Wyniki wyszukiwania - BazTech

1

Analiza konstrukcji gruntowo-powłokowej poddanej działaniu wody

Łydżba D., Różański A., Sobótka M., Stefaniuk D., Chudy G., Wróblewski T.

Mosty

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2017

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nr 1

20--28

PL

Celem analiz numerycznych jest ocena możliwości użytkowania mostu gruntowo-powłokowego zlokalizowanego w czaszy suchego zbiornika przeciwpowodziowego. Zamodelowano fazę budowy oraz użytkowania obiektu przy rożnych stanach piętrzenia: zbiornik suchy, maksymalne piętrzenie, opadanie wody w zbiorniku. Analizowano zmiany sił wewnętrznych i naprężenia w powłoce wywołane wskutek kilku cykli ruchomego, quasi-statycznego obciążenia taborem samochodowym.

EN

The planned construction of a dry reservoir Roztoki Bystrzyckie is a part of the flood control program in the Kłodzko Valley. The project includes, i.a., the construction of a new section of road with a soil-steel bridge over the Nowinka stream. The road crosses the reservoir basin, which can be filled with water during flood. The aim of the numerical analysis presented in the paper is the assessment of the possibility of using the structure under varying water conditions. The structure under consideration is a three-span soil-steel bridge made of corrugated steel sheets. 2D calculations are carried out assuming elastic-plastic behavior of soil and varying pore pressure distributions. First, the construction stage is modelled. This includes laying and compaction of the backfill. Then, the bridge in operation is investigated under three different water conditions: normal use (dry reservoir), maximum water level (flood) and lowering of the water level in the reservoir. The main part of the analysis concerns mainly the variation of both internal forces and stress in the shell due to quasi-static live load.

2

Zastosowanie mikrotomografii komputerowej do oceny ewolucji sieci spękań w materiałach kruchych

Łydżba D., Pachnicz M., Rajczakowska M., Różański A., Sobótka M., Stefaniuk D.

Materiały Budowlane

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2017

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nr 6

48--49

PL

W artykule przedstawiono analizę wyników badania w mikrotomografie komputerowym sieci spękań w próbkach skalnych, poddanych testom jednoosiowego ściskania. Próbki były skanowane w mikrotomografie komputerowym przed testem, następnie po obciążeniu siłą o wartości 40 – 50% siły niszczącej, a także po osiągnięciu granicy makrodylatancji (lub granicy wytrzymałości). Analiza uzyskanych trójwymiarowych obrazów skanowania pozwoliła opisać w sposób ilościowy morfologię sieci spękań: porowatość, rozkłady przestrzenne szerokości spękań i krętości, a także wskaźnik SMI (ang. structure model index). Znajomość wymienionych wielkości jest przydatna przy określaniu parametrów przepuszczalności badanego materiału.

EN

The paper presents the analysis of crack network development induced in rock samples, subjected to uniaxial compression. The samples were scanned using micro-computer tomography after three stages of load: before loading, after application of a force equal to 40–50% of ultimate limit and, finally, after reaching microdilatancy threshold (or ultimate limit force). The analysis of acquired 3D images at every loading stage included fracture network segmentation and determination of chosen quantities describing its morphology: porosity (fraction of void space), spatial distribution of fracture aperture, tortuosity as well as structure model index (SMI). The parameters can be used to determine permeability parameters of cracked material.

3

Wykorzystanie nanoindentacji w sposób sekwencyjny do oceny właściwości strukturalnych materiałów mikroniejednorodnych

Łydżba D., Pachnicz M., Rajczakowska M., Różański A., Sobótka M., Stefaniuk D.

Materiały Budowlane

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2017

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nr 6

50--51

PL

W artykule przedstawiono wyniki testów nanoindentacji przeprowadzone na próbce skalnej. Zastosowano sekwencyjną indentację, tj. autorski program obciążenia próbki. Pozwoliło to obserwować zmienność modułu sprężystości w zależności od skali obserwacji. Wydzielono dwie skale obserwacji, tj. mikro i mezo. Najmniejsza stosowana siła indentacji 0,5 mN prowadzi do odpowiedzi mechanicznej składników tworzących szkielet. Wyniki uzyskane w przypadku najwyższej siły – 500 mN, reprezentują parametr efektywny dla tzw. zastępczej mikrostruktury jednorodnej.

EN

The paper presents results of nanoindentation tests carried out for intact rock specimen. The sequential nanoindentation is used and the novel loading schedule, for prescribed tip position, is applied. It enables us to identify the mechanical morphology at different observation scales. Two scales were identified, i.e., micro- and meso-scale. The lowest value of indentation force, 0.5 mN, provides the mechanical response of the constituents forming the skeleton. The results obtained for the highest value of indentation force, 500 mN, represent the effective property for the so-called „equivalent” homogeneous microstructure.

4

Ocena stateczności zapory ziemnej zbiornika przeciwpowodziowego Roztoki Bystrzyckie

Łydżba D., Batog A., Sobótka M., Pachnicz M., Różański A., Stefaniuk D., Wróblewski T., Chudy G.

Geoinżynieria : drogi, mosty, tunele

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2017

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nr 3

34--38

PL

Metodyka oceny stateczności skarp i zboczy budowli hydrotechnicznych podlega, w myśl aktualnych przepisów, dwóm różnym rozporządzeniom. Z jednej strony obowiązują zasady projektowania geotechnicznego, podane w Eurokodzie 7, z drugiej (równolegle) zapisy rozporządzenia ws. warunków technicznych, jakim powinny odpowiadać budowle hydrotechniczne i ich usytuowanie. W artykule podjęto próbę udzielenia odpowiedzi na pytanie, w jakim stopniu wybór pomiędzy wymienionymi podejściami wpływa na uzyskiwane wyniki analizy stateczności zapory suchego zbiornika przeciwpowodziowego Roztoki Bystrzyckie.

EN

The methodology of the scarps and slopes stability assessment of the hydrotechnical structures can be considered in relation to two different regulations: Eurocode 7 and Polish geotechnical design regulations. The authors attempt to define what kind of regulations should be followed, concerning the hydrotechnical structures and their localizations. In the article there is presented an answer to the question: how the choice of the regulations affects the stability assessment of the earth fill dam of the storage reservoir Roztoki Bystrzyckie.

5

Mechanical behavior of soil-steel structure subjected to live loads and different water conditions

Łydżba D., Różański A., Sobótka M., Stefaniuk D., Chudy G., Wróblewski T.

Archiwum Instytutu Inżynierii Lądowej

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2017

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Nr 23

163--174

EN

The paper describes the analysis of a three-span soil-steel bridge along the road section crossing a dry anti-flood reservoir. The structure can be occasionally filled with water. The authors investigate internal forces and stresses in the shells due to live loads at different water conditions. Finite element simulations are carried out assuming elastic-plastic behavior of soil, elastic shell and nonlinear (frictional) contact zone. The analysis takes into account soil load history. In particular, the construction and operation of the bridge under quasi-static live loads is considered. The construction stage includes laying and compaction of the backfill. Then, the bridge in operation is investigated at three different water conditions: normal use (dry reservoir), maximum water level (flood) and lowering of the water level in the reservoir. The results show that during the flood the maximum stress in the shell significantly increases. Moreover, some of non-linear effects, typical in such structures, e.g. hysteretic effect, become more evident in comparison to normal use of the bridge.

6

Recovery of microstructure properties: random variability of soil solid thermal conductivity

Stefaniuk D., Różański A., Łydżba D.

Studia Geotechnica et Mechanica

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2016

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Vol. 38, nr 1

99--107

EN

In this work, the complex microstructure of the soil solid, at the microscale, is modeled by prescribing the spatial variability of thermal conductivity coefficient to distinct soil separates. We postulate that the variation of thermal conductivity coefficient of each soil separate can be characterized by some probability density functions: fCl(λ), fSi(λ), fSa(λ), for clay, silt and sand separates, respectively. The main goal of the work is to recover/identify these functions with the use of back analysis based on both computational micromechanics and simulated annealing approaches. In other words, the following inverse problem is solved: given the measured overall thermal conductivities of composite soil find the probability density function f(λ) for each soil separate. For that purpose, measured thermal conductivities of 32 soils (of various fabric compositions) at saturation are used. Recovered functions f(λ) are then applied to the computational micromechanics approach; predicted conductivities are in a good agreement with laboratory results.

7

Durability of crystalline phase in concrete microstructure modified by the mineral powders: evaluation by nanoindentation tests

Rajczakowska M., Łydżba D.

Studia Geotechnica et Mechanica

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2016

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Vol. 38, nr 1

65--74

EN

This paper presents the nanoindentation investigation of the evolution of concrete microstructure modified by the Internal Crystallization Technology mineral powders. The samples under study were retrieved from a fragment of a circular concrete lining of the vertical mine shaft at a depth of approximately 1,000 m. Due to the aggressive environment and exposure to contaminated water, the internal surface of the structure was deteriorated, decreasing its strength significantly. The mineral powders were applied directly on the surface lining. The specimens were investigated one month, three months and one year after the application of the aforementioned substance in order to verify the time dependence of the strengthening processes and durability of the crystalline phase. The microstructural changes of concrete were assessed with the use of nanoindentation technique. The testing procedure involved including the previously cut specimens in the epoxy resin and grinding and polishing in order to reduce the surface roughness. As a result of the nanoindentation tests the hardness as well as Young’s modulus of the material were evaluated. The results were then compared and statistically analyzed. As a consequence, the disintegration time of the crystalline network in the pores of concrete was identified.

8

Wybrane badania betonu Hali Stulecia we Wrocławiu (obiekt UNESCO)

Jasieńko J., Bednarz Ł., Piechówka-Mielnik M., Łydżba D., Rajczakowska M.

Wiadomości Konserwatorskie

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2015

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Nr 42

18--32

PL

W pracy przedstawiono wyniki badań właściwości chemicznych i fizycznych betonu znajdującego się w dolnym pierścieniu obwodowym kopuły Hali Stulecia w Wrocławiu. Badania przeprowadzone były w drugiej połowie 2009 roku oraz w pierwszej połowie 2015 roku. Ponadto wykonano dodatkowo badania mikrostruktury betonu przy użyciu tomografu komputerowego oraz, na podstawie serii testów nanoindentacji, wykonanych w nanoindenterze. Dotychczas przeprowadzone badania potwierdzają wysoką jakość betonu. Kruszywo znajdujące się w badanych próbkach to w większości łamany granit strzegomski. W kruszywie o frakcjach poniżej 8 mm zaobserwowano występowanie żużlu paleniskowego o dużej porowatości oraz wtrącenia w postaci ścinków drewnianych. Ocenę składu mineralogicznego betonu wykonano wykorzystując wyniki analizy składu tlenkowego. Przez zmniejszoną zawartość CaO skład tlenkowy zbliżony jest do składu cementu hutniczego. Wprowadzając świadomie do mieszanki betonowej żużel paleniskowy uzyskano zwartą mikrostrukturę betonu. Stwardniały zaczyn w badanym betonie wykazuje doskonałą przyczepność do łamanego kruszywa granitowego. Posiada strukturę zwartą, gęstą, o bardzo niskiej nasiąkliwości. Mikrotwardość badanego betonu wyniosła 1,8 GPa, a moduł sprężystości E = 33 GPa. W badaniach wykonanych za pomocą mikrotomografu komputerowego oznaczona porowatość w badanych próbkach wyniosła ok. 10%. W strukturze przeważają mikropory poniżej 300 μm.

EN

The paper reports on results of chemical and physical testing of concrete sampled from the lower circumferential ring of the dome of the Centennial Hall In Wrocław. Testing was conducted in the second half of 2009 and in the first half of 2015. Additionally, an analysis of the concrete microstructure was undertaken using a computer tomography and a number of nano-indentation tests were carried out with a nanoindentation device. Analysis of the concrete carried out to date confi rms high concrete quality. The aggregate in tested specimens comprises mainly crushed Strzegom granite. In aggregate fractions lower than 8 mm, the presence of high porosity slag and wood chip inclusions was observed. Analysis of concrete mineral composition was conducted using results of an oxide composition analysis. The oxide composition of this cement is close to the composition of blast-furnace cement. Introduction of slag into the concrete mix resulted in a dense microstructure of the concrete. The hardened cement paste in the tested concrete demonstrates excellent adhesion to crushed granite aggregate. This is characterised by a dense structure, with low absorbability. Micro-hardness of tested concrete was determined to equal 1,8 GPa and the modulus of elasticity E = 33 GPa. In studies conducted using micro-CT the porosity for tested samples found to be approximately 10%. In the structure the majority are micropores smaller than 300 μm.

9

Microstructure characterization by means of X-ray micro-CT and nanoindentation measurements

Rajczakowska M., Stefaniuk D., Łydżba D.

Studia Geotechnica et Mechanica

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2015

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Vol. 37, nr 1

75--84

EN

The aim of this paper is to present an example of the material microstructure characterization with the use of X-ray micro-CT and nanoindentation measurements. Firstly, the current scope of application of the aforementioned techniques is provided within different fields of science. Then, background of each of the methods is presented. The methodology of X-ray micro-CT is described with the emphasis on the Beer’s law formulation. In addition, the basics of the nanoindentation technique are outlined and major formulas for the hardness and Young’s modulus calculation are given. Finally, example results for a concrete sample are presented. The microstructure of the selected material is firstly characterized in terms of geometry using the results from the microtomograhy measurements, e.g., porosity and attenuation profiles, pore and aggregate size distribution, shape factor of pores, etc. Next, the results of the nanoindentation tests are provided, namely the hardness and Young’s modulus versus the height of the sample. The influence of the number of tests and statistical analysis on the final results is underlined.

10

Evaluation of bearing capacity of strip footing using random layers concept

Kawa M., Łydżba D.

Studia Geotechnica et Mechanica

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2015

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Vol. 37, nr 3

31--39

EN

The paper deals with evaluation of bearing capacity of strip foundation on random purely cohesive soil. The approach proposed combines random field theory in the form of random layers with classical limit analysis and Monte Carlo simulation. For given realization of random the bearing capacity of strip footing is evaluated by employing the kinematic approach of yield design theory. The results in the form of histograms for both bearing capacity of footing as well as optimal depth of failure mechanism are obtained for different thickness of random layers. For zero and infinite thickness of random layer the values of depth of failure mechanism as well as bearing capacity assessment are derived in a closed form. Finally based on a sequence of Monte Carlo simulations the bearing capacity of strip footing corresponding to a certain probability of failure is estimated. While the mean value of the foundation bearing capacity increases with the thickness of the random layers, the ultimate load corresponding to a certain probability of failure appears to be a decreasing function of random layers thickness.

11

State of strength in massive concrete structure subjected to non-mechanical loads

Łydżba D., Sobótka M.

Studia Geotechnica et Mechanica

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2014

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Vol. 36, nr 2

37--43

EN

The paper deals with an impact of non-mechanical loads on the state of strength in massive concrete hydraulic structures. An example of hydroelectric plant subjected to the effect of water temperature annual fluctuation is considered. Numerical analysis of transient thermal-elasticity problem was performed. After determining the temperature distributions within the domain, the Duhamel–Neumann set of constitutive equations was employed to evaluate fields of mechanical quantities: displacement, strain and stress. The failure criterion proposed by Pietruszczak was adopted in assessing whether the load induces exceeding of strength of concrete within the structure volume. The primary finding is that the temperature effect can lead to damage of concrete in draft tubes and spirals, especially in winter months.

12

Identification of the carbonation zone in concrete using X-ray microtomography

Łydżba D., Rajczakowska M., Stefaniuk D., Kmita A.

Studia Geotechnica et Mechanica

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2014

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Vol. 36, nr 1

47--54

EN

The article presents an application of X-ray microtomography for identification of the carbonation zone in concrete material. A concrete specimen subjected earlier to harsh environmental conditions is investigated. The material is firstly checked with the use of chemical corrosion indicators and then is subjected to microstructural analysis performed with the use of X-ray microtomography. Two different settings of scanning parameters are applied implying the image resolutions of approximately 14 μm per 1 pixel and about 7 μm per 1 pixel, respectively. The results obtained are then compared and analyzed. The depth of the carbonation zone is evaluated based on the attenuation curve. The paper highlights also the significance of the corrosion phenomenon in concrete structures. Details of the deterioration mechanisms in concrete are shortly presented.

13

Efficiency of the needle probe test for evaluation of thermal conductivity of composite materials: two-scale analysis

Łydżba D., Różanski A., Rajczakowska M., Stefaniuk D.

Studia Geotechnica et Mechanica

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2014

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Vol. 36, nr 1

55--62

EN

The needle probe test, as a thermal conductivity measurement method, has become very popular in recent years. In the present study, the efficiency of this methodology, for the case of composite materials, is investigated based on the numerical simulations. The material under study is a two-phase composite with periodic microstructure of “matrix-inclusion” type. Two-scale analysis, incorporating micromechanics approach, is performed. First, the effective thermal conductivity of the composite considered is found by the solution of the appropriate boundary value problem stated for the single unit cell. Next, numerical simulations of the needle probe test are carried out. In this case, two different locations of the measuring sensor are considered. It is shown that the “equivalent” conductivity, derived from the probe test, is strongly affected by the location of the sensor. Moreover, comparing the results obtained for different scales, one can notice that the “equivalent” conductivity cannot be interpreted as the effective one for the composites considered. Hence, a crude approximation of the effective property is proposed based on the volume fractions of constituents and the equivalent conductivities derived from different sensor locations.

14

Microstructure measures and the minimum size of a representative volume element: 2D numerical study

Łydżba D., Różański A.

Acta Geophysica

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2014

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Vol. 62, no. 5

1060--1086

EN

In the paper, a numerical study of the size of a representative volume element (RVE) for both the heat flow as well as the linear elasticity problems is presented. A particular two-phase random microstructure is studied and the method is applied to the digital image of reconstructed 2D realization of random media. The minimum size of RVE is deter-mined by the investigation of the convergence of apparent properties as the size of RVE is increasing. Then, two estimates of the minimum RVE size are proposed and it is shown that the estimates are in a good agreement with the results determined by the investigation of the convergence of apparent properties. The minimum size of RVE can be successfully predicted based only on the microstructure morphology. The statistical measures used in this work are: the two-point probability and the lineal-path functions.

15

Shape optimization of underground excavation by simulated annealing

Sobótka M., Łydżba D, Różański A.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 1

209--218

EN

The paper deals with the problem of shape optimization of underground tunnel excavation. In the pioneering work of Sałustowicz, the elliptic shape was assumed a priori to be an optimal one and then a determination of suitable semi-axes ratio was only the question. Two cases were distinguished there: self-supporting excavation and excavation with the structural support. An evolutionary structural optimization (ESO) procedure, employed in 2005 to optimize shape of underground excavation, confirms the assumptions concerning the case of self-supporting excavations. The case of supported excavation is considered in the present work. Optimization procedure of the simulated annealing (SA) is incorporated in the study. An energetic optimality condition, formulated in the authors’ previous papers is also adopted. Itasca FLAC software is utilized in numerical examples. Four different in situ stress ratios are investigated. The numerical results obtained confirm that the optimal shape tends to be an ellipse. The semi-axes ratio demonstrates compliance with the assumptions already existing in literature.

16

Numerical study of the size of representative volume element for linear elasticity problem

Różański A., Łydżba D., Jabłoński P.

Studia Geotechnica et Mechanica

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2013

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Vol. 35, nr 2

67--81

EN

In the paper, a numerical study of the size of representative volume element for the linear elasticity problem is performed. The calculations are carried out for three different types of random microstructures: checkerboard, the Ising model microstructure and Debye microstructure. It is postulated and then verified that there exists a relation between the morphology of microstructure contained in the lineal-path function and the minimum RVE size. It is confirmed, on the basis of numerical examples, that for all the microstructures considered the largest lineal-path can be treated as the size of RVE.

17

Preliminary study of failure anisotropy characterization of varved clay

Łydżba D., Tankiewicz M.

AGH Journal of Mining and Geoengineering

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2012

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Vol. 36, no. 2

229-234

EN

The paper presents the results of preliminary laboratory investigations of the failure characteristics of structured soil. A particular type of microstructure has been investigated, i.e. vertically laminated clayed soil called varved clay. The examinations have been made on soil deposited near the city of Bełchatów. The physical and mechanical properties of the soil have been estimated as: soil texture, moisture content, particle density, bulk density, Atterberg limits, plasticity and consistency index. Next the unconfined compression as well as triaxial test with different confining pressures have been conducted for several different orientation of microstructure. Anisotropy characteristics have been specified for the different values of bedding planes orientation and the different values of confining pressure, namely: 0 kPa, 50 kPa, 200 kPa. The laboratory examinations were carried out with special attention to failure mechanism identification. For the selected values of the bedding plane orientation photos of the failure mechanism have been presented in the paper. The results of the examinations clearly show a high dependence between layer orientation and the strength of the soil.

PL

W pracy zaprezentowano wyniki wstępnych badań anizotropii wytrzymałości gruntu z mikrostrukturą warstwową. Badania przeprowadzono na próbkach iłu warwowego występującego w okolicach Bełchatowa. Dla gruntu wykonano oznaczenie podstawowych właściwości fizycznych oraz wskaźników klasyfikacyjnych tj. składu granulometrycznego, wilgotności naturalnej, gęstości właściwej, gęstości objętościowej, granic Atterberga, wskaźnika plastyczności oraz wskaźnika konsystencji. Następnie przeprowadzono badania jednoosiowego ściskania oraz w trójosiowym stanie naprężeń dla szeregu różnych orientacji uwarstwienia gruntu. Wyniki doświadczeń przedstawiono w postaci zależności: kąt uwarstwienia mikrostruktury i odpowiadająca temu nośność graniczna. Stworzono w ten sposób charakterystyki wytrzymałości w odniesieniu do orientacji mikrostruktury dla różnych wartości ciśnień okólnych wywieranych na próbkę tj. 0 kPa, 50 kPa, 200 kPa. Ze względu na kierunkową orientację mikrostruktury iłów warwowych badania wytrzymałościowe przeprowadzono ze szczególnym uwzględnieniem identyfikacji mechanizmów niszczących. W pracy zamieszczono zdjęcia prezentujące te mechanizmy dla wybranych kątów uwarstwienia. Otrzymane wyniki jednoznacznie wskazują na silną zależność pomiędzy orientacją mikrostruktury a jej wytrzymałością.

18

An annual cycle of changes in water temperature as a cause of cracking in massive concrete hydraulic structures

Łydżba D., Różański A., Sobótka M.

AGH Journal of Mining and Geoengineering

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2012

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Vol. 36, no. 2

217-227

EN

The paper deals with the problem of temperature effect on a massive concrete hydraulic structure. The article is split into two parts. In the first part is an investigation concerning temperature distribution in a concrete wall of a hydraulic structure due to annual changes in water temperature. The conclusion of these considerations is that the temperature distribution in the concrete element, due to slow annual changes in temperature of flowing water, is almost uniform in space. The advantage of this fact is taken into consideration in another part in which the results of a numerical analysis concerning a HPP on the Vistula river is presented. Final conclusion is that water temperature changes can easily cause cracking in concrete hydraulic structures.

PL

W artykule rozważany jest wpływ temperatury na masywne konstrukcje betonowe obiektów hydrotechnicznych. Praca składa się z dwóch zasadniczych części. W pierwszej określany jest rozkład temperatury występujący w betonowej ścianie budowli wodnej na skutek rocznych, wolnych zmian temperatury wody. Wniosek z tych rozważań, tj. że rozkład temperatury wewnątrz elementu betonowego jest prawie jednorodny jest wykorzystany jako założenie w drugiej części pracy. Analizie numerycznej poddana jest jedna z elektrowni wodnych na Wiśle. Z przeprowadzonych obliczeń wynika, że zmiany temperatury wody, występujące w klimacie charakterystycznym dla Polski, mogą prowadzić do powstawania pęknięć w betonowych elementach budowli hydrotechnicznych.

19

From digital image of microstructure to the size of representative volume element: B4C/Al composite

Różański A., Łydżba D.

Studia Geotechnica et Mechanica

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2011

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Vol. 33, nr 1

55-68

EN

In the field of micromechanics, the notion of representative volume element (RVE) and its quantitative definition are of the paramount importance. The definitions of RVE, used by scientists for different purposes, are mathematically strict but do not quantify its size. Furthermore, all the methods of RVE size determination (available in a voluminous literature) require a large number of numerical calculations like, for instance, those of finite element or other numerical techniques. In this paper, it is shown that the size of RVE can be evaluated based only on the morphology of microstructure that is involved in the statistical microstructure descriptor, namely the two-point correlation function. A methodology is applied to the digital image of the reconstructed 2D realization of the boron-carbide/aluminum (B4C/Al) composite. The condition for the minimum size of RVE used in the numerical procedure has been formulated in previous work of authors. The size of RVE is determined for different values of estimation error and the contrast in phase properties. The method is verified by performing numerical calculations of effective thermal conductivity coefficient.

20

Ocena właściwości makroskopowych geokompozytów na podstawie obrazu ich mikrostruktury

Łydżba D., Różański A.

Górnictwo i Geoinżynieria

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2011

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R. 35, z. 2

403-413

PL

W pracy sformułowano i omówiono procedurę oceny właściwości makroskopowych geokompozytów na podstawie obrazu ich mikrostruktury. Wielkość makroskopowa kompozytu to wartość oczekiwana z odpowiadającej jej wielkości mikroskopowej będącej tzw. funkcją struktury. Matematycznie, wartość oczekiwana to średnia ze wszystkich możliwych realizacji ośrodka losowego których, w ogólności, jest nieskończenie wiele. Wykorzystując miarę mikrostruktury w postaci prawdopodobieństwa 2-punktowego sformułowano oryginalną metodę oceny właściwości makroskopowych jako wartość z próby którą tworzy skończona liczba, określonego i tego samego rozmiaru, tzw. Reprezentatywnych Elementarnych Objętości (REO). Odpowiednio dobrana próba, tj. jej wielkość będąca liczbą REO oraz rozmiar REO, zapewnia poprawną ocenę właściwości makroskopowej kompozytu, z założonym błędem estymacji. W pracy przedstawiono warunki i procedury numerycznej identyfikacji rozmiaru REO oraz wielkości próby. Do określenia rozmiaru REO wykorzystano prawdopodobieństwo 2-punktowe oraz metodę symulacji Monte Carlo natomiast do określenia wielkości próby - Centralne Twierdzenie Graniczne.

EN

The paper proposes and discusses the procedure of evaluation of overall properties of geocomposites based on a digital image of their microstructure. The overall property of composite is defined as an expectation of an associated microscopic variable called as a structural function. Mathematically, expectation is an average over all the possible realization of random medium, i.e. the infinite number of realizations. The paper formulates an original method of overall properties evaluation using the so-called 2-point probability function. The procedure proposed involves the notion of a sample and that of Representative Volume Element (RVE). The expectation is evaluated as an average over the sample. The sample is defined to be a set of a finite number of RVE elements, each of them of the same size. Proper evaluation of the expectation requires, within this method, an estimation of the appropriate size of the sample and the RVE element. The size of RVE element is proposed to be determined based on the 2-point probability function and the Monte Carlo simulation whereas the sample size is estimated based on the Central Limit Theorem.