observed. Points near the toe have larger displacements. FS values for displacements greater than cm are constant. In addition, in examining the FS/step curve a point of deflection is observed at the same step and the same displacement. 4 EXAMPLES A few examples having different dimensions (length and depth) are analyzed in uniform soil conditions. Graphs defining the dependence of length, depth and factor of safety are presented. 4.1 Soil conditions In the examples, uniform ground conditions with the Coulomb criterion are analyzed. The material parameters are presented in Table 1. No water level is considered. The unit slurry weight is.5 kn/m 3. No filtration or improvement of the soil conditions in the surrounding layer is considered. Table 1. Parameters of the homogeneous soil. γ K a φ c E ν kn/m 3 kpa MPa Clay 0 0, Trench dimensions An analysis of typical trench dimensions was conducted for the following dimensions: length L 3 to m, width B 1.0 m and depth H to m. 4.3 Results During the excavation process, soil and slurry pressures acting on the trench sides are in equilibrium. No change in the stresses around the trench is observed. At the toe of the trench, the force exerted by the slurry causes a reduction of the stress in the soil. This is also influenced by the smaller unit weight of the suspension compared to the soil. Figure presents the total displacements after excavation with the largest values of 5.5 mm occurring at the center of the toe. This is typical for the rebound connected

with the removal of the overburden load. In this case, the exerted pressure decreases. θ - inclination of failure surface 0 75 70 65 60 55 50 3 5 7 9 L - length of trench D Figure 3. Plots of θ cr vs.

4 with the removal of the overburden load. In this case, the exerted pressure decreases. θ - inclination of failure surface L - length of trench D Figure 3. Plots of θ cr vs. section length L for different depths H of the trench simplified calculations. Figure. 3D total displacements for a 6 m long trench after excavation finite element method. Figure 3 confirms the spatial working conditions. For every trench depth the inclination of the failure surface decreases with the increase in its length. This is caused by the different share of forces acting on the trench sides and the wedge weight in the P h value. The following rule applies: a longer trench leads to a smaller share of acting forces. For very long trenches the inclination angle is the same as the D Coulomb solution and is equal to θ cr = π/4 + φ / (dotted line). Due to cohesion forces, the inclination angle is greater than for cohessionless soil [1]. For comparing the results of the simplified calculation method and the numerical calculations, the factor of safety is defined as follows: tan φ c FS = = () tanφ red c red where: tan φ red and c red are reduced values reached in calculation step assumed as a failure. The limit equilibrium P h = P s must be reached for φ red. This definition does not reveal any local areas of instability and it only has a global character. FS - limit equilibrium method 4,5 4 3,5 3,5 1, L - length of trench Figure 4. Plots of FS vs. section length L for different depths of the trench limit equilibrium method. FS - finite element method 4,5 4 3,5 3,5 1, L - length of trench Figure 5. Plots of FS vs. section length L for different depths of the trench finite element method.

This is not observed for the finite element method (Figure 5 and Table 3) and is caused by the formulation of method solutions.

5 The general rule that factors of safety decrease with an increase in length for the same depth of trench is fulfilled (Figures 3, 4 and 5). For the limit equilibrium method a surprising phenomenon occurs, i.e. the tendency of higher FS values for very short trenches of the same depth (Figure 4 and Table ). This is not observed for the finite element method (Figure 5 and Table 3) and is caused by the formulation of method solutions. Very short trenches shear and cohesion forces have a determinant influence on the earth pressure value. This is also a result of the arching effect. If the trench length increases, acting forces decrease and the arching effect disappears. Table. FS values limit equilibrium method. H depth of L length of the trench the trench Table 3. FS values finite element method. H depth of L length of the trench the trench Figure 7. 3D total displacements for a 3 m long trench at failure finite element method. Results of this phenomenon are observed on displacement maps. In figure 6, the shape of the wedge is easily recognized. It can be assumed that the prism approximation used in the limit equilibrium method is acceptable. The shape and the inclination of the failure surface (θ = 65 ) is close to the simplified calculations. Washbourne assumption [11] for sides inclination angle α is highly underestimated. If the length of the trench decreases, the displacements at the higher part increase very slowly during excavation progress after it reaches 6m (see Figure 7). For a 3 m long trench, no wedge is observed. FS - limit equilibrium method 4,5 4 3,5 3,5,5 3 3,5 4 4,5 FS - finite element method Figure 6. 3D total displacements for a 6 m long trench at failure finite element method. Figure. A set of points FS finite element vs. FS limit equilibrium method for the same geoengineering data.

6 A comparison of results from both methods is presented in Figure. Each concentration of results represents different lengths of the trench. The bottom points represent a 6 m long trench while the top points represent a 3 m trench. The limit equilibrium method produces higher factor of safety values than the finite element method. In the figure, the dashed line shows a perfect correlation of results. Although the limit equilibrium method gives results in a very short time, one should take into consideration the overestimated values of FS. Another advantage of this method is that a specialized computation program is not necessary. For engineering purposes, the results obtained from the limit equilibrium method can be taken into consideration only when employing a factor, which would reduce the value of the earth pressure. This kind of factor is used by Piaskowski and Kowalewski [6] and it is a function of the length, the depth and the friction angle. 5 CONCLUSIONS Short trenches in cohesive soil are under a large influence of the arching effect and cohesive forces. The wedge is not observed in the finite element method. In the limit equilibrium method factors of safety are greater for deeper trenches. Curves on the graph intersect. The failure surface inclination decreases with the length of the trench. The Coulomb criterion is the lower bound estimation. FS values are between.5 and 4.5 and are much higher than expected to fulfill the stability conditions. The limit equilibrium method can be used under the condition of employing a factor which reduces the value of the earth pressure. This kind of factor is used by Piaskowski and Kowalewski [6] and it is a function of the length, the depth and the friction angle. REFERENCES [1] W. Brzakala, K. Gorska, On safety of slurry wall trenches, Studia Geotechnica et Mechanica XXX No.1 (00), [] G.M. Filz, T. Adams, R.R. Davidson, Stability of long trenches in sand supported by bentonite water slurry, Journal of Geotechnical and Goenviromental Engineering 130(9) (006), 9 91 [3] I. Hanjal, J. Marton, Z. Regele, Construction of slurry walls, Akad.Kiado, Budapest, 194. [4] N.R. Morgenstern, J. Amir-Tahmasseb, The stability of a slurry trench in cohesionless soils, Geotechnique (4) (1965), [5] J.K.T. Nash, G.K. Jones, The support of trenches using fluid mud, Grouts and Drilling Muds in Engineering Practice (1963), [6] A. Piaskowski, Z. Kowalewski, Application of tixotropic clay suspensions for stability of vertical sides of deep trenches without strutting, 6th Int.Conf.SMFE Montreal Vol.III (1965), [7] E.G Prater, Die Gewölbewirkung der Schlitzwände, Bauingenieur 4 (1973), [] A.F. van Tol, V. Veenbergen, J. Maertens, Diaphragm walls, a reliable solution for deep excavations in urban areas?. In s.n. (Ed.) DFI and EFFC, London, Deep Foundation Institute, (0), 1-9. [9] J.S. Tsai, J.C. Chang, Three dimensional stability analysis for slurry trench wall in cohesionless soil, Canadian Geotechnical Journal 33 (1996), [] C. Veder, Excavation of trenches in the presence of bentonite suspension for the construction of impermeable and load bearing diaphragms. Proceedings of Symposium on Grouts and Drilling Muds in Engineering Practic,. London, (1963), [11] J. Washbourne, The three dimensional stability analysis of diaphragm wall excavation, Ground Engineering 17(4) (194), 4 9. [] P.P. Xanthakos, Slurry wall as structural system, McGraw Hill, New York, 1979.

On Stability Analysis of Slurry Wall Trenches

On Stability Analysis of Slurry Wall Trenches Wlodzimierz BRZAKALA, Karolina GORSKA, Institute of Geotechnics and Hydroengineering, Faculty of Civil Engineering Wroclaw University of Technology, Wybrzeze