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Article
Bearing Capacity of Pile Group and Piled Raft Foundations on Sandy Soil
قابلية تحمل مجاميع الركائز و الأسس الحصيرية المدعمة بركائز على ترب رملية

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Abstract

This paper presents an experimental study to investigate the behavior of piled raft system in different types of sandy soil. A small scale “prototype” model was tested in a sand box with load applied to the foundation through a compression jack and measured by means of a load cell. The settlement was measured at the raft by means of dial gauges, three strain gauges were attached on piles to measure the strains and to calculate the load carried by each pile in the group by the strain indicator. Nine configurations of pile groups (1x2, 1x3, 1x4, 2x2, 2x3, 2x4, 3x3, 3x4 and 4x4) were tested in the laboratory as a free standing pile group (the raft is not in contact with the soil) and as a piled raft (the raft is in contact with the soil), in addition to tests for a raft (unpiled) with different sizes. Three different densities of sand were used for some tests.It is found that the piles work as settlement reducers effectively when the number of piles is greater than (6) than when the number of piles is less than (6). The settlement can be increased by about 8 times in (1x2) free standing pile group compared to the piled raft of the same size. The effect of piled raft in reducing the settlement vanishes when the number of piles exceeds (6). For piled rafts (3x3) and (4x4) embedded in loose, medium and dense sand; an increase in the ultimate capacity by about 93%, 96% and 98% is obtained when the group is enlarged from (3x3) to (4x4). This is attributed to increase in footing size (cap) and the increase of the number of piles in the group

يمثل هذا البحث دراسة عملية للتحري عن تصرف منظومة الأساس الحصيري المدعم بالركائز في ترب رملية مختلفة. تم فحص نموذج مختبري مصغر في صندوق من الرمل مع حمل مسلط على الأساس من خلال مرفاع ضغط هيدروليكي و مقاسا بواسطة خلية حمل. و قد قيس الهبوط في الأساس بواسطة مقاييس ازاحة و ربطت مقاييس انفعال بالركائز لقياس الانفعالات و من ثم حساب الحمل الذي تحمله كل ركيزة في المجموعة بواسطة قاريء انفعالات. و قد فحصت تسعة أشكال من مجاميع الركائز (1x2, 1x3, 1x4, 2x2, 2x3, 2x4, 3x3, 3x4, 4x4) باعتبار أن الركائز حرة النهايات و أن قبعة الركائز ليست في تماس مع التربة، ثم فحصت المجاميع بجعل قبعة الركائز بتماس مع التربة بالاضافة الى فحص أساس حصيري (بدون ركائز) بأحجام مختلفة. و قد أستعمل رمل بكثافات مختلفة في بعض الفحوص. و قد وجد أن الركائز تعمل كمقللات هبوط بكفاءة عندما يكون عدد الركائز أكبر من (6) عن حالة عدد الركائز أقل من (6). ان الهبوط يمكن أن يزداد بحدود (8) مرات في مجموعة الركائز (1x2) مقارنة مع أساس حصيري مستند على ركائز بنفس الحجم. ان دور الأساس الحصيري المستند على ركائز في تقليل الهبوط يتلاشى عندما يتجاوز عدد الركائز (6). و للأساس الحصيري المستند على ركائز بحجم (3x3) و (4x4) المستند على تربة رملية مفككة و متوسطة و كثيفة، لوحظ حصول زيادة في قابلية التحمل بحدود 93% و 96% و 98% على التوالي عند زيادة حجم المجموعة من (3x3) الى (4x4) بسبب الزيادة في حجم الأساس (القبعة) و زيادة عدد الركائز في المجموعة.


Article
A Comparative Study between Piled-Raft and Two Soil Improvement Techniques
دراسة مقارنة بين الأساس الحصيري المدعم بالركائز وبين اثنين من تقنيات تحسين التربة

Authors: Maki Jafar M. Al-Waily --- Ala’a Ali S. Al-Ta’ai --- Suad Mohammed H. Al-Janabi
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2013 Volume: 31 Issue: 20 Part (A) Engineering Pages: 409-421
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

This investigational study was directed to establish the correlation between piled raft foundation and two soil improvement techniques, stone columns and lime columns to evaluate the bearing improvement ratio BCR for the soft clay soil with three values of undrained shear strength, 8 kPa,10 kPa and 12 kPa. The 12 model tests was conducted in the present work, three models of untreated soil, three models of soil with piled raft, three models of soil treated with stone columns and three models of soil treated with lime columns. The container used in experimental works was made of steel with plane area of 500 mm * 500 mm and 500mm in height. The thickness of soil sample inside the container was 400 mm.The study showed that the piled raft was more efficient in the bearing capacity improvement than the two soil improvement techniques. The bearing improvement ratio were 3.39, 3.27 and 2.78 in the three model tests of piled-raft for three samples of soil, respectively, while the lime columns provided the lowest values of the bearing improvement ratio were 1.64, 1.67 and 1.8 respectively.

وجهت هذه الدراسة الاستكشافية لتحديد علاقة بين الاساس الحصيري المدعم بالركائز وبين تقنيتين من تقنيات تحسين التربة وهما الاعمدة الحجرية واعمدة النورة لتقييم نسبة تحسين التحمل BCR لتربة طينية رخوة مع ثلاث قيم لمقاومة القص غير المبزولة وهي kPa8 و kPa 10 و kPa12. تم اجراء اثنا عشر نموذج فحص في هذا العمل توزعت بواقع ثلاثة نماذج لتربة غير معالجة وثلاثة نماذج لتربة مع الاساس الحصيري المدعم بالركائز وثلاثة لتربة مع عمود حجري وثلاثة لتربة مع عمود نورة. لقد استخدمت حاوية مصنوعة من الفولاذ بابعاد mm 500 * mm 500 في المساحة و mm 500 في الارتفاع, علما بان سمك نموذج التربة داخل الحاوية كان يساوي mm 400. لقد بينت هذه الدراسة بان الأساس الحصيري المدعم بالركائز كان أكثر كفاءة في تحسين قابلية التحمل من تقنيتي تحسين التربة حيث أعطى قيما لنسبة تحسين التحمل BCR تساوي 3.39 و 3.27 و 2.78 في نماذج الفحوصات الثلاثة للاساس الحصيري المدعم بالركائز لثلاث نماذج من التربة على التوالي, بينما اعطت اعمدة النورة اقل لنسبة تحسين التحمل BCR وهي 41.6 و 1.67 و 1.8 لنفس نماذج التربة على التوالي.


Article
Evaluation of Sand Constitutive Models for Analysis of Piled Raft Foundation

Author: Hassan O. Abbase حسن عبيد
Journal: DIYALA JOURNAL OF ENGINEERING SCIENCES مجلة ديالى للعلوم الهندسية ISSN: 19998716/26166909 Year: 2018 Volume: 11 Issue: 1 Pages: 28-32
Publisher: Diyala University جامعة ديالى

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Abstract

Constitutive models play an important origin in the geotechnical problems design. In order to make the models useful to geotechnical engineers, some numerical predictions are presented to compare the performance of different models with experimental results (Full scale tests). It was found from this study that hardening soil model (HS small model) gave good prediction of settlement more than hardening model and Mohr-Coulomb model. Also, the errors in prediction of maximum settlement pile raft, pile group and raft are ranged (3-4) %, (6-7) % and (27-36) % for hardening soil with small strain model, hardening model and Mohr-Coulomb model respectively.


Article
Behavior of Experimental Model of Piled Raft Foundations on Clayey Soils
سلوك النموذج المختبري للأسس الحصيرية المقامة على الترب الطينية

Authors: Mahmoud AL-Qaissy --- Hussein H. Karim --- Mudhafar K. Hameedi
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2013 Volume: 31 Issue: 20 Part (A) Engineering Pages: 288-408
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

Piled raft foundations are a geotechnical composite construction consisting of three elements: piles, raft and soil. In the design of piled rafts, the load is assumed to be shared between the piles and the raft. Therefore, this may improve the ultimate load capacity and reduce settlements in a very economic way as compared with the traditional foundation concepts. Due to the development of structures that use piled rafts as a foundation system, an extensive experimental study was performed by two different scale models with the same L/Dp (Embedment length to pile diameter ratio) and L/Br (Embedded length to raft width ratio Br) to achieve the scale effect and plane stress condition for the large scale model and plane strain condition for the small scale model. The load carrying capacity of the piles and raft have been studied and presented as load-settlement illustrations. From a comparison between the two models of the experimental work, it is found that the effect of scale cause an increase in carrying load of piled raft with increasing the number of piles. It was found that the percentage of the load carried by raft to the total applied load of the experimental model in the case of four piles with raft is ranged between 60.6 - 64.8 %.

ان الأسس الحصيرية المدعمه بالركائز هي منشئ جيوتكنيكي مركب يتألف من ثلاث عناصر هي: الركائز والحصيرة والتربة. في الاساس الحصيري المدعم بالركائز, يتوزيع الحمل بين الركائز والاساس الحصيري. هذا النوع من الاسس فعال في زياده التحمل و تقليل الهطول وذو تكلفة اقل من أسس مجاميع الركائز. ونظرآ لزيادة المنشأت التي يستخدم معها الأساس الحصيري المدعم بالركائز، لقداجريت دراسة عملية مكثفة تضمنت أستخدام نموذجين مختلفين في المقياس وذو نسب (L/Dpو L/Br ) متساوية لدراسة تأثير مقياس النموذج ولتحقيق أجراء الفحوصات عن طريق تسليط الأجهاد وتسليط الأنفعال. وتم دراسة تأثير المقياس على مقدار قابلية التحمل في الاساس المدعم بالركائز وتم توضيحها في مخطط العلاقة بين الحمل - الهطول. من مقارنة النموذجين المختبريين, وجد ان تأثير المقياس في قابلية التحمل يزداد بزيادة عدد الركائز المستخدمة في الاساس الحصيري المدعم بالركائز. وجد ان النسبة المئوية لقابلية تحمل الأساس الحصيري الى الحمل الكلي للنموذج العملي في حالة أربعة ركائز مع الأساس تتراوح ما بين 60.6 الى 64.85 %.


Article
Behavior of Piled Raft Foundation Model Embedded within a Gypseous Soil Before and after Soaking

Authors: N.A. Ab-dullah --- M.R. Mahmood --- H.H. Baqir
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2017 Volume: 35 Issue: 5 Part (A) Engineering Pages: 445-455
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

The paper explain an experimental study to show piled raft system behavior when embedded within gypseous soil in three different stats (dry, socking for 1 day and placing a bearing layer of dense sand below the gypseous soil when socking for 1 day). A small-scale “prototype” model of steel box with dimension of (60cm length x 60cm width x 75cm heights) was used for carried out the model tests. Two different lengths of reinforced concrete pile models (40cm and 45cm) of 2.0cm dia. were used to keep the same imbedded length ratio during testing piled raft and piles only. Three different configurations of pile groups (single, three and six piles) were tested in the laboratory in two ways, first; the raft does not contact with the soil and the second; the raft is in contact with the soil. In dry state, the gypseous soil showed a very high carrying capacity with reduction in settlement. Piled raft foundations show an efficient in dry state, where the load carrying capacity increased and the settlement decreased. The improvement ratios in the load carrying capacity were about 16% for single piled raft and 39% for group of three-piled raft, while settlement reduction ratios were about 18% for single piled raft and 45% for group of six-piled raft. When the gypseous soil socked with water for 1 day, the ultimate bearing capacity of foundations is generally reduced by about (69%-83%) compared with dry state for all model configurations. The improvement ratios in ultimate bearing capacity due to using piled raft in soaking state was about (11% -50%) whilst the reduction settlement ratios was about (16% -44%).


Article
EXPERIMENTAL STUDY OF MODEL PILED RAFT FOUNDATION EMBEDDED WITHIN PARTIALLY SATURATED COHESIONLESS SOILS

Authors: Mahmood Rashid Al-Qayssi --- . Saad Faik Al-Wakel --- Ahmed Khairalla Abdlazez Kando
Journal: Journal of Engineering and Sustainable Development مجلة الهندسة والتنمية المستدامة ISSN: 25200917 Year: 2018 Volume: 22 Issue: 3 Pages: 62-75
Publisher: Al-Mustansyriah University الجامعة المستنصرية

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This paper presents an experimental study conducted on model piled rafts in partially saturated sandy soil. The aim of the experimental program is to study the effect of matric suction on the load carrying capacity of piled rafts embedded within partially saturated sandy soil .The influence of number of piles are presented and discussed in this study. The piled raft is arranged in different configurations of piles (single, double and triple piled raft with spacing 3.5D c/c) with the same area ratio (raft area to the cross section area of piles) to avoid different contact pressure area and to show the effect of different piles number and its group action. The influence of matric suction (i.e., capillary stresses) in partially saturated zone is typically not taken into account in the conventional design of both shallow and deep foundations so that the present research study the determination and contribution of matric suction towards the load carrying capacity of piled raft. The experimental work consist of 3 models of footing "single piled raft (8.3 x 5) cm, double piled (16.6 x 5) cm and triple piled raft (25 x 5) cm". All these models are loaded and tested under both of fully saturated condition (i.e., matric suction equals to 0kPa) and unsaturated conditions (i.e., matric suction value equals to 6kPa , 8kPa and 10kPa), which are achieved by predetermined lowering of water table. The relationship between matric suction and depth of ground water table was measured in suction profile set by using three Tensiometers (IRROMETER). The soil, water characteristic curve (SWCC) estimated by applying fitting methods through the program (SoilVision). The results of experimental work demonstrate that the load carrying capacity of piled raft increases with increasing all values of matric suction as the number of piles supporting the raft increases. And the matric suction has a significant influence on the load carrying capacity of all tested models. The increasing value of the ultimate bearing capacity for single, double and triple piled raft under unsaturated conditions is approximately (2.1-4.47), (2-4.44) and (1.5-3.54) times higher than that at saturated condition respectively


Article
Three-Dimensional Analysis for the Effect of Piles Geometry and Arrangement on the Dynamic Response of Piled Raft Foundation
تحليل ثلاثي الأبعاد لتأثير خواص الركائز على الإستجابة الحركية لأساس حصيري مدعم بالركائز مطمور في الرمل

Authors: Mahmood Rashid Al-Qayssi --- Saad Faik Al-Wakel --- Ihab Ghaleb Abdulwahhab
Journal: Journal of Engineering and Sustainable Development مجلة الهندسة والتنمية المستدامة ISSN: 25200917 Year: 2018 Volume: 22 Issue: 5 Pages: 68-82
Publisher: Al-Mustansyriah University الجامعة المستنصرية

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Abstract

In the present study, three-dimensional analysis is presented to investigate the effect of pile dimensions and configuration on the dynamic response of piled raft foundation subjected to vertical vibration. The analysis considered several factors effecting on the maximum amplitude of vertical displacement of deep foundation such as length, diameter, number of piles and spacing between piles. Furthermore, a validation for an experimental piled raft models depending on a scale factor of (20) using (Plaxis 3D) computer software is presented. The sand is simulated using (mohr-coloumb) model, while the concrete is simulated as linear elastic material. It has been found that the increasing length and diameter of piles lead to decrease the maximum amplitude of displacement. On the other hand, the results showed that the increasing number of piles and increasing the spacing between piles can minimize the dynamic response of the foundation.


Article
Numerical Analysis of Piled Raft Foundation on Clayey Soil
التحليل العددي للأساس الحصيري المدعم بالركائز في التربة الطينية

Authors: Hussein H. Karim --- Mahmoud R. AL-Qaissy --- Mudhafar K. Hameedi
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2013 Volume: 31 Issue: 7 Part (A) Engineering Pages: 1297-1312
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

The piled raft foundations allow an increase in the load capacity and reduction of settlements in a very economic way as compared with the traditional foundation concepts. Due to the development of structures that use piled rafts as a foundation system, an extensive numerical modeling study was performed considering different factors and conditions. This study highlights the percentage ratio of bearing loads between the pile and the pile cap (raft). Present modeling results obtained by computer program (Plaxis 3D Foundation V 1.1) have been verified with an experimental work of the same problem using the same configuration but extended to include 8 and 16 piles with raft for different soil layers. In addition, a comparison of the present results is achieved with another a theoretical study using the program (Ansys). The finite element method through Plaxis program evaluates the effect of parameter on the load-settlement behavior of the piled raft foundation. The effect of spacing between piles on the load-settlement behavior of the piled raft foundation was also studied. The percentage of the load carried by piles to the total applied load of the numerical model for case sixteen piles with raft is around 42%. The contribution to carry the load of piles relative to the total load is decrease with the increase of the spacing to diameter ratio. The percentage of the load carrying for piled raft for the case of two piles with raft only decreases about 23% when the spacing between piles increases from 3 to 10 times pile diameters.

ان الأسس الحصيرية المدعمة بالركائز تسمح بزيادة التحمل و تقليل الهطول وبشكل اقتصادي بالمقارنة مع مجاميع الأسس التقليدية. ونتيجة التطور الحاصل في التراكيب المستخدمة للأسس الحصيرية المدعمة بالركائز, أجريت هذه الدراسة النمذجية أخذين بنظر الاعتبار عوامل وظروف مختلفة. تسلط الدراسة الحالية الضوء على النسبة المئوية للتحمل ما بين الركيزة والأساس. تم التحقق من نتائج النمذجة الحالية المستحصل عليها باستخدام برنامج (PLAXIS 3D Foundation V 1.1) من خلال مقارنتها مع عمل مختبري يعالج نفس المشكلة وبنفس الترتيب وتم حل النموذج مع اضافة حالتين هما 8 و 16 ركيزة مع الأساس و لطبقات تربة مختلفة. وبالإضافة إلى ذلك، تم إجراء مقارنة اخرى بين النتائج الحالية مع دراسة نظرية باستخدام برنامج (ANSYS). تهدف البرامج التي تعتمد طريقة العناصر المحددة من خلال برنامج (PLAXIS)الى تقييم تأثيرسلوك علاقة الحمل- الهطول للأسس الحصيرية المدعمة بالركائز. كما درس تأثير المسافة بين الركائز على هذه العلاقة. وجدت النسبة المؤية لقابلية تحمل الركائز الى الحمل الكلي في النموذج النظري لحالة ستة عشر ركيزة مع الاساس هي بحدود 42 %. وتبين من الدراسة أن مقدار مساهمة الركائز في قابلية التحمل الكلية تقل بزيادة المسافة بين الركائز. وقد وجد في حالة ركيزيتين مع الأساس الحصيري تقل قابلية التحمل بمقدار 23 % مع زيادة المسافة بين الركائز من ثلاثة أضعاف الى عشرة أضعاف قطر الركيزة.


Article
Experimental and Numerical Analysis of Piled Raft Foundation Embedded within Partially Saturated Soil

Authors: M.R. Mahmood --- S.F.A. Al-Wakel --- A.A. Hani
Journal: Engineering and Technology Journal مجلة الهندسة والتكنولوجيا ISSN: 16816900 24120758 Year: 2017 Volume: 35 Issue: 2 Part (A) Engineering Pages: 97-105
Publisher: University of Technology الجامعة التكنولوجية

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Abstract

This paper presents an experimental and numerical study to investigate the load carrying capacity of piled raft foundation embedded within partially saturated sandy soil. The effect of matric suction on the bearing capacity of the foundation system was investigated. The experimental work consists of two models of foundation, circular raft foundation and circular piled raft foundation. The circular raft foundation has dimensions of 10cm in diameter, and 2.5cm thickness, while the piled raft foundation has the same dimensions of the circular raft model but with a single pile of 2.0cm in diameter and 40.0cm in length fixed at the center of the raft. Both models are loaded and tested under both fully saturated condition and unsaturated conditions, which are achieved by, predetermined lowering of water table. The lowering of water table below the soil surface was achieved in to two different depths to get different values of matric suction and the relationship between matric suction and depth of ground water table was measured in suction profile set by using three Tensiometers (IRROMETER). The soil water characteristic curve (SWCC) estimated by applying fitting methods through the software (SoilVision). A validation process then was carried out for the case of circular piled raft foundation with lowering the water table 45cm bellow soil surface in the aid of a sufficient finite element computer program ABAQUS 6.12. An eight-node axisymmetric quadrilateral element CAX8RP and CAX8R were used to simulate the soil continuum and piled raft respectively. The interaction method used to simulate the intersect surfaces of the system (pile-raft-soil) is a surface-to-surface discretization method under the concept of master and slave theory. The behavior of piled raft material is simulated by using a linear elastic model while the behavior of soil is simulated by an elasto-plastic model by the use of the Mohr-Coulomb failure criterion. The results of the experimental work demonstrate that the matric suction has a significant role on the bearing capacity of all tested models. It shows that the ultimate bearing capacity of circular raft foundation under a partially saturated condition is increases by about (7.0-8.0) times than the ultimate bearing capacity of fully saturated condition when lowering the water table 45 cm below the soil surface. While the ultimate bearing of circular piled raft foundation under partially saturated condition increases by about (8.0-9.0) times than the ultimate bearing capacity of fully saturated condition when lowering the water table 45 cm below the soil surface. The results of the ultimate bearing capacity of piled raft foundation that obtained from the experimental model and from the numerical modelling for the same soil condition and same matric suction indicate that a successful validation is achieved for the simulation process.


Article
Experimental and Numerical Analysis of Piled Raft Foundation with Different Length of Piles Under Static Loads
دراسة عملية وتحليلية للاسس الحصيرية المدعمة بالركائز مختلفة الاطوال تحت الاحمال الساكنة

Authors: Mosa Jawad Al-mosawe موسى جواد الموسوي --- A’amal Abdul Ghani Al-Saidi امال عبد الغني حسين السعيدي --- Faris Waleed Jawad فارس وليد جواد
Journal: Journal of Engineering مجلة الهندسة ISSN: 17264073 25203339 Year: 2013 Volume: 19 Issue: 5 Pages: 543-549
Publisher: Baghdad University جامعة بغداد

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Abstract

In order to understand the effect of (length of pile / diameter of pile) ratio on the load carrying capacity and settlement reduction behavior of piled raft resting on loose sand, laboratory model tests were conducted on small-scale models. The parameters studied were the effect of pile length and the number of piles. The load settlement behavior obtained from the tests has been validated by using 3-D finite element in ABAQUS program, was adopted to understand the load carrying response of piled raft and settlement reduction. The results of experimental work show that the increase in (Lp/dp) ratio led to increase in load carrying capacity by piled raft from (19.75 to 29.35%), (14.18 to 28.87%) and (0 to 16.49%) , the maximum load carried by piles decrease from (9.1 to 22.72%), (15.79 to 47.37%) and (44 to 81.05%) and the response of settlement piled raft decrease from (16.67 to 23.33%), (9.09 to 39.39%) and (30%) with increase the number of piles from 4 to (6 and 9) and (length of pile / diameter of pile) ratio increase to (14.14 and 21.2), respectively. The numerical and model test results are found to be in a good agreement.

من اجل فهم تأثير نسبة (طول الركيزة/ قطر الركيزة) على مقدار التحمل والهطول للأساس حصيري مدعم بالركائز جالس على تربة رمليه مفككة تم بناء نموذج مختبري مصغر. العوامل التي تم دراستها هي تأثير طول الركيزة وزيادة عدد الركائز. النتائج التي تم الحصول عليها مختبريا سوف يتم تأكد منها ومقارنتها عدديا باستخدام العناصر المحددة المتاحة في برنامج ABAQUS)) لقد أظهرت النتائج أن زيادة في نسبة (طول الركيزة/ قطر الركيزة) يؤدي إلى زيادة في سعة تحمل الأساس الحصيري المدعم بالركائز من (19.75 الى 29.355 ), (14.18 الى 28.87%) و (0 الى 16.49%) (, نقصان في بمقدار سعة التحمل للركائز من (9.1 الى 22.72%), (15.79 الى 47.37%) و (44 الى 81.05%) وان مقدار التقليل في الهطول الاساس الحصيري المدعم بالركائز بلغ ( 16.67 الى 23.33%), (9.09 الى 39.39%) و (30%) مع زيادة عدد الركائز من (4) الى (6 و 9) وزيادة نسبة (طول الركيزة/ قطر الركيزة) من (21.2 الى 14.14) على التوالي . وان المقارنة النتائج العملية والعددية باستخدام العناصر المحددة أظهرت توافق جيد.

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