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1

Study of bearing capacity of skirted irregular pentagonal footings on different sands

Thakur A, Dutta R. K.

Journal of Achievements in Materials and Manufacturing Engineering

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2021

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Vol. 105, nr 1

5--17

EN

Purpose: The paper presents an experimental and numerical study to evaluate the bearing capacity of unskirted, singly and doubly skirted irregular pentagonal footings on different sands (S1, S2, S3) at a relative density of 30 %. The skirt depth of the footing was varied from 0.0B to 1.5B (B is the width of the square footing). Design/methodology/approach: The experimental and numerical study of the singly and doubly skirted irregular pentagonal footing resting on sands was modelled in a test tank and Plaxis 3D software respectively. Findings: The results of this study reveal that the bearing capacity was higher for the skirted irregular pentagonal footings on sand S3 followed by sand S2 and S1. The lowest percentage improvement for the singly skirted footing on sand S3 was 18.51% at a Ds/B = 0.25 whereas the highest improvement was 90.81% at a Ds/B = 1.50 for the singly skirted footing on sand S2. The highest percentage improvement for the doubly skirted footing on sand S2 was 95.13% at a Ds/B = 1.5 whereas the lowest improvement was 23.70% at a Ds/B = 0.25 the doubly skirted footing on sand S3. The results further revealed that the numerically obtained bearing capacity was marginally higher in comparison to the one obtained experimentally for the footings on all sands. Further, the experimental results validated the results obtained numerically with an average deviation of 8%. The percentage improvement in the bearing capacity was higher for the irregular pentagonal footing resting on sand S2 in comparison to sand S3 and S1. The settlement response of the irregular pentagonal footings is unchanged by increasing the number of elements beyond 7700. Both the experimental and numerical studies revealed a linear elastic behaviour at Ds = 0.5B, while the experimentally obtained pressure-settlement ratio plot shows a clear failure at Ds= 1B and 1.5B. Research limitations/implications: The results presented in this paper were based on the experimental and numerical study conducted on small scale model footings. However, for the actual footings, further study is recommended using full-scale field size footings to generalize the results. Originality/value: No experimental and numerical studies on singly and doubly skirted irregular pentagonal footings were conducted so far. Hence, an attempt was made in this article to predict the bearing capacity of these footings experimentally and using Plaxis 3D respectively.

2

Bearing capacity of rectangular footing on layered sand under inclined loading

Panwar V., Dutta R. K.

Journal of Achievements in Materials and Manufacturing Engineering

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2021

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Vol. 108, nr 2

49--62

EN

Purpose: The study presents the numerical study to investigate the bearing capacity of the rectangular footing on layered sand (dense over loose) using ABAQUS software. Design/methodology/approach: Finite element analysis was used in this study to investigate the bearing capacity of the rectangular footing on layered sand and subjected to inclined load. The layered sand was having an upper layer of dense sand of varied thickness (0.25 W to 2.0 W) and lower layer was considered as loose sand of infinite thickness. The various parameters varied were friction angle of the upper dense (41° to 46°) and lower loose (31° to 36°) layer of sand and load inclination (0° to 45°), where W is the width of the rectangular footing. Findings: As the thickness ratio increased from 0.00 to 2.00, the bearing capacity increased with each load inclination. The highest and lowest bearing capacity was observed at a thickness ratio of 2.00 and 0.00 respectively. The bearing capacity decreased as the load inclination increased from 0° to 45°. The displacement contour shifted toward the centre of the footing and back toward the application of the load as the thickness ratio increased from 0.25 to 1.25 and 1.50 to 2.00, respectively. When the load inclination was increased from 0° to 30°, the bearing capacity was reduced by 54.12 % to 86.96%, and when the load inclination was 45°, the bearing capacity was reduced by 80.95 % to 95.39 %. The results of dimensionless bearing capacity compare favorably with literature with an average deviation of 13.84 %. As the load inclination was changed from 0° to 45°, the displacement contours and failure pattern shifted in the direction of load application, and the depth of influence of the displacement contours and failure pattern below the footing decreased, with the highest and lowest influence observed along the depth corresponding to 0° and 45°, respectively. The vertical settlement underneath the footing decreased as the load inclination increased, and at 45°, the vertical settlement was at its lowest. As the load inclination increased from 0° to 45°, the minimum and maximum extent of influence in the depth of the upper dense sand layer decreased, with the least and highest extent of influence in the range of 0.50 to 0.50 and 1.75 to 2.00 times the width of the rectangular footing, respectively, corresponding to a load inclination of 45° and 0°. Research limitations/implications: The results presented in this paper were based on the numerical study conducted on rectangular footing having length to width ratio of 1.5 and subjected to inclined load. However, further validation of the results presented in this paper, is recommended using experimental study conducted on similar size of rectangular footing. engineers designing rectangular footings subjected to inclined load and resting on layered (dense over loose) sand. Originality/value: No numerical study of the bearing capacity of the rectangular footing under inclined loading, especially on layered soil (dense sand over loose sand) as well as the effect of the thickness ratio and depth of the upper sand layer on displacement contours and failure pattern, has been published. Hence, an attempt was made in this article to investigate the same.

3

Bearing capacity of E-shaped footing on layered sand

Nazeer S., Dutta R. K.

Journal of Achievements in Materials and Manufacturing Engineering

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2021

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Vol. 105, nr 2

49--60

EN

Purpose: The purpose of this study is to estimate the ultimate bearing capacity of the E-shaped footing resting on two layered sand using finite element method. The solution was implemented using ABACUS software. Design/methodology/approach: The numerical study of the ultimate bearing capacity of the E-shaped footing resting on layered sand and subjected to vertical load was carried out using finite element analysis. The layered sand was having an upper layer of loose sand of thickness H and lower layer was considered as dense sand of infinite depth. The various parameters varied were the friction angle of the upper (30° to 34°) and lower (42° to 46°) layer of sand as well as the thickness (0.5B, 2B and 4B) of the upper sand layer. Findings: The results reveal that the dimensionless ultimate bearing capacity was found to decrease with the increased in the H/B ratio for all combinations of parameters. The dimensionless ultimate bearing capacity was maximum for the upper loose sand friction angle of 34° and lower dense sand friction angle of 46°. The results further reveal that the dimensionless bearing capacity of the E-shaped footing was higher in comparison to the dimensionless bearing capacity of the square footing on layered sand (loose over dense). The improvement in the ultimate bearing capacity for the E-shaped footing was observed in the range of 109.35% to 152.24%, 0.44% to 7.63% and 0.63% to 18.97% corresponding to H/B ratio of 0.5, 2 and 4 respectively. The lowest percentage improvement in the dimensionless bearing capacity for the E-shaped footing on layered sand was 0.44 % at a H/B = 2 whereas the highest improvement was 152.24 % at a H/B = 0.5. Change of footing shape from square to E-shaped, the failure mechanism changes from general shear to local shear failure. Research limitations/implications: The results presented in this paper were based on the numerical study conducted on E-shaped footing made out of a square footing of size 1.5 m x 1.5 m. However, further validation of the results presented in this paper, is recommended using experimental study conducted on similar size E-shaped footing. Practical implications: The proposed numerical study can be useful for the architects designing similar types of super structures requiring similar shaped footings. Originality/value: No numerical study on E-shaped footing resting on layered sand (loose over dense) were conducted so far. Hence, an attempt was made in this article to estimate the bearing capacity of these footings.

4

Bearing capacity of embedded and skirted E-shaped footing on layered sand

Nazeer S., Dutta R. K.

Journal of Achievements in Materials and Manufacturing Engineering

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2021

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Vol. 108, nr 1

5--23

EN

Purpose: The purpose of this study is to investigate the ultimate bearing capacity of the embedded and skirted E-shaped footing resting on two layered sand using finite element method. The analysis was carried out by using ABACUS software. Design/methodology/approach: The numerical study of the ultimate bearing capacity of the embedded and skirted E-shaped footing resting on layered sand and subjected to vertical load was carried out using finite element analysis. The layered sand was having an upper layer of loose sand of thickness H and lower layer was considered as dense sand of infinite depth. The various parameters varied were the friction angle of the upper (30° to 34°) and lower (42° to 46°) layer of sand, the skirt depth (0B, 0.25B, 0.5B and 1B), the embedment depth (0B, 0.25B, 0.5B and 1B) and the thickness (0.5B, 2B and 4B) of the upper sand layer, where B is the width of the square footing. Findings: The ultimate bearing capacity was higher for the skirted E-shaped footing followed by embedded E-shaped footing and unskirted E-shaped footing in this order for all combinations of variables studied. The improvement in the ultimate bearing capacity for the skirted E-shaped footing in comparison to the embedded E-shaped footing was in the range of 0.31 % to 61.13 %, 30.5 % to 146.31 % and 73.26 % to 282.38% corresponding to H/B ratios of 0.5, 2.0 and 4.0 respectively. The highest increase (283.38 %) was observed at φ1 =30° and φ2 =46° corresponding to H/B and Ds/B ratio of 4.0 and 1.0 respectively while the increase was lowest (0.31 %) at φ1 =34° and φ2 =46° at H/B ratio of 0.5 and Ds/B ratio of 0.5. For the skirted E-shaped footing, the lateral spread was more as in comparison to the embedded E-shaped footing. The bearing capacity of the skirted footing was equal the sum of bearing capacity of the surface footing, the skin resistance developed around the skirt surfaces and tip resistance of the skirt with coefficient of determination as 0.8739. The highest displacement was found below the unskirted and embedded E-shaped footing, and at the skirt tip in the case of the skirted E-shaped footing. Further, the displacement contours generated supports the observations of the multi-edge embedded and skirted footings regarding the ultimate bearing capacity on layered sands. Research limitations/implications: The results presented in this paper were based on the numerical study conducted on E shaped footing made from a square footing of size 1.5 m x 1.5 m. However, further validation of the results presented in this paper, is recommended using experimental study conducted on similar size E shaped footing. Practical implications: The proposed numerical study can be an advantage for the architects designing similar types of super structures requiring similar shaped footings. Originality/value: No numerical study on embedded and skirted E shaped footing resting on layered sand (loose over dense) were conducted so far. Hence, an attempt was made in this article to estimate the bearing capacity of the same footings.

5

A proposal for descriptive geometry term papers

Koźniewski E

Journal Biuletyn of Polish Society for Geometry and Engineering Graphics

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2014

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Vol. 26

33--40

EN

Designing roofs and embankments proves to be a good topic for a term paper for students of Descriptive Geometry. It is an excellent opportunity for actual application of the Monge method (2D structures) in 3D modelling using CAD software and also physical creation of a model of a roof (using paper) and embankment (using powders). The present paper includes an interesting proposal of conducting a project which could verify the theorem in practice as early as at the beginning of one’s technical course at university.

PL

Kształtowanie dachów oraz nasypów okazuje się być dobrym tematem na prace semestralne dla studentów w ramach przedmiotu geometria wykreślna. Stwarza znakomitą okazję do realnego zastosowania w praktyce metody Monge’a (konstrukcje 2D) i modelowania 3D za pomocą programu CAD, a także wykreowania fizycznego modelu dachu (konstrukcja z papieru) i nasypu (model utworzony z materiału sypkiego). Praca zawiera propozycję zrealizowania ambitnego projektu z zakresu weryfikacji teorii w praktyce już na początku studiów technicznych.

6

Opory tarcia na styku geosyntetycznych ekranów przeciwfiltracyjnych w wałach przeciwpowodziowych

Borys M.

Woda-Środowisko-Obszary Wiejskie

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2007

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T. 7, z. 2b

21-31

PL

W ostatnich latach znacznie wzrosło zainteresowanie zastosowaniem geosyntetyków do uszczelniania wałów przeciwpowodziowych. W ramach odbudowy lub modernizacji obwałowań wykonuje się z nich pochyłe ekrany przeciwfiltracyjne. Zaprojektowanie, a następnie budowa ekranu przeciwfiltracyjnego wymaga wykonania obliczeń stateczności, do czego niezbędna jest znajomość oporów tarcia na styku poszczególnych warstw uszczelnienia. Celem badań opisanych w niniejszym artykule było określenie, jaki wpływ ma rodzaj gruntu (grunty grubo-, średnio- i drobnoziarniste, w tym spoiste) i jego zmieniająca się wilgotność (od stanu powietrznie suchego przez wilgotny do mokrego) na wartość kąta tarcia na jego styku z geosyntetykami najczęściej wykorzystywanymi do budowy ekranów przeciwfiltracyjnych, jak też określenie wartości kąta tarcia na styku różnych geosyntetyków, mogących tworzyć ekrany wielowarstwowe. Wykazano m. in., że bardzo duży wpływ na wartości kąta tarcia na styku gruntu i ekranu ma wilgotność gruntu spoistego, dlatego też geomembrany nie powinny być układane na podłożu z gruntu spoistego o dużej zawartości frakcji pylastej i ilastej ani też przykrywane taką warstwą ochronną, szczególnie gdy grunty te mogą ulec nawodnieniu. Kąty tarcia na styku geosyntetyków ze sobą są mniejsze niż tychże geosyntetyków z gruntami, dlatego w obliczeniach stateczności wałów z ekranami wielowarstwowymi, składającymi się z różnych geosyntetyków, należy założyć poślizg nie tylko na styku ekran-grunt, ale też na styku warstw o najmniejszych oporach tarcia.

EN

Interest in using geosynthetics to seal flood embankments has markedly increased in recent years. Sloping anti-filtration screens are made of geosynthetics in the construction or modernization of flood embankments. Design and construction of an anti-filtration screen needs stability calculations which in turn require the knowledge of friction forces at the junction of particular sealing layers. Studies described in this paper were undertaken to estimate the effect of soil type (coarse, medium and fine-grained, including coherent soil) and its changing moisture (from air-dry to moist to wet) on the friction angle at its junction with geosynthetics most often used in the construction of anti-filtration screens and to estimate the friction angle at the junction of various geosynthetics that form multi-layer screens. It was shown that for cohesive soil the moisture exerts significant effect on the friction angle at the soil-screen junction. Therefore, geomembranes should not be placed on substratum made of cohesive soils of a high content of silt and clay fraction nor covered with such protective layer particularly when soils might become watered. Friction angles at the junction of geosynthetic layers are smaller than those at the junction of the geosynthetics with soils. Therefore, when calculating stability of embankments with multi-layer screens made of various geosynthetics, one should assume a slide not only at the soil-screen junction but also at the junction of layers with the least friction forces.

7

Normowe wartości kąta tarcia gruntów niespoistych w świetle badań

Parylak K.

Zeszyty Naukowe Politechniki Białostockiej. Budownictwo

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2006

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Z. 28, t. 1

249-257

PL

W pracy przeanalizowano różnice wartości kąta tarcia wewnętrznego trzech drobnoziarnistych niespoistych jednakowo uziarnionych piasków pylastych, uzyskane w badaniach trójosiowego ściskania, które porównano z wartościami ? podanymi w normie B - 03020. Jednakowo uziarnione grunty o szeroko zróżnicowanych cechach kształtu cząstek badano w stanie suchym przy 4 jednakowych stopniach zagęszczenia. Każdą serię próbek ścinano w aparacie trójosiowego ściskania przy naprężeniach ?3 10, 25, 50, 100 i 200 kPa. Dla uzyskanych obwiedni zinterpretowano wartości ? metodą stycznych. Uzyskane wartości porównano z kątami tarcia wewnętrznego piasku pylastego i drobnego podanymi w normie. Wykazano, że normowe wartości ? w przybliżeniu odpowiadają ?cv gruntu skomponowanego z kulek szklanych, a więc niewystępującego w naturze gruntu o idealnie gładkich i okrągłych ziarnach. Stąd dalsze zmniejszanie wartości tego parametru przy wymiarowaniu o 10 % wartość m dodatkowo zaniża go do nierealnych wartości. W przypadku naturalnego pyłu piaszczystego wartości ? są większe od normowych od 7 do 11o. Prowadzi to do niepotrzebnego przewymiarowywania budowli.

EN

The difference between values of tangent angle of shear resistance and values proposed in polish standard PN-81/B-03020 were analyzed. The series of three silty - sand mixture about the same grain size distribution were tested in traxial test. The series of dry samples were compacted to different initial relative density Dr 0,10 - 0,30, and tested in stress range from 10 to 200 kPa. The values proposed by polish standard are approximated to ?cv obtained in glass ballotini, and are smaller from natural silty - sand mixture about 5o to 12o.

8

Liniowe prawa tarcia warstwy ziarna zbóż

Molenda M., Horabik J.

Inżynieria Rolnicza

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2002

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R. 6, nr 6

149--156

PL

Analizowano czynniki wpływające na tarcie ziarna zbóż. Stwierdzono, że zawartość wody, poziom naporu normalnego i procedura konsolidacji próbki wpływają istotnie na wyniki pomiaru współczynnika tarcia. Zależności naporu stycznego od naporu normalnego modelowano przebiegami liniowymi. Stwierdzono, że w zakresie zawartości wody 0,11-0,25 kg/kg i w zakresie naporu 20-100 kPa model liniowy bez wyrazu wolnego wystarczająco dokładnie opisuje tarcie ziarna pszenicy.

EN

Some factors affecting the friction of cereal grain were considered. Grain moisture content, the level of normal pressure and the procedure of sample consolidation were found to influence significantly the results of measuring friction coefficient. Linear relationship between frictional load and normal load were fitted to experimental results. The linear model without any free term was found to describe adequately the friction of wheat grain at the moisture content (dry basis) ranging from 0.11 to 0.25 kg/kg and the pressure range within 20-100 kPa.

9

Wykorzystanie teorii rzutu ukośnego w modelowaniu tryjera do gryki

Rawa T., Kaliniewicz Z.

Problemy Inżynierii Rolniczej

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2001

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R. 9, nr 2

13-20

PL

Przedstawiono eksperymentalno-analityczną metodę wyznaczania rozkładu kąta wypadania nasion z wgłębień rowkowych tryjera do gryki, rozkładu kąta wpadania nasion do rynienki oraz rozkładu kąta tarcia nasion o podstawę wgłębienia. Praca zawiera podstawy teoretyczne metody i opis stanowiska laboratoryjnego do eksperymentalnego wyznaczania rozkładu nasion w locie swobodnym. Stwierdzono, że uklad eksperymentalny jest pomiarowo stabilny już przy jednostkowych pomiarach i stwarza możliwosci zmniejszenia błędów przez pomiary z replikacjami.

EN

An experimantal-analytical method to determine the distribution of angle at which the buckwheat seeds fall out from the trieur grooves, the distribution of angle at which the seeds fall into trough, and the distribution of angle of seeds' friction against groove base were presented. Paper discussed the theoretical foundations of the method, also the laboratory stand for experimental determination of seeds' disatribution at free flight, was described. It was stated that the experimental arrangement was stable in terms of measuring even at individual measurements and made it possible to reduce the errors through the measurements with replications.