Assessing potential cracking zones in embankment dams

Transcription

1 Southern Cross University 23rd Australasian Conference on the Mechanics of Structures and Materials 2014 Assessing potential cracking zones in embankment dams Ke He University of New South Wales Chongmin Song University of New South Wales Robin Fell University of New South Wales Publication details He, K, Song, C, Fell, R, Birk, C 2014, 'Assessing potential cracking zones in embankment dams', in ST Smith (ed.), 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23), vol. II, Byron Bay, NSW, 9-12 December, Southern Cross University, Lismore, NSW, pp ISBN: epublications@scu is an electronic repository administered by Southern Cross University Library. Its goal is to capture and preserve the intellectual output of Southern Cross University authors and researchers, and to increase visibility and impact through open access to researchers around the world. For further information please contact epubs@scu.edu.au.

2 23rd Australasian Conference on the Mechanics of Structures and Materials (ACMSM23) Byron Bay, Australia, 9-12 December 2014, S.T. Smith (Ed.) ASSESSING POTENTIAL CRACKING ZONES IN EMBANKMENT DAMS Ke He* Kensington, NSW, 2052, Australia. (Corresponding Author) Chongmin Song Kensington, NSW, 2052, Australia. Robin Fell Kensington, NSW, 2052, Australia. Carolin Birk Kensington, NSW, 2052, Australia. ABSTRACT Internal erosion and piping is the cause of about half of large embankment dam failures. Most internal erosion and piping failures occur due to concentrated leak erosion which is initiated by a crack in an embankment or its foundation. Differential settlements occur due to the variations in the height of the embankment across the valley in which the dam is constructed. This can lead to low stress and tensile strain zones in which cracks may form. This paper presents two dimensional numerical analyses of the deformations and stresses in the cross valley profile during construction, and assesses the potential cracking zones. These analyses are based on the use of the commercial finite element software ABAQUS and staged construction simulation is incorporated in the models. It is shown that tensile and low stress zones form at the crest of the dam near the abutments, and large tensile strain zones may occur over discontinuities and irregularities in the cross valley profile. A parametric study has been carried out to assess the effect of the abutment slope, step width and height on these potential cracking zones. KEYWORDS Embankment, concentrated leak erosion, cracking, numerical modelling. INTRODUCTION Concentrated leak erosion is a form of internal erosion and piping which occurs in embankment dams, levees, and their foundations. Internal erosion and piping is the cause of about half of large embankment dam failures (Foster et al, 2000). Most internal erosion and piping failures occur due to concentrated leak erosion which is initiated by a crack in an embankment or its foundation. As an embankment dam is constructed the partially saturated compacted soil in the embankment consolidates and settlement occurs. Where the valley sides are steep and/or have steps in the profile, such as shown in Figure 1, differential settlements occur due to the variations in the height of the embankment, and these can lead to low stress and tensile strain zones in which cracks may form. Hydraulic fracture through these critical zones as the dam is filled or under flood conditions is an associated phenomenon This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit 721

3 as discussed by Sherard et al (1972), and Sherard (1985,1986). For most dams, about 80% to 90% of the total settlement occurs during construction (Hunter et al, 2003), so the stresses and strains set up in the construction phase largely control the likelihood of these critical zones and cracking. Numerical modelling can be a very useful tool for the potential cracking zone prediction and specification. A subsequent parametric study can present a better view of these zones as the valley geometry changes. Bui et al (2004, 2005) carried out extensive numerical modelling to determine the conditions which are conducive to cracking and low stress zones due to cross valley differential settlements. This paper extends these studies and tries to capture the possible tensile strain localizations over discontinuities in the abutment during staged construction of the dams. These possible tensile strain localizations in the cross valley profile are potentially dangerous because they are conducive to the development of transverse cracks. Transverse cracks are potentially the most dangerous because they are oriented in the direction of the seepage path. If such cracks form inside of the dam body which are not easy to be observed during construction, progressive concentrated leak erosion may lead to serious failure before the danger is recognized and remedial measures are taken. METHOD OF SOLUTION Assumptions and Modelling Details The modelling has been carried out using the commercial finite element program ABAQUS with the following details: The Mohr-Coulomb failure criterion was used so the soils are assumed to be elastic-perfectly plastic material. Plane strain condition was assumed for the 2D cross valley model analyses. 8-node quadrilateral and 6-node triangle elements were used. The embankment was constructed numerically in 10 layers, to allow the effects of yielding and stress redistribution during construction to be modelled. Each layer has 7 elements and a convergence study has been carried out for the mesh. A very small incremental load step was specified to facilitate the convergence of the program. The modelling of the cross valley section has been carried out using effective stress strengths cˈ = 10 kpa, φˈ = 25 o which was considered fairly typical for dam core materials. Pore pressures are not modelled, so the strength will be underestimated in the upper partially saturated part of the dam, and overestimated in the lower part which will become saturated when the depth of fill above it is sufficient. Pore pressures will in reality vary with elevation in the dam (negative pore water pressure in the upper part, positive pore water pressure in the lower part), and the compaction water content and density ratio. Ignoring pore pressure affects the available shear strength, and hence the extent of yielded zones. Poisson s ratio is dependent on the water content of compaction of the soil. For soils compacted just dry of optimum water content (say <OWC-0.5% or OWC-1%), ν 0.3 to 0.35 so Poisson s ratio of 0.3 was used. Geometry and Loading River Piezo Level H D b h 1 L/2 Figure 1. Definition of terms used to describe cross valley geometry ACMSM

4 Figure 1 and Table 1 show the cross valley models geometry and soil properties which were analyzed. The boundary conditions assumed were a rigid foundation, with fixed restraint at the foundation in both the x and y directions. The valleys were assumed to be axi-symmetric. A parametric study has been carried out to assess the effect of the valley geometry on the potential cracking zones. The objectives of the cases analyzed were: Models C1, C2, C3 and C4 investigate the effect of the width of the step in the cross valley profile. Models C1, C5 and C7 investigate the effect of the slope of the abutment in the cross valley profile without steps. Models C3, C6 and C8 investigate the effect of the slope of the abutment in the cross valley profile with a step. Models C9, C10, C3, C11, C12, C13 and C14 investigate the effect of the step height in the cross valley profile. Table 1. Cross valley model geometries and soil properties Model Geometry H (m) D (m) h1 (m) B (m) θ ( o ) β ( o ) L/2 (m) C C C C C C C C C C C C C C RESULTS AND DISCUSSIONS Tensile Stress Zones Soil Properties ( Mohr Coulomb) v = 0.3 E = 30 MPa ρ = 2038 kg/m 3 φˈ= 25 o cˈ= 10 kpa Figure 2. Maximum principal stress of cross valley model C3 Figure 2 depicts the maximum principal stresses calculated for the valley section with a step in the abutment profile after construction. It is shown that tensile stress zones occur at the crest of the dam near the abutments, and these tensile stresses are mainly due to the lateral stresses hence the lateral displacements of the embankment. During construction of the embankment, tensile stress zones form over the step but these change back into compression as the embankment is raised. The effect of the abutment slope, step width and height on these tensile stress zones have been assessed through the parametric study. The results show that, for tensile stress zones forming at crest of the dam near the abutment, the amount of tensile stress is greater but the width of these zones is ACMSM

5 narrower for the steeper abutment slope. The abutment slope has very little effect on the depth of these tensile stress zones. If a step has significant width in the cross valley profile, a second tensile stress zone is likely to form at top of the step to the direction of the abutment side below the step. If the step is located closer to the crest, this second tensile stress zone will become more significant. Tensile Strain Zones Figure 3 depicts the maximum principal strains developed over the step and sides of valley near the abutment after construction. For the tensile strain zones occur over the step, they are due to differential settlements between the section in the middle of the valley and the section close to valley sides above the step. These differential settlements will create a shear band between these two sections so it is likely to propagate along the abutment side below the step to the upper part of the dam. The maximum principal strains in the band are in tension and direct away from the band. The maximum principal stresses are in compression and direct towards the band. The directions of both maximum principal strains and stresses are roughly horizontal because of the lateral deformation of the core. Additionally, besides the strain localizations over the step, there are stress concentrations over the step corner as shown in Figure 2. This will result in a reduction in stresses in the layers above the step corner. If the maximum principal stress is less than the water pressure at that depth hydraulic fracture may occur. For the tensile strain zones close to sides of valley near the abutment, they are due to cross valley arching and vertical stresses are shed onto the sides of the valley. The vertical and horizontal movements cause yielding of the earthfill near the abutment. This means there is likely to be shearing of the earthfill near the contact with the abutment. A B Figure 3. Maximum principal strain of cross valley model C3 The tensile strains developed in these areas are cumulative strains during construction of the embankment. Although the stresses change back into compression, the strains are still in tension and cumulative as the embankment is raised. The maximum range of the tensile strains at failure was about 0.05% to 0.33% and can be significantly influenced by the moisture content or by the compaction effort (Leonards and Narain, 1963). This range estimated from the measured deflection curves, laboratory beam tests and in-situ measurements on the crest. The maximum tensile strain over the step calculated in some of the models was around 0.4%. Therefore, the magnitude of the tensile strains developed over the discontinuities in these models may be sufficient to cause transverse cracks. Compared with the tensile strains developed close to sides of the valley near the abutment, tensile strains developed in the shear band over the step are potentially more dangerous. They may not be observable during construction. In practice for new dams, filters are provided to control internal erosion which may develop in the cracks but in older dams filters may not have been provided or are not designed to properly control erosion. Accordingly, a comprehensive study has been carried out to assess the effect of the valley geometry on the tensile strain localization zones over the step in an elemental scale. Because of the limited inaccuracy of results resulting from the distorted elements close to the sharp corner of the step, the tensile strain of the element located around one layer (5m) above the step in the band was selected as the representative tensile strain developed over the step. Differential settlements between the section in the middle of the valley and the section above the step ACMSM

6 are the cause of these large tensile strain localization zones. In order to estimate the degree of the differential settlement, the differential settlement ratio (DSR) is defined. This ratio is calculated by dividing the differential settlement occur between the node in the middle of the valley (A) and the node above the step (B) by the length between these two nodes, as shown in Figure 3. This ratio is proportional to the degree of the differential settlement occurring over the step. Effect of abutment slope Figure 4 depicts the effect of the abutment slope on the tensile strain zones formed over the step. It is shown that the amount of cumulative tensile strains is increased by steeping the slope. The blue line represents the tensile strains and the red line denotes the differential settlement ratios (DSR). It can be seen that the degrees of the differential settlements are in good agreement with the trend of tensile strains developed over the step. Effect of step width Figure 4. Effect of abutment slope on tensile strain over step Figure 5 depicts the effect of the step width on the tensile strain zones formed over the step. It shows that the widths of the steps have very little effect on the amount of tensile strains developed around the steps. This may due to the fact that the differential settlements do not vary significantly over the step by changing the width of the step. Effect of step height Figure 5. Effect of step width on tensile strain over step Figure 6 depicts the effect of the step height on the tensile strain zones formed over the step. The results show that the amount of the tensile strains experienced a parabolic variation with respect to the height of the step. These steps are symmetric about the middle height of dam (25m) and it can be seen that the amount of the tensile strains is greater with the step in the lower part of the dam than the corresponding symmetric step in the upper part of the dam. This may result from the greater distance away from the middle of the valley where maximum settlements occur hence less differential settlement effect. If the step height is high enough (>0.6 of the dam height), these zones are propagated from the step corner up to the crest of the dam. ACMSM

7 Figure 6. Effect of step height on tensile strain over step CONCLUSIONS Based on the results of two dimensional numerical analyses of the deformations and stresses during construction, potential cracking zones have been assessed in the cross valley profile as a result of differential settlements along the axis of the dam. It is shown that tensile and low stress zones occur at the crest of the dam near abutments, and large tensile strain zones may occur over discontinuities and irregularities in the cross valley profile. A parametric study has been carried out to assess the effect of the abutment slope, step width and height on these potential cracking zones. The potential cracking zones developed at crest are usually observable, while the internal potential cracking zones formed over discontinuities and irregularities are not, and hence they are potentially more dangerous to initiate concentrated leak erosion during the subsequent filling of the reservoir. It should be recognized the modelling in this study is a simplification of the real situation, and the results are intended to be an aid to judgment, not a definitive modelling. Further research is under way including coupling analysis by considering the pore water pressure and also the modelling of the development and propagation of cracking so the depth and width of the potential cracks and flaws in these areas can be modelled. REFERENCES Bui, H., Fell, R., & Song, C. (2004). Two and three dimensional numerical modelling of the potential for cracking of embankment dams during construction., UNICIV Report No. R-426,The School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia. Bui, H., Tandrijana, V., Fell, R., Song, C., & Khalili, N. (2005). Two and three dimensional numerical modelling of the potential for cracking of embankment dams -supplementary report., UNICIV Report No. R-438, The School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia. Foster, M., Fell, R., & Spannagle, M. (2000). The statistics of embankment dam failures and accidents. Canadian Geotechnical Journal, 37(5), Hunter, G., & Fell, R. (2003). The deformation behaviour of embankment dams., UNICIV Report No. R-416, School of Civil and Environmental Enginnering, The University of New South Wales, Sydney, Australia. Leonards, G. A., & Narain, J. (1963). Flexibility of clay and cracking of earth dams., Journal of the Soil Mechanics and Foundations Division, ASCE March 1963 (SM2), Sherard, J. L. (1985). Hydraulic Fracturing in Embankment Dams, in Seepage and Leakage from Dams and Impoundments., ASCE Geotechnical Engineering Division Conference, Sherard, J. L. (1986). Hydraulic Fracturing in Embankment Dams., Journal of Geotechnical Engineering, 112(10), Sherard, J. L., Decker, J. L., & Ryker, N. L. (1972). Hydraulic Fracturing in Low Dams of Dispersive Clay., Proc. Specialty Conf. on Performance of Earth and Earth Supported Structures, ASCE, 1, 1, ACMSM