Available online at www.sciencedirect.com ScienceDirect Aquatic Procedia (2015) 240 – 247 INTERNATIONAL CONFERENCE ON WATER RESOURCES, COASTAL AND OCEAN ENGINEERING (ICWRCOE 2015) Analysis of the Effect of Anchor Rod on the Behavior of Diaphragm Wall Using Plaxis 3d Yajnheswarana*, Ranjan H Sa, Subba Raoa a, Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal-575025, Mangalore, India Abstract Diaphragm walls and anchor rods are generally provided to support open berth structures in marine soils The diaphragm walls are subjected to loads due to the soil layer on one side of the structure Anchor rods may be provided in order to strengthen the structure and to resist the lateral loads and reduce the deflection to a large extent In this paper the deep draft berth of new mangalore port provided with diaphragm wall and anchor rods is analysed using finite element software PLAXIS 3D The displacement, shear force and bending moment are found out for diaphragm wall for the cases of with and without anchor The comparison is made on depth V/s bending moment, depth V/s shear force and depth V/s deflection of the diaphragm wall In the case of diaphragm wall without anchor rod, the maximum bending moment, shear force and deflection were found to be 23553 kN-m, 1743 kN and -0.0693m respectively The percentage reduction in bending moment, shear force and deflection were found to be 63.06%, 18.53% and 93.56% for the case of diaphragm wall with anchor at +2.5 m In this research paper, analyses are performed by varying the location of anchors to find the optimum © 2015 2015The TheAuthors Authors.Published Published Elsevier © byby Elsevier B.V.B.V This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of organizing committee of ICWRCOE 2015 (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of organizing committee of ICWRCOE 2015 Keywords: Diaphragm wall, Anchor rod, Berthing structure, Dredging, Lateral loads *Corresponding author Tel.: +0-949-748-1974; fax: +0-000-000-0000 e-mail address:yajneshholla@gmail.com 2214-241X © 2015 The Authors Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of organizing committee of ICWRCOE 2015 doi:10.1016/j.aqpro.2015.02.033 241 Yajnheswaran et al / Aquatic Procedia (2015) 240 – 247 Introduction Berthing structures are constructed in ports and harbors to provide facilities for berthing and mooring of vessels, loading and unloading of cargo and for embarking and disembarking of passengers and vehicles In berthing structures, lateral forces are caused by impact of berthing ships, pull from mooring ropes, pressure of wind, current, wave and floating ice, seismic force, active earth pressure, differential water pressure, in addition to self-weight of the structure and live load Diaphragm walls and anchor rods are provided to support open berth structures in marine soils The diaphragm walls are subjected to loads due to the soil layer on one side of the structure In case of dredging, additional lateral loads are derived from landside earth pressure [1] If not properly designed, the structure may fail due to these loads Hence, the study of diaphragm walls subjected to dredging is necessary to check the adequacy of the structure [2] Anchor rods may be provided in order to strengthen the structure and to resist the lateral loads and reduce the deflection to a large extent [4] The use of tie rod anchors in berthing structures will reduce the bending moment and lateral deflection and thus the required cross sectional area of the pile and the amount of reinforcement can be reduced resulting in an economical design of the structure Hence, the analysis of berthing structures provided with both diaphragm walls and tie rod anchors are essential for their economic design and strength [4] In this paper, the effect of anchor rod on the diaphragm wall is studied The analysis is done using finite element software PLAXIS 3D and the displacements of the structure subjected to static loads are investigated and the results are compared Details of Berthing structure The cross section of deep draft berth is shown in Fig The components of the berth includes diaphragm wall, deck slab, longitudinal and cross beams, pile cap, pile and anchor rod The diaphragm wall is located at 33 m from left most pile and it is of 1100 mm thickness The tie rod anchor is inclined at an angle of 45° and it is pre-stressed to a load of 225 Tones The anchor rods are provided at every 2.5 m interval The width and depth of the beams are 1200×1200mm The maximum span of the longitudinal beam is 10m and the minimum is 3m The slab is simply supported having dimensions of 10m×5m and the thickness of the slab is 600mm The width of the berthing structure is 33 m The berth is supported by a diaphragm wall and rows of 1200mm diameter piles The piles are terminated at a depth of -30 m The pile spacing is 10m center to center The dredge depth is -10m near the diaphragm wall and -17 m near the first pile as shown in fig Hard rock is found at a depth of -30 m The chart datum is at m Table Input Parameters of structural elements Material Model Axial modulus Rigidity modulus poisons ratio Pile Elastic 4.552E7 5.570E6 0.15 Diaphragm wall Elastic 1.775E7 6.544E7 0.15 Beam Elastic 1.775E7 5.324E5 0.15 Rod anchor Elastic 2.080E10 242 Yajnheswaran et al / Aquatic Procedia (2015) 240 – 247 Table Soil Properties Material Model Elastic Young’s modulus 80000 fine sand Ɣsat N(Nue) Cref Φ (phi) 18.0 0.3 0.5 medium sand Elastic 70000 18.0 0.3 0.45 30.0 marine clay Elastic 20000 18.0 0.49 17.0 0.0 coarse sand Elastic 60000 18.0 0.25 0.4 30.0 30.0 Fig Cross-Section of Deep Draft Berth The different parameters to be inputted into the PLAXIS 3D software include the structural details of the different elements and also the properties of the different soil layers All the details to be inputted are collected from New Mangalore Port Trust Numerical Modelling Numerical models involving FEM can offer several approximations to predict true solutions The accuracy of these approximations depends on the modeler’s ability to portray what is happening in the field Often the problem being modeled is complex and has to be simplified to obtain a solution Finite element method has become more popular as a soil response prediction tool This has led to increased pressure on researchers to develop more comprehensive descriptions for soil behavior, which in turn leads to more complex constitutive relationship Prevost and Popescu state that for a constitutive model to be satisfactory it must be able to: (1) define the material behavior for all stress and strain paths; (2) identify model parameters by means of standard material tests; and (3) physically represent the material response to changes in applied stress or strain Previous studies have explored constitutive models and found that the use of isotropic models such as elasto-plastic Mohr–Coulomb and Drucker–Prager models are sufficiently accurate [8] In the past, linear elastic constitutive models have been commonly used in are three-dimensional finite element analysis, plain strain analysis and axisymmetric finite element analysis In this present study, three-dimensional finite element approach is adopted Description of approach In this study the 3D finite element program ‘‘PLAXIS 3D’’ was used for the analysis of Diaphragm wall supported berthing structure The cross section of the model shown in Fig 1.The cross-section of the diaphragm wall supported berthing structure is modelled in the PLAXIS 3D (Input window as shown in Fig 2) The model includes soil strata and structural elements The length and depth of the model is taken as 66m and 29.5m as per the drawings provided by New Mangalore Port The diaphragm wall is modelled as a single panel The length of the panel is taken as 5m 243 Yajnheswaran et al / Aquatic Procedia (2015) 240 – 247 The diaphragm wall is provided with anchors at a spacing of 2.5m The live load acting on the berthing structure is 50 kN/m2 The following analyses are carried out for the diaphragm wall supported berthing structure CASE 1: Analysis of diaphragm wall in loaded condition in the absence of anchor rod CASE 2: Analysis of diaphragm wall in loaded condition, Anchor rod at a depth of 2.5 m CASE 3: Analysis of diaphragm wall in loaded condition, Anchor rod at a depth of 4.5m CASE 4: Analysis of diaphragm wall in loaded condition, Anchor rod at a depth of m CASE 5: Analysis of diaphragm wall in loaded condition, Anchor rod at a depth of -6.0 m CASE 6: Analysis of diaphragm wall in loaded condition, Anchor rod at a depth of -10.0 m Fig 2: The c/s of diaphragm wall supported berthing structure modelled in PLAXIS 3D Results 5.1 Case Analysis of diaphragm wall in loaded condition in the absence of anchor rod The extreme total displacement in this case was found to be around - 0.0693 m The diaphragm wall in the absence of anchor rod behaves like a cantilever beam with the bottom end fixed In a cantilever beam, the maximum displacement of -0.0693 m occurs at the free end which in this case is at the top of the wall The displacement of the diaphragm wall is zero at the bottom The variation of displacement of the diaphragm wall with increasing depth of the diaphragm wall is shown in Fig 10 -0.06 -0.04 -0.02 -10 -20 Displacement (m) -30 Fig 3: Variation of displacement of diaphragm wall when no anchor is present 0.00 Depth (m) -0.08 244 Yajnheswaran et al / Aquatic Procedia (2015) 240 – 247 The variation of shear forces is as shown in Fig Since no external force acts at a depth of + 4.5 m, the value of shear force is zero at the top of the diaphragm wall Till a depth of -10 m only force due to the active earth pressure acts on the diaphragm wall The passive force starts to act from -10 m The maximum shear force is obtained at the bottom of the diaphragm wall The considerable reduction in the shear force at a depth of -18 m is due to change in the soil layer from marine clay to coarse sand As the force in marine clay is very high as compared to coarse sand due to the change in φ value, at the interface of the two soil strata, the shear force value shows a considerable decrease in value This is evident from Fig The maximum value of shear force obtained is at the bottom of the diaphragm wall and is equal to 1743 kN/m 10 Depth (m) -10 500 1000 1500 2000 -20 -30 Shear Force (kN/m) Fig 4: Variation of Shear forces in diaphragm wall when no anchor is present Depth (m) The variation of bending moment in the diaphragm wall is shown in Fig The extreme value is obtained at the bottom of the diaphragm wall The bending moment value is dependent on the value of shear force So the bending moment is zero at the top The maximum bending moment is obtained at the bottom of the diaphragm wall The maximum value of bending moment which is obtained at the bottom of the diaphragm wall is 23553 kNm/m 10 -5 5000 10000 15000 20000 25000 -10 -15 -20 -25 -30 Bending Moment (kN-m/m) Fig 5: Variation of Bending moments in diaphragm wall when no anchor is present 5.2 Case 2: Analysis of diaphragm wall for varying locations of anchor rod The anchor rod is placed at different locations and its effect on the displacement of the diaphragm wall is studied to find the most suitable one The different locations considered in the analysis are: i At the surface of the structure, at 4.5 m ii At the water table, at m iii At the different soil levels, at 2.5 m, -6m and -10 m The displacement, axial force, shear force and bending moment of the diaphragm wall for the various locations of anchor rod is as in Table 3: 245 Yajnheswaran et al / Aquatic Procedia (2015) 240 – 247 Table 3: Extreme values of Displacement, Shear force and Bending moment for varying locations of anchor 0.45m -0.00548 1490 9560 Total displacement(m) Extreme shear force (kN/m) Extreme bending moment (kN-m/m) 0.25m 0m -0.00446 -0.00328 1420 1310 8700 7460 0.6m 1m -0.00092 -0.00469 -1120 -1470 3600 4490 The depth vs displacement, depth vs shear force and depth vs bending moment of diaphragm wall for different locations of anchor rod are as shown in figures 10 -0.006 -0.004 -0.002 -50.000 at +4.5 m 0.002 0.004 -15 -20 -25 -30 Displacement (m) Depth (m) -10 at +2.5 m at m at - m at - 10 m ` Fig 6: Variation of Displacement with depth for the diaphragm wall for different anchor rod locations From fig 6, it is clear that the maximum displacement of diaphragm wall depends on the location of anchor When the anchor is placed at +4.5m, the maximum displacement of the wall is obtained as 0.00548m at -9.0m The variation of shear force with depth of diaphragm wall is shown in fig.7.The shear force is zero at the top and gradually increases as the depth increases till -10m After -10m the shear force value starts to decrease due to the presence of passive earth pressure The maximum value of positive and negative shear forces are obtained when the anchor is at +4.5m and -10m respectively The variation of bending moment is shown in fig8.The maximum value of positive and negative bending moment is obtained when the anchor is placed at +4.5m 246 Yajnheswaran et al / Aquatic Procedia (2015) 240 – 247 10 -2000 -1000 -5 1000 2000 at +2.5m -10 at m -15 Depth (m) at +4.5 m at -6 m -20 at -10 m -25 -30 Shear force kN/m Fig 7: Variation of Shear force with depth for the diaphragm wall for different anchor rod locations 10 -10000 -5000 5000 10000 15000 -5 at +4.5 m at + 2.5 m -10 at m at - m Depth (m) -15 at - 10 m -20 -25 -30 Bending moment (kN-m/m) Fig 8: Variation of Bending moment with depth for the diaphragm wall for different anchor rod locations Conclusion The percentage reduction in the displacement of the diaphragm wall due to the presence of anchor rod at 2.5 m is 93.56%, shear force is 18.53% and bending moment is 63.06% The displacement of the diaphragm wall can be considerably reduced by providing an anchor rod The studies also shows that there is due importance for the location of the anchor rod The provision of an anchor rod at the optimum location will increase the stability of the Yajnheswaran et al / Aquatic Procedia (2015) 240 – 247 247 berthing structure By knowing the reduced displacement, shear force and bending moment of the diaphragm wall, alternative cost effective procedures can be implemented with reduced sizes of pile and diaphragm wall Acknowledgements The authors are thankful to the Director of National Institute of Technology Karnataka, Surathkal, and Head of the Department of Applied Mechanics and Hydraulics for the facilities provided for the investigation and permission granted to publish the results References Chen W, Saleeb A (1983) Constitutive equations for engineering, edn PWS Publishing, Melbourne Everaars, M.J.C 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