Ανάλυση αστοχιών γεωτεχνικών έργων θεωρητική ανάπτυξη, 3-διάστατη συμπεριφορά

The re-examination of significant and well documented case histories of failure or foundation performance using modern methods of analyses, adds a measure of realism to the validation of the traditional design methods. Moreover, the incorporation of relevant aspects of the state-of-the-art knowledge and modern research into geotechnical problems, contributes to the decrease of gap existing between theory and practice. In some cases, the revisiting procedure can trigger off further theoretical development of interesting geotechnical issues, where the literature is quite limited. Following the above-mentioned, the subjects of the present doctoral thesis are: (a) Parametric analyses of the behaviour of retaining structures by prestressed anchorages under 3D and 2D conditions. (b) Re-evaluation of geotechnical failures, performing 3D and 2D F.E. analyses, with special emphasis on in-situ conditions or inherent factors, which had been ignored or underestimated from the original design. (c) Theoretical analyses of several issues arose from the investigated case histories. 1. 3D Behaviour of retaining structures with prestressed anchorages The behaviour of retaining structures of vertical cuts supported with prestressed anchorages on piles, especially the global safety factor (SF) and the displacements, horizontal (ux) or vertical-settlements (uy), were investigated by 3D and 2D F.E. analyses. The influence of several important factors was examined, as: i) The relative embedded depth of piles D/H (H the height of slope). ii) The shear strength, which is mobilized due to the prestress forces, for two basic soil types, S1 (weathered weak rock with high internal friction) and S2 (very stiff O.C. clay with high cohesion), using the linear elastic-perfectly plastic model according to Mohr-Coulomb. Additionally, the corresponding soil types HS1 and HS2 for soil simulation, according to Hardening Soil Model were introduced in the F.E. analyses. iii) The normalized total design resistance of the anchorages R = ΣRa,d/s∙γ∙Η2 (Ra,d: design resistance of each anchorage, s: horizontal distance between supporting piles), iv) The normalized length of the excavation L/H and the aspect ratio L/B of the plan view, as well. v) The coefficient of in situ effective horizontal stresses at rest, Ko. Referring to the global safety factor, from the more important 3D analyses, it was verified that the ratio L/H has a dominant effect on SF. For the narrower investigated case L/H = 1 (and aspect ratio L/B = 1), the resulted SF is much higher than this from 2D conditions. Nevertheless, the favourable effect of triaxial conditions (owed to the contribution of shear forces at the edges) significantly decreases for L/H ≥ 2. Moreover, the favourable effect of increasing R on the SF becomes insignificant for low L/H values (i.e. for L/H = 1 the safety factor remains practically constant for increasing R, mainly in the case of soil type S2). On the other hand, for plain strain conditions (from 2D F.E. analyses), one of the basic factors, which influences the global safety factor is the normalized resistance of the anchorages, R. The rate of SF increase is higher in the soil with the higher angle of internal friction, φ΄. Another important factor which influence directly the mode of failure and indirectly the factor SF is the normalized embedded depth of piles, D/H, while the coefficient of horizontal stresses at rest, Ko has not any effect. Although most of the analyses were carried out for three rows of anchors (n = 3) and H = 12 m, additional calculations for n = 2-6 (and variable height H) verified that the effect of R on SF is almost independent from the number of anchors. The most important factor, which influences the horizontal displacements ux at the crest of retaining structure, besides the soil type, is the earth pressure coefficient at rest, Ko. The maximum horizontal displacements in 3D conditions, ux and uz, are sometimes lower and sometimes higher than those resulting from 2D F.E. analyses. Despite the fact that generally, these horizontal displacements were decreasing with the increase of the anchor forces, in 3D conditions the effect of normalized design resistance, R, becomes less significant for low values L/H. Especially for L/H = 1, the displacements ux, uz seem not to be influenced from the total resistance, R. The non-uniform distribution of horizontal displacements along the crest was investigated though the ratio of minux at the corners and maxux at the middle, ranging in the analyzed cases from 0.10 to 0.15. As it is already known from the literature, the distribution of surface settlements, based on measurements, has usually the shape of hogging or sagging. The probability of damages on surface structures depends not only on the maximum settlements, but on the shape of the deformed surface in the primary zone of influence, as well. From 3D F.E. analyses the settlements distribution along the cross-section at the axis of symmetry was presented in diagrams, indicating in most cases sagging, since the maximum settlement develops at a distance from the crest. On the contrary, 2D analyses resulted in lower displacements and heave at the crest. The basic differences between 2D and 3D analyses are pinpointed at the unavoidable non accurate simulation of the embedded part of piles below the excavation level, as continuous plates (2D) and not distinct elements, as in the 3D case. A more accurate simulation in 2D was achieved through appropriately lower shear strength reduction factor, Rint, below the level of excavation. The application of soil model HSM (in order to differentiate the modulus of elasticity for loading and unloading) results in more reliable surface settlement distribution, since the effects of soil heave due to the excavation, become less important. Usually, in the literature, the surface settlements were normalized in the form uy/H and relevant diagrams have been repeatedly presented, mainly for braced excavations. However, the settlements must be proportional to the term γ∙Η2 (and not to the height H) and also depend on a basic modulus of elasticity (E for the model EL-PL and E50 for the HSM). Consequently, the presented diagrams in the doctoral thesis were illustrated the relationship ux,y ∙(E/γ∙Η2) − xo/H, where xo the distance from the face of excavation. 2. Back analyses of geotechnical failures The selection of case histories was based on the sufficient documentation, the interest of the case, as well as on the previous investigations. The new analyses were performed by the F.E. method, using 3D and 2D programs. In total, six slope cases of failure and four cases of foundation failure were analyzed. Among the slope failure cases, the following were included: i) A major slide occurred in the Kimola Canal (Helsinki, Finland) area, which is covered by N.C. or slightly overconsolidated clay. ii) Slope failure at the portal excavation of the tunnel S2 (Egnatia Highway, Epirus, Greece), in weathered flysch formation. iii) A great slope failure at an open pit mine (Megalopolis, Greece), in a short-term slope. iv) Landslide along a presheared surface in marly clay (Crete, Greece). v) Failure of a slope temporary stabilized by bored piles (Highway, Attica, Greece). Following the last case (restraint of slope by piles), the 3D behaviour of slopes stabilized by piles was investigated by coupled analyses, which consider simultaneously the piles response, the displacements and the safety factor. The effects of some important factors were investigated either by main 3D parametric analyses or 2D simplified ones: i) The influence of normalized distance of piles (arching effects), ii) The interplay of normalized pile length, iii) The position of the row of piles on the slope. Two representative cases of the piles arrangement and three soil types were considered in the parametric analyses. Among the foundation failure cases, the collapse of Transcona Grain Elevator (Canada) has a special interest. The new analyses were performed after the accurate simulation of structure (in 3D), the available geotechnical data and the loading steps. During the 3D F.E. analyses, the consolidation process was taken into consideration, due to its great importance. The basic conclusions from the new analyses are the following: (a) A main reason of the catastrophic failure was the rapid loading by the grain in conjunction with the low permeability of soft clay layers consisting the subsoil in the area. (b) The elevator was underlain by a two-layered soil system, where a weaker clay layer was located below the typical stiff clay crust of the area. These soil conditions had not been detected during the design of foundation, since the fined-grained sediments were seemingly uniform. (c) From the current 3D F.E. analyses, the global safety factor just after the loading step at the time of failure was estimated slightly higher than unity. However, it was verified that several factors, as the exact level of bedrock the scattering of undrained shear strength values or even temporary horizontal forces could influence the SF value. The potential effects of an initial tilt ωο of structure on bearing capacity and leaning stability were estimated by 3D F.E. analyses after the calculation of secondary rotation Δω. It was confirmed that the contribution of low tilt of the order of ωο = 1° on the foundation failure should be quite low. The results from simplified calculations using the simulation after Winkler were compared with those from more rigorous 3D F.E. analyses and the convergence or deviation were commented. 3. Leaning instability of high structures−The Tower of PisaFor an initial tilt ωο of a high structure, the secondary rotation Δω, due to the diversion of gravity center, the concentration of contact pressures at the foundation, e.t.c. can be calculated. The final tilt at equilibrium (if this is the case), ω = ωο + Δω is of peculiar interest.

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