OPTIMIZING THE LOCATION OF CONTRACTION EXPANSION JOINTS IN CONCRETE CANAL LINING y

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1 IRRIGATION AND DRAINAGE Irrig. and Drain. 58: (2009) Published online 22 July 2008 in Wiley InterScience ( OPTIMIZING THE LOCATION OF CONTRACTION EXPANSION JOINTS IN CONCRETE CANAL LINING y H. AHMADI 1 *, H. RAHIMI 2 AND J. ABDOLLAHI 3 1 Department of Water Engineering, University of Tehran, Karaj-Iran Karaj Tehran 54521, Islamic Republic of Iran 2 Professor of Civil Engineering, University of Tehran, Islamic Republic of Iran 3 University of Tehran, Islamic Republic of Iran ABSTRACT In the present paper, the interaction between subgrade soil and canal lining under different operating conditions has been analysed using finite element models. Analysis was made by determining stress strain relationships of soil concrete lining. Based on the results of the analysis, the best location for providing contraction expansion joints on the lining was determined in a way to minimize the risk of cracking for any operating condition of canals of different sizes. According to the findings, providing a longitudinal joint at the lower 1/3 depth of small to medium size canals would eliminate any possibility of cracking by reducing the bending moment to 1/10 in comparison with a lining having no joint at the same location. To generalize the results, effects of subgrade soil characteristics such as modulus of elasticity and Poisson s ratio on the magnitude of the bending moments and deformations have been investigated. It was proved that the results are valid for all possible soil characteristics. Copyright # 2008 John Wiley & Sons, Ltd. key words: finite elements; concrete lining; irrigation canal; contraction expansion joint Received 5 October 2007; Revised 7 January 2008; Accepted 8 January 2008 RÉSUMÉ Le présent papier analyse l interaction entre le sol sous-jacent et le revêtement en béton d un canal sous différentes conditions de fonctionnement en utilisant la méthode des éléments finis. L analyse a été faite en déterminant les relations de contrainte-tension entre le sol et le revêtement. A partir des résultats de l analyse, le meilleur endroit pour situer les joints de dilatation a été déterminé de manière à réduire au minimum le risque de fissuration pour n importe quelle situation d exploitation de canaux de différentes tailles. Selon les résultats, un joint longitudinal au 1/3 inférieur de la profondeur des canaux de taille petite à moyenne éliminerait toute possibilité de fissuration en ramenant le moment de flexion à 1/10 en comparaison d un revêtement sans joint. Pour généraliser les résultats on a analysé les effets des caractéristiques du sol sous-jacent telles que le module d élasticité et le rapport de Poisson sur l importance des moments de flexion et des déformations. On a montré que les résultats sont valides pour toutes les caractéristiques possibles de sol. Copyright # 2008 John Wiley & Sons, Ltd. mots clés: éléments finis; revêtement béton; canal d irrigation; joint de dilatation * Correspondence to: H. Ahmadi, PhD student of Hydraulic Structures, Irrigation and Reclamation, Department of Water Engineering, University of Tehran, Karaj-Iran Karaj Tehran 54521, Islamic Republic of Iran. hojjat.a@gmail.com y Optimisation de l emplacement des joints de dilatation dans les canaux bétonnés. Copyright # 2008 John Wiley & Sons, Ltd.

2 OPTIMIZING LOCATION OF CONTRACTION EXPANSION JOINTS IN CONCRETE CANAL LINING 117 INTRODUCTION Existing published resources state that cracking of linings has been the primary source of damage to the 35 km (22 mile) El Dorado irrigation water conveying canal during its 40 years of operation (Bate, 2004; El Dorado Irrigation District, 2004). In many cases the researchers link canal lining failures to problematic subgrade soil. Having investigated the behaviour of linings of the Shoabie Irrigation Unit canals in Iran, Rahimi and Barootkoob (2002) came to the conclusion that swelling of the subgrade soil was the major cause of failure and rupturing of the canal linings. Alrefaii (1976) identified gypsum in the texture of subgrade soil of Syria s Euphrates catchment and indicated that its solubility was the main cause for failure of the region s canals. Rahimi and Abbasi (2001) have discussed how dispersive sand in the subgrade soil led to the failure of Iran s Saveh irrigation system canals. Since the concrete used in construction of canal linings is usually non-reinforced, it is not able to cope with large bending moments. Hence, risk of rupture of concrete lining under the effect of its own weight, elasto-plastic behaviour of the subgrade soil and uplift pressure is not unlikely. Typical side slopes for designing canals with concrete lining are 1:1 to 1:1.5. French (1986) recommends that, for slopes steeper than 1: 0.7, earth pressure from the surrounding soil must also be taken into account. The main objective of the present paper is to analyse the state of stresses and strains in concrete canal lining under different operating conditions for the purpose of optimising the location of contraction expansion joints. MATERIALS AND METHODS To perform numerical computations of this research, finite element analysis along with PLAXIS software, V was employed (PLAXIS, 1998). The Mohr-Coulomb model was selected as the constitutive model and six-node triangular elements were used for the analysis. To model the behaviour of concrete lining panels, an elasto-plastic theory was assumed. The necessary input data for stress strain governing equations and soil properties were taken from United States Bureau Reclamation (USBR) and Deutsches Institut für Normung (DIN) classifying system respectively (USBR, 1967, 1998; Paul and Jan, 2003). Since the modulus of elasticity of soil has the largest range of variation (from 2000 to almost kpa) and also the Poisson ratio plays a primary role in stress strain equations, their values were first assumed to be equal to 2000 kpa and 0.2 respectively. Finally, a sensitivity analysis was performed to investigate the effect of various numerical values of these parameters on the results obtained. The necessary data to define properties of concrete lining consist of unit weight, modulus of elasticity and Poisson ratio, for which typical values used in the analysis are given in Table I (Deputy of Technical Affairs, 1994). The coefficient of friction on the contact surface of the canal lining and subgrade soil was assumed to be proportional to the soil s internal friction angle. To increase the accuracy of the computations and, therefore, determination of the pattern of deformations and to locate the locus of the maximum acting moments, the whole cross section of the canal lining was considered. To investigate the effect of various operating conditions, three different cases, i.e. end of construction stage, canal with full capacity and rapid drawdown (reverse seepage from banks into the canal section) were considered. In defining the geometry of the canal section, the following assumptions were made: side banks width, 4 m (with a service road assumed to be available); impervious layer is 4 m below the canal bottom; total depth of canal ranges from 0.5 to 6 m; three side wall slopes which are typical for design purposes are assumed to be 1:1, 1:1.5 and 1:2; 20% of the total depth of the canal was considered as its freeboard (Figure 1). In the case of rapid drawdown, the phreatic surface was assumed to be at a depth of 0.2H from below the ground surface, at a distance of 4 m. This gives conservative results for a safety factor. Drained conditions were assumed for both the end of construction and full capacity cases, while undrained conditions prevail for the Table I. Assumed properties of concrete for analysis of lining Tensile strength (kn m 2 ) Compressive strength (kn m 2 ) Poisson ratio Modulus of elasticity (MPa) Unit weight (kn m 3 )

3 118 H. AHMADI ET AL. Figure 1. The geometry of the canal in the full capacity case Figure 2. A schematic view of unstructured triangular mesh. This figure is available in colour online at rapid drawdown case. Figure 2 depicts a schematic view of the mesh diagram of the model geometry, when the canal is operating at full capacity. The overall strategy was first to assume the geometry of the model (canal cross section and banks) with no concrete lining and groundwater table far below the canal bottom. By selecting the gravitational loading case (since the soil surface is not horizontal), initial stresses due to the soil weight were calculated at each node of the elements and unrealistic deformations appearing in the model geometry were removed. To study the interaction between the lining and subgrade soil, a concrete layer was assumed and calculations for the first of the three operating cases, i.e. the end of the construction stage, were performed. For the second operating case, i.e. full capacity, the groundwater table was assumed to be at a depth of 0.2H below the ground. Before filling of the canal, the underlying soil is dry and the weight of water is only a normal force acting on the lining. After some time seepage water begins and the subgrade soil gradually becomes saturated and pore water pressure develops. It is obvious that in such a case, the most critical condition is during the first hours after the filling operation begins, in which the subgrade soil is still dry and the maximum bending moment due to the weight of water is applied to the concrete panels. Obviously, the assumed conditions for full capacity case can only last for a short period of time. In the third case, i.e. rapid drawdown, the water depth in the canal was assumed to be equal to 20% of that of the canal depth. The rate of reverse seepage from the banks into the canal was calculated according to the boundary conditions, and associated net flow was used for computation of uplift pressure. Calculations were performed for canal depths varying from 0.5 to 6 m at 0.5 m intervals. RESULTS Typical pattern of deformations and bending moments The first part of the calculations was aimed at determining the deformation patterns and magnitude of bending moments acting upon the lining. For this purpose, no joints were provided in the concrete lining; therefore, it was regarded as a continuous panel. Figure 3 shows the deformation pattern and distribution of bending moments on the concrete lining of a canal with side slope of 1:1.5 for the three operating conditions mentioned. The graphs in Figure 4 show variation of bending moments versus the ratio of canal depth to bed width for the given three operating conditions and side slopes. As can be seen from the magnitudes of the bending moments, only the case of end of construction poses no threat. But for the other two cases, the magnitude of bending moments is high and the lining would experience brittleness and cracking. Hence, to control and resist the acting moments, it is necessary to provide contraction joints where the moments are too high.

4 OPTIMIZING LOCATION OF CONTRACTION EXPANSION JOINTS IN CONCRETE CANAL LINING 119 Figure 3. Deformation pattern and distribution of bending moments on concrete canal lining for three operation conditions (Z ¼ 1.5). This figure is available in colour online at The most critical condition of lined canals At the end of construction, the/weight of the lining is the only acting force. By the time the canal is filled with water, forces from the conveyed water are also added and in the case of rapid drawdown, uplift pressure and side pressure due to reverse seepage flow must also be taken into account. As a result, the direction of forces and moments in the last case will be different from the previous two cases. Comparison of the acting bending moments imposed on concrete lining for the other two cases, i.e. full capacity and reverse seepage, shows that, considering canal dimensions and side slopes, one of these two cases may be identified as the most critical. Figure 5 shows the magnitude of bending moments as a function of canal depth for canal side slopes of 1:1, 1:1.5 and 1:2. As shown, for Z ¼ 1, bending moments are larger for the case of full capacity up to 4 m, establishing the critical situation, but the case of reverse seepage is more critical for depths larger than 4 m. The reason for this is the increased uplift pressure resulting from increased depth and bottom width of the canal. For Z ¼ 1.5, the most critical situation belongs to the case of full capacity for depths up to 2.25 m, while for greater depths, reverse seepage is the critical situation due to increased bending moments. Likewise, the above situation occurs at canal depth of 2.2 m, when Z ¼ 2. Overcoming the moments acting on the lining To overcome acting moments, one of the following methods may be considered: increasing concrete lining thickness or using reinforced concrete to increase the strength against bending moments; providing joints at appropriate locations to counteract the bending moments.

5 120 H. AHMADI ET AL. Figure 4. Bending moments acting on canal panels, for different side slopes and operating conditions

6 OPTIMIZING LOCATION OF CONTRACTION EXPANSION JOINTS IN CONCRETE CANAL LINING 121 Figure 5. Comparison of bending moments acting on canal concrete panels in full capacity and rapid drawdown conditions As shown in Figure 5, the magnitude of bending moments acting upon linings is appreciable and there will be a dramatic increase in lining thickness when it is necessary to overcome the bending moments. Obviously, use of reinforced concrete is too expensive and not efficient from an economic point of view. Therefore, the most feasible solution is providing the lining with joints and determining their optimum location, which makes them as efficient as possible. The role of these joints will be similar to that of hinges in beams. Optimised location of the joints To investigate the effects of location of construction expansion joints on the magnitude of bending moments, an appropriate analysis was carried out and the results are shown in Figure 6. This figure illustrates the variation of bending moment versus its location as a function of depth of canal. As is shown, the maximum bending moment is produced at the lower 1/3 depth of the canal. This would be the best location for providing an expansion contraction joint. This finding is in complete agreement with experimental findings of Rahimi and Barootkoob (2002). The more the number of joints, the greater their mitigating effect. However, employing an excessive number of joints may result in higher costs, construction difficulties and wasting of precious water. Therefore, in selecting the number of joints, it is important that sufficient attention be paid to the economic considerations. As the calculations show, joints, when provided in side walls, have a considerable effect on reducing the magnitude of bending moments. Based on the results of the current investigations, the highest magnitudes of bending moments are produced at the lower 1/3 of the canal depth and, therefore, providing a joint at this location would reduce the bending moments to approximately 1/10 of that for a lining with no joints. Joints in the bottom slab of the canal Providing expansion contraction joints at appropriate locations in the canal s side slabs also substantially reduces the bending moments in the bottom slabs. For canals 3 5 m wide and less than 4 m deep, using a joint in the

7 122 H. AHMADI ET AL. Figure 6. Effect of location of joints on canal side panels in reduction of bending moment, L ¼ h/h centre line of the bed decreases the bending moments by a considerable amount, in such a way that the risk of rupturing canal linings thicker than 20 cm will be negligible. However, it is necessary that reinforced concrete or flexible linings be used for canals of larger dimensions. Effect of modulus of elasticity of the subgrade According to existing data, the modulus of elasticity of soils can vary from a minimum value of 2000 (kpa) to a maximum of (kpa). Therefore, it is expected that this parameter would considerably influence the magnitude of bending moments. To investigate the effect of soil modulus of elasticity (E s ) on the value of bending moments, calculations were performed for canals with different side slopes (the same depth and bed width as assumed before). The results show that assigning various values to E s in the above-mentioned range may result in as much as 45% variation in corresponding values of bending moments. Figure 6 shows the effect of the location of longitudinal contraction joints on bending moments for three different canal depths. For all side slopes under investigation, this parameter has its maximum effect when the canal is operating at full capacity, and its minimum effect in the case of rapid drawdown in which uplift pressure is the greatest contributing factor in determining the magnitude of bending moments. Figure 7 shows the results of computations as variation of E 1 /E 2 versus M 1 /M 2 for three operating cases of canals having 6 m depth and 9 m bottom width and three side slopes of Z ¼ 1, 1.5 and 2, where M 1 and M 2 are the corresponding moments for values of E 1 and E 2 respectively. For this calculation, the Poisson ratio was assumed to be constant, equal to 0.2. The analysis showed that soil modulus of elasticity has less effect in canals of shallower depths. Effect of the Poisson ratio Compared to the modulus of elasticity, the Poisson ratio of the solids lies within a shorter range of variation, usually between 0.2 and 0.4 for various soil types. Results of calculations on the effects of the Poisson ratio for various side slopes and operating conditions, indicate that this factor has its maximum effect on milder slopes, and

8 OPTIMIZING LOCATION OF CONTRACTION EXPANSION JOINTS IN CONCRETE CANAL LINING 123 Figure 7. Effect of elasticity modulus of the soil on bending moment the magnitude of bending moments is mostly influenced by this factor where there is a reverse seepage condition. The results of computations for a 6 m deep canal show that, in the reverse seepage case, increasing the value of the Poisson ratio from 0.2 to 0.4 will lead to a decrease in bending moments of 36%. Similarly, in other operating conditions, the maximum effect is 7 and 4% for the end of construction and full capacity cases, respectively. However, these values are the results of computations for the largest canal dimensions considered here and the most critical conditions. Obviously, for canals with smaller dimensions the effect will be less (Figure 8). Figure 8. Effect of soil Poisson ratio on bending moment

9 124 H. AHMADI ET AL. CONCLUSIONS The overall results of the present research can be summarized as follows: As shown in Figure 2, the distribution of bending moments acting on rigid concrete lining of irrigation canals is such that the lower regions of the lining experience maximum values of bending moments. This is due to increasing total stresses with depth, which increases the corresponding horizontal stresses and therefore, increases bending moments on lower regions, reaching its maximum value at the intersection of the bottom slab and the side slab. In the full capacity case, due to weight of the water, maximum bending moments are exerted upon the central part of the bottom slab. Due to hydrostatic pressure of the water, the maximum bending moment acting upon side slabs occurs at a depth of approximately the lower 1/3 of canal depth. An increase in canal depth results in a proportional increase of bending moments. Bending moments at the end of construction stage would not pose any real threat to the lining, unless the lining is statically unstable. For the cases of full capacity and reverse seepage, the moments acting upon the lining are much larger than the normal strength of a 20 cm thick concrete slab. According to the results obtained, any increase in the ratio of canal bottom width to its depth will cause an increase in associated acting moments, being higher for larger bottom width to canal depth ratios. Analysis shows that in the cases of full capacity and end of construction, larger bending moments occur for steeper side walls. However, the opposite occurs for the case of reverse seepage. This can be helpful in conditions where the canal is going to be designed for terrain with a high groundwater table. The most critical operating conditions are directly related to canal dimensions. As was shown in Figure 4, for Z ¼ 1, bending moments are larger for the case of full capacity up to 3.8 m depth, establishing the critical condition, and so is the case of reverse seepage for depths greater than 4 m. This is due to increased uplift pressure resulting from increased depth and bottom width of the canal. For Z ¼ 1.5, the most critical condition belongs to the case of full capacity for depths up to 2.25 m, while for deeper canals, the reverse seepage case is dominant in establishing the critical condition with regard to increased bending moments. Likewise, for Z ¼ 2, the above situation occurs at a depth of 2.2 m. In order to decrease the magnitude of bending moments, construction contraction joints should be placed in locations so that in addition to their common task, they are able to reduce bending moments appreciably. Construction joints are usually used where there are problems in concrete placing operations and casting, while expansion joints are provided to control stresses resulting from concrete deformations associated with temperature variations. Nonetheless, the location of these joints may be determined such that they have a third useful task. For canals less than 4 m deep, the risk of rupture of the lining can be minimized by providing a longitudinal joint at a depth equal to 1/3 of the total canal depth from the bed. For deeper canals, in addition to these joints, other joints must also be provided where bottom and side wall slabs meet and in the centre line of the canal bed. The results obtained in this research were based on the assumption of a modulus of elasticity and Poisson ratio of 2000 (kpa) and 0.2 respectively. Assigning other values to these parameters showed that their variation has no considerable effect on the bending moments and, therefore, regardless of the type of the soil, the results of the investigation is valid for any soil type. However, the practical case of the interface (void) between the concrete lining and the soil base caused by settlement and soil saturation after canal filling, which itself is due to poor compaction and or natural low density, is not considered in this study. This interface is often aggravated by the removal of fine materials during rapid drawdown condition. ACKNOWLEDGEMENTS The authors wish to express their deepest appreciation to the deputy chancellors for research affairs of the University of Tehran and University College of Agriculture and Natural Resources for their full support of the project.

10 OPTIMIZING LOCATION OF CONTRACTION EXPANSION JOINTS IN CONCRETE CANAL LINING 125 REFERENCES Alrefaii N Problems of irrigation networks on gypsum soils in Euphrates catchments -Syria. Journal of Iranian Irrigation and Drainage Committee No.16. Tehran, Iran. Bate J Project 184: El Dorado Canal Damage Total $3 Million. Deputy of Technical Affairs General Design Criteria of Irrigation and Drainage System. Iranian Management and Planning Organisation, Publication No.107, Tehran, Iran. El Dorado Irrigation District Project 184: Canal Failure Frequency and Analysis. El Dorado Irrigation District: Colorado, USA: 1 9. French HR Open Channel Hydraulics. McGraw-Hill: New York, USA. Paul VS, Jan B Geotechnic Engineering Handbook, vol. 1. Ernest and Sons Publishers: New York. PLAXIS (Version 7) Finite Element Code for Soil and Rock Analysis. Balkema: Rotterdam, Netherlands. Rahimi H, Abbasi N Problems of canal linings constructed on sandy soils. Case study of Saveh Irrigation Network. In Proceedings of First Conference on Water and Soil Resource of West-Azerbaijan Province, Urmia University, Urmia, Iran. Rahimi H, Barootkoob SH Concrete canal lining cracking in low to medium plastic soils. Irrigation and Drainage 51(2): United States Bureau of Reclamation (USBR) Design Standards No.3: Canals and Related Structure. Colorado, USA. United States Bureau of Reclamation (USBR) Earth Manual, 3rd edn, Part 1. Colorado, USA.