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1

Assessment of susceptibility to liquefaction of saturated road embankment subjected to dynamic loads

Borowiec A., Maciejewski K.

Studia Geotechnica et Mechanica

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2014

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Vol. 36, nr 1

15--22

EN

Liquefaction has always been intensely studied in parts of the world where earthquakes occur. However, the seismic activity is not the only possible cause of this phenomenon. It may in fact be triggered by some human activities, such as constructing and mining or by rail and road transport. In the paper a road embankment built across a shallow water reservoir is analyzed in terms of susceptibility to liquefaction. Two types of dynamic loadings are considered: first corresponding to an operation of a vibratory roller and second to an earthquake. In order to evaluate a susceptibility of soil to liquefaction, a factor of safety against triggering of liquefaction is used (FSTriggering). It is defined as a ratio of vertical effective stresses to the shear stresses both varying with time. For the structure considered both stresses are obtained using finite element method program, here Plaxis 2D. The plastic behavior of the cohesionless soils is modeled by means of Hardening Soil (HS) constitutive relationship, implemented in Plaxis software. As the stress tensor varies with time during dynamic excitation, the FSTriggering has to be calculated for some particular moment of time when liquefaction is most likely to occur. For the purposes of this paper it is named a critical time and established for reference point at which the pore pressures were traced in time. As a result a factor of safety distribution throughout embankment is generated. For the modeled structure, cyclic point loads (i.e., vibrating roller) present higher risk than earthquake of magnitude 5.4. Explanation why considered structure is less susceptible to earthquake than typical dam could lay in stabilizing and damping influence of water, acting here on both sides of the slope. Analogical procedure is applied to assess liquefaction susceptibility of the road embankment considered but under earthquake excitation. Only the higher water table is considered as it is the most unfavorable. Additionally the modified factor of safety is introduced, where the dynamic shear stress component is obtained at a time step when its magnitude is the highest – not necessarily at the same time step when the pore pressure reaches its peak (i.e., critical time). This procedure provides a greater margin of safety as the computed factors of safety are smaller. Method introduced in the paper presents a clear and easy way to locate liquefied zones and estimate liquefaction susceptibility of the subsoil – not only in the road embankment.

2

Influence of inertia forces on soil settlement under harmonic loading

Wrana B., Pietrzak N.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 1

245--258

EN

The paper deals with the comparison of Biot’s model for saturated, porous soils with other simplified models used in dynamic analysis. The purpose of this paper is to determine some limits of validity of the various models. In order to do this a full set of governing, dynamic equations of Biot model and a series of simplifying models such as u-p simplification and quasi-static consolidation models are considered. These formulations are applied to a simple soil layer under periodic surface loading. A displacement of skeleton and a displacement of fluid are shown and compared with each model for various formulations.

3

A discontinuous Galerkin finite element method for dynamic of fully saturated soil

Wrana B.

Archives of Civil Engineering

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2011

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Vol. 57, nr 1

119-134

EN

The fully coupled, porous solid-fluid dynamic field equations with u - p formulation are used in this paper to simulate pore fluid and solid skeleton responses. The present formulation uses physical damping, which dissipates energy by velocity proportional damping. The proposed damping model takes into account the interaction of pore fluid and solid skeleton. The paper focuses on formulation and implementation of Time Discontinuous Galerkin (TOG) methods for soil dynamics in the case of fully saturated soil. This method uses both the displacements and velocities as basic unknowns and approximates them through piecewise linear functions which are continuous in space and discontinuous in time. This leads to stable and third-order accurate solution algorithms for ordinary differential equations. Numerical results using the time-discontinuous Galerkin FEM are compared with results using a conventional central difference, Houbolt, Wilson Fi, HHT-alfa, and Newmark methods. This comparison reveals that the time-discontinuous Galerkin FEM is more stable and more accurate than these traditional methods.

PL

Artykuł podejmuje zagadnjenie analizy rozchodzenia się fal naprężenjowych w gruncie w ujęciu metody elementów skończonych bazując na sformułowaniu rozwiązania ciągłego w przestrzeni i nieciągłego w dziedzinie czasu Galerkina (space and time-discontinous Galerkin TDG finite element method). W tym sformułowaniu zarówno przemieszczenia jak i prędkości są wielkościamj nieznanymi wzajemnie niezależnymi aproksymowanymi ciągłymi funkcjami kształtu w przestrzeni i nieciągłymi funkcjami kształtu w czasie. Do opisu zachowania się gruntu w pełni nasyconego wodą zastosowano sformułowanie u-p w ujęciu metody elementów skończonych. Grunt traktowany jest, jako ośrodek dwufazowy składający się ze szkieletu i wody w porach. Zastosowane sformułowanie uwzględnia tłumienie ośrodka przez uwzględnienie dyssypacji energii proporcjonalnej do prędkości wody względem szkieletu. W artykule przedstawiono porównanie proponowanej metody rozwiązania numerycznego w dziedzinie czasu do metod obecnie stosowanych, takich jak: metoda różnicy centralnej, metoda Houbolta, Wilsona fi, HHT-alfa oraz najczęściej stosowanej metody Newmarka. Z porównania wynika, że proponowana metoda jest metodą stabilną o małym błędzie numerycznego rozwiązania.

4

Charakterystyka parametrów dynamicznych gruntu

Wrana B.

Czasopismo Techniczne. Środowisko

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2008

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R. 105, z. 3-Ś

195-210

PL

W artykule przedstawiono zagadnienia doboru parametrów dynamicznych gruntu, które przyjmowane są w obliczeniach komputerowych. Rozważane są dwa główne parametry: moduł odkształcenia postaciowego gruntu G oraz parametr tłumienia D przy obciążeniach cyklicznych (harmonicznie zmiennych).

EN

In this paper the parameters of soil in dynamic analysis are presented. Considered two main parameters: soil stiffness G as well as parameter of damping D at cyclic loads. Article gives state of art of different definitions of these parameters and presents main FEM systems, which are used to dynamic calculation of soil.