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Mocth Ta TyHe^i: Teopia, goe^ig^eHHH, iipau'inu'a, 2016, № 9
MOCTH TA TYHE^I: TEOPM, ^OŒI^EHHfl, nPÄKTHKÄ
UDC 624.138.22-032.61
Y. L. VYNNYKOV1, T. V. LYTVYNENKO2*
1 Depart. «Highways, geodesy, land management and rural buildings», Poltava National Technical Yuri Kondratyuk university, Pershotravnevyi avenue, 24, Poltava, Ukraine, 36011, tel. +38 (099) 292 96 94, e-mail vynnykov@yandex.ru, ORCID 0000-0003-2164-9936
2* Depart. «Highways, geodesy, land management and rural buildings», Poltava National Technical Yuri Kondratyuk university, Pershotravnevyi avenue, 24, Poltava, Ukraine, 36011, tel. +38 (099) 413 59 99, e-mail tatiana.jasmine.litvinenko@mail.ru, ORCID 0000-0002-4747-3353
CORRECT CONDITIONS OF CLAY SOILS BEING A PART OF HIGHWAY EMBANKMENT COMPACTION FE MODELING
Purpose. Finite elements method (FEM) spatial tasks decisions using elastic-plastic soil models show the possibility of correct soil compaction modeling, but unresolved is the item of testing these solutions for clay soils compaction process modeling being a part of highway embankment by the condition of their long-term strength ensuring, which was the aim of the work. Methodology. To simulate the process of layered clay soils compaction being a part of highway embankment, it is used well tested software package «PRIZ-Pile», which implemented the FEM-stepping iterative methods axisymmetrical task of physically and geometrically nonlinear statement with representation of soil isotropic or orthotopic environment. Findings. As a result of numerical simulation three-factors analysis of the impact on the skeleton density average value in the compacted soil initial clay soil skeleton density within the layer after its dumping and leveling, initial thickness of filled and planned to horizontal level subgrade by grader or bulldozer layer, reduction of each clay soil layer surface under the smooth roller was performed. With high statistical indicators values the empirical equation of the relationship between clay soil skeleton density in each compacted layer and above mentioned parameters is obtained. Originality. New correct conditions of FEM modeling in physically and geometrically nonlinear statement the process of layered clay soils compaction being a part of highway embankment, resulting a designer receives soil skeleton density and its deformation module in each layer are established. Practical value. The optimum silty loam moisture for their layered compaction depending on the project soil skeleton density value within the embankment and plasticity number is determined.
Keywords: clay soil; highway embankment; soil skeleton density; soil compaction; FEM modeling
Introduction
From the analysis of recent studies [1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14] author [1, 3], in particular, found that the finite elements method (FEM) is well suited for tasks with substantial strength properties heterogeneity. Compared with variational methods algorithmic it is more flexible in describing the geometry and boundary conditions, physically obvious, universal.
Purpose
FEM spatial tasks decisions using elastic-plastic soil models show the possibility of correct soil compaction modeling, but unresolved is the item of testing these solutions for clay soils compaction process modeling being a part of highway embankment by the condition of their long-term
strength ensuring, which was the purpose of the work.
Methodology
To simulate the process of layered clay soils compaction being a part of highway embankment, it is used well tested software package «PRIZ-Pile», which was created by author [1] and S. F. Klovanych, which implemented the FEM-stepping iterative methods axisymmetrical task of physically and geometrically nonlinear statement with representation of soil isotropic or orthotopic environment [1, 4].
Application of eight-node isoparametric ax-isymmetrical finite elements with properties to significantly change the shape and volume, allows to use both rectangular and curved finite element mesh, and taking into account of these changes -
МОСТИ ТА ТУНЕЛ1: ТЕОР1Я, ДОСЛЩЖЕННЯ, ПРАКТИКА
determination the displacements, stresses and these soil properties at each step of bases placement and load. Their construction modeling is to assign displacement of finite element mesh nodes with strain-stress state (SSS) panel assessment.
To simulate the compaction process by clay soils ramming it is enough to use only the first phase of «compression task» of «PRIZ-Pile» program complex.
At this stage the compaction process of clay soils layers in subgrade is modeling. The compaction influence is set in a forced vertical displacement of finite element mesh nodes, that lie at the upper limit of estimated area, what simulates soil roller displacement process. These movements lead to the finite elements volume reduction, and therefore, soil porosity reducing and its deformation modulus and strength increasing.
Since the forced displacement commensurate with the finite elements size, at each step it is adjusted the original design model specification units coordinate considering displacements, obtained in the previous step. With the coordinates change the finite elements volumes are changing, makes it possible to clarify the deformation modulus value of soil in each finite element by formula (1) for compression tests under the ramming regime.
Void volume ratio at each finite element in this case is
e, = -(1 + )(1 -VjV) .
(1)
The result of the first stage (and, if necessary, and each of its steps) are new coordinates of the finite elements nodes, reduced soil properties (frequent pd, e , E), finite elements mesh nodes displacement, stresses, particularly vertical (isobars c z) and radial (thrust cr) that presented in the tables form, graphs, contours.
Calculation of the first stage linked to stepped task solving on the given displacement and doing by the deform scheme at every step. At that, as a rule, the significant change of finite elements is taking place, what can leads to finite element degeneration («coordinate transformation jacobian becomes non-positive»).
To avoid this nodes displacement it is setting no more than multiplication value of finite element size and soil porosity in it or appropriately selected finite elements size. If you still need the calculation on a larger displacement they're to setting by step parts, the number of what is specified in the control data.
Axisymmetrical estimated area task of clay soils layers ramming modeling in highway embankment - a cylinder (Fig. 1, a), what was obtaining by rectangular settlement area inversion (Fig. 1, b) around the symmetry axis OA.
a)
b)
Fig. 1. Initial estimated area of axisymmetric task in a cylinder form:
a - calculated area; b - rectangular calculation area; c - stress components; 1 - calculation area division segment; 2 - finite element
МОСТИ ТА ТУНЕЛ1: ТЕОР1Я, ДОСЛЩЖЕННЯ, ПРАКТИКА
Settlement area sizes for this task is set as follows:
- lateral boundaries OA and BC respectively taken on the axis symmetry and a sufficient distance from the forced displacement to minimize the impact of conditions to avoid the horizontal displacement, stress concentration and soil compaction in contact with calculated area outer limit. For this condition completion in the task of soil compaction by roller settlement area diameter should be accept no less than 10b, where b - the drum roller length;
- upper (horizontal) limit OB is placed at the layer surface of banking soil before its ramming;
- the first modeling stage the lower horizontal boundary AC it is accepted the roof of already compacted soil layer;
- the second modeling stage the lower horizontal boundary AC should be in layer, what doesn't have special properties and is suitable as a natural basis; the compressed thickness lower boundary is accepted as the depth of estimated area according to appendix D DBN B.2.1-10-2009 [2].
Sequentially numbered nodes and finite elements are adopted. They are numbered, starting with the lower finite element and the axis of symmetry. The finite elements dimensions is taken mainly to the value of forced displacement in the first modeling stage. Of course finite element mesh is thickened (reducing their size) in areas where the first phase provided the largest forced displacement (and hence a significant change in physical and mechanical soil characteristics and SSS array), and the second - the soil displacement and stress concentration in it.
Following the appointment of settlement area size and dividing it into finite elements boundary conditions, corresponding to natural conditions development and work of bases and foundations under the load is setting, namely all nodes that located at the lower boundary of AC, firmly fixed; lateral units limit OA and BC can not have horizontal displacement, except those units that at the first stage forced displacement is setting and that are close to the last (usually they are lying on axis OA).
As a result of the first stage calculations nodal points displacements are finding, new deformed scheme coordinate nodes, strains, stresses, given soil skeleton density value, deformation modulus and other characteristics of each finite element, modified by reducing of its volume.
From the previous experience [1] solutions reliability, obtained by FEM modeling for the software package «PRIZ-Pile», provided by the finite elements form and properties, settlement area shape and size, by selecting the appropriate settlement FEM schemes of soils subgrade layers ramming, model compliance parameters to the actual soil condition at its construction.
As initial it is used the data of compacted clay soil layer by layer highway embankment erection at the object «Khrestyshchenske GCD construction, Khrestyshchenske BCS reconstruction».
In particular, numerical experiment with the impact on the average of clay soil skeleton density in each compacted layer three technological factors is planned:
- initial clay soil skeleton density within the layer after its dumping and leveling pd 0;
- initial thickness of filled and planned to horizontal level subgrade by grader or bulldozer layer;
- reduction of each clay soil layer surface under the smooth roller Ah .
According to field research it is assumed that the optimal passes number of smooth self-propelled pneumatic roller HammHD 150 TT by the one track was 14.
When modeling clay soil layer ramming the original design scheme is adopted, what comprising 550 finite elements (55 x 10), 1781 finite elements mesh nodes, of which 151 - fixed.
Findings
As a result of numerical simulation three-factors analysis of the impact on the skeleton density average value in the compacted soil layer (respectively pd, t/m3) technological factors was performed:
1) initial clay soil skeleton density within the layer after its dumping and leveling (in the experiments pd = 1,30 t/m3; 1,35 t/m3; 1,40 t/m3);
2) initial thickness of filled and planned to horizontal level subgrade by grader or bulldozer layer h (in the experiments - h = 0,15 m; 0,20 m; 0,25 m);
3) reduction of each clay soil layer surface under the smooth roller Ah (in the experiments -Ah = 0,02 m; 0,03 m; 0,04 m).
Therefore, the finite elements size in experiments is 200x15 mm, 200x20 mm and 200x25 mm.
According rectangular creating size calculation area (look Fig. 1, b) was 11,0x0,15 m, 11,0x0,20 m and 11,0x0,25 m.
МОСТИ ТА ТУНЕЛ1: ТЕОР1Я, ДОСЛ1ДЖЕННЯ, ПРАКТИКА_
Laying, already compacted, layer cap is taken as incompressible. Forced vertical displacement is setting to all nodal points of the calculated area upper limit (condition of «compression problem»). In particular, 111 units (from 1671 to 1781) vertical displacement is setting in the value Ah = 15 mm, 20 mm (look Fig. 1, b) and 25 mm.
Thus, the total experiments number composed n=27. For further analysis it was accepted only 14 results of numerical simulation in which real values of clay soil skeleton density in each compacted layer pd = 1,55...1,75 t/m3 is obtained. As a result of three-factors analysis the following equation of the relationship between clay soil skeleton density in each compacted layer pd and the initial clay soil skeleton density within the layer after its dumping and leveling pd0, the initial thickness of filled and planned to horizontal level subgrade by grader or bulldozer layer h, reduction of each clay soil layer surface under the smooth roller Ah :
Pd = a0 + a1 -Pd.0 + a2 • h + a 3 ■Ah , (2)
where are ao = 0,4716 t/m3; ax = 0,8703; a2 =-1,4648 t/m4; a3 = 8,5459 t/m4 - empirical coefficients of equation (2).
For equation (2) multiple correlation coefficient is r=0,9279, and Fisher's ratio test F = 7,1976, what more than its table-valued Ftable «2,65 at test significance p = 5 % and the degree of freedom v1 = 13 and v2 = 10So, equation (1) is completely correct. Relative deviation of simulated values pd comparatively with field experiments does not exceed 2,24 %.
Scientific novelty and practical importance
New correct conditions of FEM modeling in physically and geometrically nonlinear statement the process of layered clay soils compaction being a part of highway embankment, resulting a designer receives soil skeleton density and its deformation module in each layer are established. The optimum silty loam moisture for their layered compaction depending on the project soil skeleton density value within the embankment and plasticity number is determined.
Conclusions
So, new correct conditions of modeling the process of layered clay soils compaction being a
part of highway embankment using the possibilities of task class «The soil work without the possibility of its lateral displacement from the working body or foundation» for the elastic-plastic phe-nomenological model of soil by the conditions of FEM axisymmetrical version in physically and geometrically nonlinear formulation, resulting a designer receives soil skeleton density and its deformation module in each layer.
With high statistical indicators values the empirical equation of the relationship between clay soil skeleton density in each compacted layer and the initial clay soil skeleton density within the layer after its dumping and leveling, initial thickness of filled and planned to horizontal level subgrade by grader or bulldozer layer, reduction of each clay soil layer surface under the smooth roller is obtained.
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3. 1нженерна геологiя. Механiка грунлв, основи i фундаменти [Текст] : тдручник / М. Л. Зоценко та ш. - Полтава : ПНТУ, 2004. - 568 с.
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© Y. L. Vynnykov, T. V. Lytvynenko, 2016
Мости та тунелк теорiя, дослщження, практика, 2016, № 9
МОСТИ ТА ТУНЕЛ1: ТЕОР1Я, ДОСЛ1ДЖЕННЯ, ПРАКТИКА_
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Ю. Л. ВИННИКОВ1, T. В. ЛИТВИНЕНКО2*
1 Кафедра «Автомобшьних дорщ геодезп, землеустрою та сшьських будшель», Полтавський нацюнальний техшчний ушверситет iменi Юрiя Кондратюка, проспект Першотравневий, 24, Полтава, Украша, 36011, тел. +38 (099) 292 96 94, e*i. пошта vynnykov@yandex.ru, ORCID 0000-0003-2164-9936
2 Кафедра «Автомобшьних дорц\ геодезп, землеустрою та сшьських будiвель», Полтавський нацюнальний техтчний утверситет iменi Юрiя Кондратюка, проспект Першотравневий, 24, Полтава, Украша, 36011, тел. +38 (099) 413 59 99, ел. пошта tatiana.jasmine.litvinenko@mail.ru, ORCID 0000-0002-4747-3353
КОРЕКТН1 УМОВИ МОДЕЛЮВАННЯ МСЕ ПРОЦЕСУ УЩ1ЛЬНЕННЯ ГЛИНИСТИХ ГРУНТ1В У СКЛАД1 ДОРОЖН1Х НАСИП1В
Мета. Рiшення просторових задач методом скiнченних елементiв (МСЕ) з використанням пружно-пластичних моделей грунту доводять можливiсть коректного моделювання його ущiльнення, але невирше-ним поки е питання апробацп цих ршень для моделювання процесу ущшьнення глинистих грунтiв у складi дорожнього насипу за умови забезпечення 1х тривало! мiцностi. Методика. Для моделювання процесу по-шарового ущiльнення глинистих грунпв у складi дорожнього насипу використано добре апробований про-грамний комплекс «PRIZ-Pile», у якому реалiзоване рiшення вюесиметрично! задачi МСЕ кроково-iтерацiйними методами у фiзично й геометрично нелiнiйнiй постановцi з представленням грунту iзотропним чи ортотропним середовищем. Результата. Пiсля чисельного моделювання було виконано трьохчиннико-вий аналiз впливу на середне значення щiльностi скелету грунту в ущ№неному шарi початково! щiльностi скелету глинистого грунту в межах шару тсля його ввдсипання та розрiвнювання, початково! товщини ввд-сипаного та спланованого до горизонтального рiвня ЗП грейдером чи бульдозером шару, зниження поверхнi цього шару грунту тд котком. З високими значеннями статистичних показникiв отримано емтричне рiв-няння взаемозв'язку мiж щшьшстю скелету глинистого грунту в кожному ущшьненому шарi та вказаними вище показниками. Наукова новизна. Встановлено новi коректнi умови моделювання МСЕ у фiзично та геометрично нелiнiйнiй постановках процесу пошарового ущшьнення глинистих грунпв у складi дорожнiх насипiв, за якими проектувальник отримуе щiльнiсть скелету грунту та модуль його деформаци. Практична значимкть. Визначено оптимальну волопсть пилуватих суглиншв для !х пошарового ущшьнення в залежносл ввд проектно! величини щiльностi скелета грунту в межах дорожнього насипу та числа пластичносп грунту.
Ключовi слова: глинист грунти; дорожнiй насип; щшьшсть скелету грунту; ущiльнення грунтiв; моделю-вання МСЕ
МОСТИ ТА ТУНЕЛ1: ТЕОР1Я, ДОСЛ1ДЖЕННЯ, ПРАКТИКА_
Ю. Л. ВИННИКОВ1, T. В. ЛИТВИНЕНКО2*
1 Кафедра «Автомобильных дорог, геодезии, землеустройства и сельских зданий», Полтавский национальный технический университет имени Юрия Кондратюка, проспект Первомайский, 24, Полтава, Украина, 36011, тел. +38 (099) 292 96 94, эл. почта vynnykov@yandex.ru, ORCID 0000-0003-2164-9936
2* Кафедра «Автомобильных дорог, геодезии, землеустройства и сельских зданий», Полтавский национальный технический университет имени Юрия Кондратюка, проспект Первомайский, 24, Полтава, Украина, 36011, тел. +38 (099) 413 59 99, эл. почта tatiana.jasmine.litvinenko@mail.ru, ORCID 0000-0002-4747-3353
КОРРЕКТНЫЕ УСЛОВИЯ МОДЕЛИРОВАНИЯ МКЭ ПРОЦЕССА УПЛОТНЕНИЯ ГЛИНИСТЫХ ГРУНТОВ В СОСТАВЕ ДОРОЖНЫХ НАСЫПЕЙ
Цель. Решение пространственных задач методом конечных эелементов (МКЭ) с использованием упруго-пластических моделей грунта доказывает возможность корректного моделирования его уплотнения, но нерешенным пока является вопрос апробации этих решений для моделирования процесса уплотнения глинистых грунтов в составе дорожной насыпи при условии обеспечения их длительной прочности. Методика. Для моделирования процесса послойного уплотнения глинистых грунтов в составе дорожной насыпи использован хорошо апробированный программный комплекс «PRIZ-Pile», в котором реализовано решение осесиметрической задачи МКЭ шагово-итерационными методами в физически и геометрически нелинейной постановке с представлением грунта изотропной или ортотропной средой. Результаты. После численного моделирования был выполнен трехфакторный анализ влияния на среднее значение плотности скелета грунта в уплотненном слое начальной плотности скелета глинистого грунта в пределах слоя после его отсыпания и разравнивания, начальной толщины отсыпанного и спланированного к горизонтальному уровню ЗП грейдером или бульдозером слоя, снижения поверхности этого слоя грунта под катком. С высокими значениями статистических показателей получено эмпирическое уравнение взаимосвязи между плотностью скелета глинистого грунта в каждом уплотненном слое и указанными выше показателями. Научная новизна. Установлены новые корректные условия моделирования МКЭ в физически и геометрически нелинейной постановках процесса послойного уплотнения глинистых грунтов в составе дорожных насыпей, по которым проектировщик получает плотность скелету грунта и модуль его деформации. Практическая значимость. Определена оптимальная влажность пилеватых суглинков для их послойного уплотнения в зависимости от проектной величины плотности скелета грунта в пределах дорожной насыпи и числа пластичности грунта.
Ключевые слова: глинистые грунты; дорожная насыпь; плотность скелета грунта; уплотнение грунтов; моделирование МКЭ
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Prof. V. D. Petrenko, Dr. Sc (Technical, Ukraine) and prof. Tiutkin O. L., Dr. Sc (Technical, Ukraine)
recommended this article to be published.
Received: Sept. 01, 2016.
Accepted: Sept. 26, 2016.
