بشرى وليث Al-Khwarizmi Engineering Journal,Vol. 12, No. Performance Assessment Bushra S. Albusoda *,**Department of Civil Engineering (Received Abstract An evaluation for the performance of model pile embedded in expansive soil was investigated program was planned to achieve the purpose of this research. Therefore, special manufactured system was prepared for studying the behavior of model pile having different length to diameter ratios (L/D). Two types of piles were used in this research, straight shaft and under reamed piles. The effect of model pile type, L/D ratio and number of wetting drying cycles were studied. It is observed that significant reductions in pile movement when under reamed piles were considered. A proposed design charts was presented for straight shaft and under reamed piles to estimate the length of both types of piles that is required to exert minimized uplift pressure when the soil swells. Keywords: Expansive soil, pile model, reamed piles 1. Introduction Although expansive soils are considered one of the problematic soils in the world and especially in Iraq, it represents serious problem when exist under the foundations, due to the volume change that exhibit when changes in moisture content were occurred. This behavior causes exte damages to structures erected on these soils. In Iraq, expansive soils are found at northern and middle parts of the country, with different swelling tendencies Foundations on expansive soils pose a unique challenge to the geotechnical engineer. They usually cost more than construction of foundations on ordinary soils as well as the site investigation and the foundation design (Nelson et al., 2012). One of the important issues is to insure the stability of the structure constructed on expans soil, a conventional solution is to use piles as a foundation for the structure so it can reach a relatively stable zone in the deep layers of the soils especially when the swelling potential of the underneath expansive soil is so high that conventional soil treatment is considered not effective or not even economical. The using of piles as a practical foundation system in expansive Khwarizmi Engineering Journal,Vol. 12, No. 2, P.P. 1- 9 (2016) Performance Assessment of Pile Embedded in Expansive Soil Albusoda* Laith A. Al-Anbary Civil Engineering/ College of Engineering/ University of Baghdad Email: albusoda@yahoo.com (Received 26 April 2015; accepted 26 November 2015) An evaluation for the performance of model pile embedded in expansive soil was investigated program was planned to achieve the purpose of this research. Therefore, special manufactured system was prepared for studying the behavior of model pile having different length to diameter ratios (L/D). Two types of piles were used in this research, straight shaft and under reamed piles. The effect of model pile type, L/D ratio and number of wetting drying cycles were studied. It is observed that significant reductions in pile movement when under reamed piles were sed design charts was presented for straight shaft and under reamed piles to estimate the length of both types of piles that is required to exert minimized uplift pressure when the soil swells. reamed piles, wetting drying cycles, pile movement. are considered one of the problematic soils in the world and especially in Iraq, it represents serious problem when exist under the foundations, due to the volume change that exhibit when changes in moisture content were occurred. This behavior causes extensive damages to structures erected on these soils. In Iraq, expansive soils are found at northern and middle parts of the country, with different Foundations on expansive soils pose a unique challenge to the geotechnical usually cost more than construction of foundations on ordinary soils as well as the site investigation and the foundation One of the important issues is to insure the stability of the structure constructed on expansive soil, a conventional solution is to use piles as a foundation for the structure so it can reach a relatively stable zone in the deep layers of the soils especially when the swelling potential of the underneath expansive soil is so high that l soil treatment is considered not effective or not even economical. The using of piles as a practical foundation system in expansive soils has been recommended in practice by many researchers such as (Chen, 1975 and Arora, 2008). Many researchers experimental, theoretical and field studies for the past five decades on piles embedded in expansive soils to make a better understanding of the behavior of the pile in such soil conditions. It was concluded from the literature that an inves of the piles’ movement and uplift force due to soil swelling when subjecting the surrounding soil to wetting-drying cycles for representing seasonal moisture content changes is needed to support the scientific and practical research. Therefore, an extensive testing program was planned to investigate each of the following: • Straight shaft and under reamed piles movement when subjecting the surrounding soil to wetting-drying cycles in order to represent seasonal moisture content changes. • Exerted uplift force from straight shaft and under reamed piles due to soil swelling for different wetting-drying cycles. • Comparison between the pullout capacity of straight shaft and under reamed piles for non swelling and swelling soil conditions Al-Khwarizmi Engineering Journal (2016) n Expansive Soil Anbary** University of Baghdad An evaluation for the performance of model pile embedded in expansive soil was investigated. An extensive testing program was planned to achieve the purpose of this research. Therefore, special manufactured system was prepared for studying the behavior of model pile having different length to diameter ratios (L/D). Two types of piles were used in this research, straight shaft and under reamed piles. The effect of model pile type, L/D ratio and number of wetting drying cycles were studied. It is observed that significant reductions in pile movement when under reamed piles were sed design charts was presented for straight shaft and under reamed piles to estimate the length of soils has been recommended in practice by many researchers such as (Chen, 1975 and Arora, 2008). Many researchers have conducted experimental, theoretical and field studies for the past five decades on piles embedded in expansive soils to make a better understanding of the behavior of the pile in such soil conditions. It was concluded from the literature that an investigation of the piles’ movement and uplift force due to soil swelling when subjecting the surrounding soil to drying cycles for representing seasonal moisture content changes is needed to support the scientific and practical research. fore, an extensive testing program was planned to investigate each of the following: Straight shaft and under reamed piles movement when subjecting the surrounding drying cycles in order to represent seasonal moisture content changes. ed uplift force from straight shaft and under reamed piles due to soil swelling for drying cycles. Comparison between the pullout capacity of straight shaft and under reamed piles for non- swelling and swelling soil conditions. Bushra S. Albusoda Al-Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 1- 9(2016) 2 2. Material Properties 2.1. Expansive Soil The expansive soil used in this research was artificially prepared by mixing Iraqi bentonite from Al-Anbar city / Bushayrah Valley, about 35 kilometers southern Al-Waleed Military Base from a depth of three and a half meters from natural ground level, with Karbala sand. In order to increase the permeability of the prepared soil and to facilitate and accelerate saturation process, several trial mixes of bentonite-sand were performed. A ratio of expansive soil to sand of (9/1) was selected. At this ratio, the soil remains highly expansive and its permeability is increased. 2.2. Model Piles 2.2.1. Straight Shaft Piles Nine straight shaft piles have been formed using solid aluminum rod with a diameter of 10mm and three different pile embedment lengths of 100mm, 150mm and 200mm that give L/D ratios of 10, 15 and 20 respectively. The dimensions are shown in Fig. 1 which illustrates that there is an extension of 20 mm in length of all piles for fixing and measurement. Fig. 1. Dimensions of model straight shaft 2.2.2. Under-Reamed Piles Nine under reamed piles with single bulb at the bottom of the pile were made using a solid aluminum rod with 200mm diameter and then formed to give the shape of an under reamed pile as shown in Fig. 2 with dimensions recommended by (Pumina, 2005) of stem diameter of 10mm, bulb diameter of 200mm and a bucket length of 10mm, the L/D ratios were 10, 15 and 20. There is an extension of 20 mm in length of all piles for fixing and measurement. The surface of the model piles has been textured to insure the interlock between the pile and the surrounding soil. Fig. 2. Dimensions of model reamed pile 2.2.3. Soil Container Twenty five soil steel containers were made using a 4mm thickness steel plate with the dimensions of (25cm × 25cm ×35cm). The sides of the containers were perforated with 25 holes each with 3mm diameter to decrease soil saturation period, the containers were painted with two coats of anti-rust paint and then two layers of gray base paint to resist the corrosion during test period. Fig. 3 shows the dimensions of the soil container Bushra S. Albusoda Fig. 3. Soil Container Dimensions 2.2.4. Manufactured Apparatuses The main goal of this research is to investigate the effect of wetting and drying cycles on the movement and uplift force of piles embedded in expansive soil which will consume too much time to cover different L/D ratios and types of model piles, for that reason, manufacturing of special devices and apparatuses was needed to shorten test period as will be discussed in details in the following sections. 2.2.5. Saturation-Drying Model for Pile Upward Movement The basic idea here is to manufacture a saturation-drying model for the soil containers; that is large enough to contain eight containers at one time, and to be the same model that the drying process would take place in, instead of transferring the soil containers to a suitable oven. For that purpose, a large tank was made of galvanized steel plate of 2mm thickness and dimensions of (150cm X 80cm X 40cm). A was then attached to the side of the model to use it when conducting drying process. In addition, a drainage valve was then fixed at the bottom of the model. Fig. 4 illustrates the dimensions and the shape of the saturation model. Fig. 4. The saturation-drying model Al-Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 3 Soil Container Dimensions. Manufactured Apparatuses The main goal of this research is to investigate the effect of wetting and drying cycles on the uplift force of piles embedded in expansive soil which will consume too much time to cover different L/D ratios and types of model piles, for that reason, manufacturing of special devices and apparatuses was needed to shorten ed in details in the Drying Model for Pile The basic idea here is to manufacture a drying model for the soil containers; that is large enough to contain eight containers at to be the same model that the drying process would take place in, instead of transferring the soil containers to a suitable oven. For that purpose, a large tank was made of galvanized steel plate of 2mm thickness and dimensions of (150cm X 80cm X 40cm). A flange was then attached to the side of the model to use it when conducting drying process. In addition, a drainage valve was then fixed at the bottom of the model. Fig. 4 illustrates the dimensions and the drying model A cap for saturation-drying model was also made using galvanized steel plate of 2mm thickness and dimensions of (160cm X 80cm X 40cm). This cap is used only when drying process is performed. For the purpose of soil drying, many researchers used electrical heaters around the soil; the defect here is that the heaters provide heat only for the vicinity area around the heaters which will cause a large gradient in the temperature between the core and the outside of the soil (especially for large soil samples). To overcome this defect, a specially designed heating source was manufactured using three rows of electrical heaters each with 7 KW capacity and a fan, all assembled in a thermally isolated aluminum box to give what is called a hea Fig. 5, also a thermometer was provided to the heating duct to control the temperature of soil drying which was fixed to 50 system for heating (drying process) can be in Fig. 6. Fig. 5. Heating Duct Details Fig. 6. Heating system for drying process Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 1- 9(2016) drying model was also made using galvanized steel plate of 2mm thickness and dimensions of (160cm X 80cm X 40cm). This cap is used only when drying process For the purpose of soil drying, many searchers used electrical heaters around the soil; the defect here is that the heaters provide heat only for the vicinity area around the heaters which will cause a large gradient in the temperature between the core and the outside of the soil for large soil samples). To overcome this defect, a specially designed heating source was manufactured using three rows of electrical heaters each with 7 KW capacity and a fan, all assembled in a thermally isolated aluminum box to give what is called a heating duct as shown in Fig. 5, also a thermometer was provided to the heating duct to control the temperature of soil drying which was fixed to 50o Celsius. The whole system for heating (drying process) can be shown Heating Duct Details. Heating system for drying process. Bushra S. Albusoda 2.2.6. Saturation-Drying Model for Pile Uplift Force Measurement Another saturation-drying model was manufactured with the same dimensions for the purpose of measuring pile upward movement. This model is similar to that illustrated in previous section with one difference that this model was provided with a rectangular steel tube frame fixed above it to hold on the proving rings installed above the piles as shown in Fig. 7. The rectangular steel frame was p adjustable screws for adjusting the distance between the proving rings and the piles. Fig. 7. Saturation-drying tank for pile uplift force measurement. Fig. 8. Details of pile pull-out loading frame 2.2.7. Pile Pull-out Loading Frame Special pull-out loading frame was manufactured for measuring pile pull as illustrated in Fig. 8. A load cell with its Al-Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 4 Drying Model for Pile Uplift Force Measurement drying model was manufactured with the same dimensions for the purpose of measuring pile upward movement. similar to that illustrated in previous section with one difference that this model was provided with a rectangular steel tube frame fixed above it to hold on the proving rings installed above the piles as shown in Fig. 7. The rectangular steel frame was provided with adjustable screws for adjusting the distance between the proving rings and the piles. drying tank for pile uplift out loading frame. out Loading Frame out loading frame was manufactured for measuring pile pull-out capacity . A load cell with its indicator was attached to measure the applied tension force on the pile, and two dial gauges were fixed above the pile cap holders to indicate the upward displacement of the pile due to applied force. 2.3. Testing Program The testing program consists mainly of two series. The first series include the physical properties tests. The second series comprises the pile model tests on both straight shaft and under reamed piles. The pile model tests consist of pile movement test due to wetting consumed 153 days (58 days for the first cycle, 49 days for the second cycle and 46 days for the third cycle) as shown in Fig. 9. a Fig. 9. Schematic view for pile movement model test a:top view, b: sec A Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 1- 9(2016) indicator was attached to measure the applied tension force on the pile, and two dial gauges were fixed above the pile cap using two magnetic holders to indicate the upward displacement of the The testing program consists mainly of two series. The first series include the physical properties tests. The second series comprises the pile model tests on both straight shaft and under reamed piles. The pile model tests consist of pile e to wetting-drying cycles which consumed 153 days (58 days for the first cycle, 49 days for the second cycle and 46 days for the third b c Fig. 9. Schematic view for pile movement model test a:top view, b: sec A-A, c: sec B-B Bushra S. Albusoda The pile uplift force test through wetting drying(six pile models were tested on three wetting-drying cycles which consumed an average period of 45) as shown in Fig. 10. a b c Fig. 10. Uplift force saturation-drying tank a: top view of the tank, b: section A c: section B-B The pull-out capacity test was performed according to ASTM D3689-07 (Section 8.1.2 quick test procedure) on six model straight shaft piles, three of them were embedded in an expansive soil prepared at initial water content of Al-Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 5 The pile uplift force test through wetting- drying(six pile models were tested on three drying cycles which consumed an average drying tank a: top view of the tank, b: section A-A, out capacity test was performed 07 (Section 8.1.2 quick test procedure) on six model straight shaft piles, three of them were embedded in an expansive soil prepared at initial water content of 2% dry of optimum and the othe embedded in expansive soil at the same initial water content but exposed to wetting that consumes 40 days for each model. Another six pile model tests were conducted on under reamed piles to determine the pull out capacity of these piles, three of them when the soil was wetted, and the other three model tests when the soil was prepared at initial water content without wetting, see Fig. 11. It is important to note that each test is conducted on three different L/D ratios (10, 15, and 20). Fig. 11. Model pile pull- testing. 2.4. Physical Properties The following table gives the physical properties of the used expansive soil, (Table 1). Table 1, Physical Properties of Expansive Soil Test Standards Soil Classification USCS Maximum Dry Density (MDD) ASTM D698 Optimum Moisture Content (OMC) Specific Gravity Gs ASTM D854 Liquid Limit ASTM D4318 Plastic Limit Plasticity Index Swelling Pressure Standard Oedometer Test Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 1- 9(2016) 2% dry of optimum and the other piles were embedded in expansive soil at the same initial water content but exposed to wetting that consumes 40 days for each model. Another six pile model tests were conducted on under reamed piles to determine the pull out capacity of these e of them when the soil was wetted, and the other three model tests when the soil was prepared at initial water content without wetting, . It is important to note that each test is conducted on three different L/D ratios (10, 15, out test system during roperties Tests The following table gives the physical properties of the used expansive soil, (Table 1). Physical Properties of Expansive Soil. Standards Results USCS CH ASTM D698-12 1.23 g/cm3 34 % ASTM D854-10 2.52 ASTM D4318-10 102 % 45 % 57 Standard Oedometer Test 312 kPa Bushra S. Albusoda Al-Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 1- 9(2016) 6 2.5. Soil Bed Preparation The soil bed is prepared in the container to be ready for performing model tests. Two trial mixes were carried out on sand mixing percentages of 5% and 10% with the soil. The two percentages of mixing reduced the swelling pressure of the soil and certainly increased the permeability. Fig. 12 shows the variation of swelling pressure with the sand mixing percentages. Fig. 12. Relationship between sand-soil mixing percentage and the resulting swelling pressure y. The soil bed was prepared on a dry density of 1.225 g/cm3, which corresponds to a water content of 2% dry of optimum. The required amount of expansive soil was placed inside the container to one fifth of the final thickness of the bed of the soil and compacted using a hand hammer with a square base of the same internal dimensions of the soil container and a hole centered on its base in order not to let the pile be affected during soil compaction as shown in Fig. 13. This method of compaction was performed by many researchers such as (Al-Ani, 1993, Al- Maamoury, 1994 and Chao, 2007). Four sand drains were formed around the pile using thin walled steel tube (10 mm diameter and 250 mm length). The sand drains were spaced 100 mm from the pile (center to center). The sand used was passing sieve No.8 and prepared at a relative density equal to 82% to decrease soil saturation period. Required amount of expansive soil is poured onto the soil container Compaction of soil to the required level by using the specially manufactured hand hammer Fig. 13. Placing of expansive soi bed layers and compaction. 3. Model Test Results 3.1. Pile Movement Model Test 3.1.1 Experimental Model Test Results The upward movement of the piles due to soil swelling and the downward movement due to soil shrinkage were recorded with time for straight shaft and under reamed piles with L/D ratios of 10, 15 and 20. Fig. 14 illustrates the recorded results. 3.1.2. Proposed Design Chart Based on the experimental model test, a design chart is presented in Fig. 15 to determine the required depth of the pile to resist the tension forces exerted by the swelling soil and produce zero or allowable upward movement. The concept of the following design chart is that the soil swelling decreases with deeper soil layers. This design chart provides values for unloaded piles so 200 250 300 350 400 450 0 5 10 S w e ll in g P re s s u re ( k P a ) Sand Mixing Percentage (%) Bushra S. Albusoda in the case of loaded piles it will be in the safe conservative side. Fig. 14. Pile movement compared to soil surface movement due to wetting-drying cycles for straight shaft and under reamed piles. Fig. 15. proposed relationship for determining required pile dimensions to resist upward movement due to soil swelling at the end of the first wetting-drying cycle 3.2. Pile Uplift Pressure Model Test Results 3.2.1. Experimental Model Tests When the soil swelling is happened, the shear strength of the soil is reduced, maximum swelling occurs in the top layers of the soil which surrounds shallower piles , thus, the maximum loss in soil shear strength during swelling occurs in the top soil layers. Therefore, shallower piles exerts less uplift forces due to soil swelling and more upward movement comparing to deeper Al-Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 7 in the case of loaded piles it will be in the safe Fig. 14. Pile movement compared to soil surface drying cycles for straight Fig. 15. proposed relationship for determining required pile dimensions to resist upward he end of the first Pile Uplift Pressure Model Test Results Experimental Model Tests When the soil swelling is happened, the shear strength of the soil is reduced, maximum swelling occurs in the top layers of the soil which surrounds shallower piles , thus, the maximum loss in soil shear strength during swelling occurs rs. Therefore, shallower piles exerts less uplift forces due to soil swelling and more upward movement comparing to deeper piles which are anchoraged in the relatively deeper soil layers that have less tendency to swelling. The magnitude of uplift resistan straight shaft and under reamed piles due to soil swelling in the first cycle is illustrated in Fig. 16. Fig. 16. Effect of L/D ratio on straight shaft and under reamed piles uplift resistance by soil swelling 3.2.2. Piles Pull-Out Capacity Model Test The model test results for piles pull upward movement behavior was presented through Table 2. For straight shaft and under reamed piles it was noticed that deeper piles with higher L/D ratios showed greater p comparing to the shallower piles for wetted and unwetted soil states. Also, the under reamed piles showed more resistance to the applied uplift forces than the stra ight shaft piles because of the presence of the base bulb which provides e soil layers and thus more pull out force resistance for the under reamed piles. Table 2, Increment in pile pull-out capacity Unwetted State L/D Straight Shaft Piles Under reamed 10 18.46 N 15 30.45 N 20 56.14 N Wetted State L/D Straight Shaft Piles Under reamed 10 16.156 N 15 26.10 N 20 35.00 N Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 1- 9(2016) piles which are anchoraged in the relatively deeper soil layers that have less tendency to swelling. The magnitude of uplift resistance from straight shaft and under reamed piles due to soil swelling in the first cycle is illustrated in Fig. 16. Fig. 16. Effect of L/D ratio on straight shaft and under reamed piles uplift resistance by soil swelling. Out Capacity Model Test The model test results for piles pull-out load - upward movement behavior was presented through Table 2. For straight shaft and under reamed piles it was noticed that deeper piles with higher L/D ratios showed greater pull out capacity comparing to the shallower piles for wetted and unwetted soil states. Also, the under reamed piles showed more resistance to the applied uplift ight shaft piles because of the presence of the base bulb which provides extra anchorage in deep soil layers and thus more pull out force resistance for the under reamed piles. out capacity. Under reamed Piles Increment Ratio% 20.77 N 12.50 39.15 N 28.57 91.23 N 38.46 Increment Ratio% Under reamed Piles 18.46 N 14.26 34.80 N 33.33 63.00 N 80.00 Bushra S. Albusoda Al-Khwarizmi Engineering Journal, Vol. 12, No. 2, P.P. 1- 9(2016) 8 4. Conclusion One of the challenges in geotechnical engineering is how to construct a stable foundation system to resist tension forces exerted by expansive soils and produce a safe building under this condition. The thought of this study was to examine the suitability of using under reamed with one base bulb as an alternative for straight shaft pile and study the behavior of both types of piles under seasonal moisture changes by applying successive cycles of wetting and drying to the soil that piles embedded in, the following points were concluded: 1- Pile upward movement due to soil swelling is reduced to about (20%-30%) when using under reamed pile with one base bulb instead of conventional straight shaft pile, deeper piles showed more resistance to upward and downward movement than shallower piles. 2- A relationship is obtained for the piles upward movement that provides the required dimensions of any unloaded pile fully embedded in a very high expansive soil for zero upward movement or any recommended tolerable movements. For loaded piles, the results obtained from this relationship will be on the safe conservative side. 3- Pile uplift force due to soil swelling is reduced to about (10%-20%) when using under reamed piles instead of conventional straight shaft piles 4- The use of under reamed piles instead of straight shaft piles for the same L/D ratio increases the pull out capacity of the piles by (12.5% -38.46%) for unwetted soil state, and about (14.26% - 80%) for wetted soil state. Notation D Pile Diameter CH Fat Clay L Pile Length 5. References [1] Al-Ani, R., 1993: “The Behavior of Model Piles in Expansive Soils”, M.Sc. Thesis, University of Technology, Iraq. [2] Al-Maamoury, H. M., 1994: “The Behavior of Reinforced Concrete Model Piles in Expansive Soil”, M.Sc. Thesis, University of Technology, Iraq. [3] Arora K.R. 2008: “Soil Mechanics and Foundation Engineering 7th edition”, Standard Publishers Distributers, Delhi, India. [4] ASTM D 4318-00: “Standard Test Method for Liquid Limit, Plastic Limit, and Plasticity Index of Soils”. [5] ASTM D2435-96: “Standard Test Method for One-Dimensional Consolidation Properties of Soils”. [6] ASTM D2487-00: “Standard Test Method for Classification of Soils for Engineering Purposes (Unified Soil Classification System)”. [7] ASTM D854-00: “Standard Test Method for Specific Gravity of Soil Solids by Pycnometer”. [8] ASTM D3689-07: “Standard Test Methods for Deep Foundations Under Static Tensile Loads”. [9] Chao, K. C., 2007: “Design Principles for Foundations on Expansive Soils”, PhD Thesis, Colorado State University, Fort Collins, USA. [10] Nelson, J. D. , Chao, K. C., Overton, D. D., Schaut, R. W., 2012: ”Calculation of Heave of Deep Pier Foundation”, Unsaturated Soil: Theory and Practice, Kasetsart University, Thailand. [11] Chen, F.H. 1975 “Foundations on Expansive Soils, , Elsevier Scientific Publication Company. �� 2، ا���د����12 ا���ارز � ا���� �� ا���� ���ى ��� ز��ر �� ،9 -1 )2016( 9 ا*(��)�� %�ب &�%$��# اداء ر!� ة **�1ظ# ا/*,�ري-,� ا���+ * ���ى ��� ز��ر ����� ���اد /���� ا� ���� /��� ا� ���� ا������** ،* �و���� albusoda@yahoo.com : ا�!� � ا�� 2���ا� �و�� ����(ه ��'ذجا اداء ت#��� ت��� �* ��� +�ص �@�م ت<��= ت� �:�>.ا��را�� ھ:ه ھ�ف ��2#�7 �6 ا��3�45 ت� *12 �����0 +/ل �- ا��,�+�� ت 4� ا�F ط'ل ���E اي �5��,� ��ط'ال ا����(ة ��'ذجا +'اص ��را��� �,��5�.-�G'� -� )H������دھ� ت� ا�Gھ:ا *� ا ،I2!ا� )H������د � ا�GJا )H��� وا� � درا�� ت�.ا��'�= ذات�LMة،��!� �'ع ت)����ط�E دورات و�Gد �4�ھ� ا�F ا����(ة ط'ل ا�� *� واTU �#<�ن �'حQ.ا����H( ت<�ف F�G ا��O�,P ا� ����اح6 ت� ت<��� �345. ا��'�= ذات ا����H( ا���5ام G�� اF�G ا�F ا����(ة ح����د � �����H( ا�GJا )H��� ا����(ة ط'ل ����5- ا��'�= ذات وا� �I�2� 0 ا���4'ب� 6�G Wا� -�� �� -� 3�U د��XJا ��G خ�,���� ا�� .ا�