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Simulation of the stress regime during grain filling in bamboo reinforced concrete silo
Journal of Stored Products Research 83 (2019) 123e129
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Journal of Stored Products Research journal homepage: www.elsevier.com/locate/jspr
Simulation of the stress regime during grain filling in bamboo reinforced concrete silo Lakshmi E. Jayachandran a, *, B. Nitin b, Pavuluri Srinivasa Rao a a b
Agricultural and Food Engineering Department, Indian Institute of Technology Kharagpur, West Bengal, 721302, India Cryogenic Engineering Centre, Indian Institute of Technology Kharagpur, West Bengal, 721302, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 August 2018 Received in revised form 4 June 2019 Accepted 19 June 2019 Available online 27 June 2019
Design and development of low-cost farm silos call for a strong understanding of its structural performance and loads. Limited studies address the effect of stored grains on silos. A farm level bamboo reinforced concrete (BRC) silo with a flat bottom has been designed for the storage of rough rice. A fullscale 3D finite element (FE) model of the BRC silo has been developed and the grain filling in progressive layers simulated in the ANSYS® software. The stored grain and silo body interactions have been modeled considering the characteristic properties of both rough rice as well as the BRC, with minimal simplifications. The numerical results have been compared with the outcomes of classical theories (Jannsen’s and Reimbert’s) and design code (IS 4995-1974). While a significant difference was observed between the lateral stress magnitudes predicted by the numerical and analytical methods, the axial wall stresses from FEM approach deviated from the IS code values by 16%. Contrary to the analytical approaches, FEM predicted non-uniform stress distribution due to the bulk grain at the silo bottom. The numerical approach could also identify the localized peak pressures and stress distribution patterns within the grain layers, which is usually beyond the scope of analytical techniques. Possible reasons for fluctuations in stress patterns are discussed in detail. The study unveiled the intricacies involved in the FEM and the analytical outcomes while predicting the stresses in small and medium scale silos intended for use on farms. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Bamboo reinforced concrete silo Filling Finite element Stress
1. Introduction Silos are storage structures which are effective in retaining food grains for long periods, with minimal spoilage. These structures are generally made of steel or concrete and are regarded as an alternative to the conventional bag storage system (Deepak and Prasanta, 2017). The high initial cost involved in the fabrication of these structures is a major hindrance for its adoption by small and medium scale farmers. Several low cost, environmentally sustainable structures have been developed across the globe in the last few decades. A few such structures include termite mount clay silo (Omobowale et al., 2015), vetiver reinforced clay silo (Hengsadeekul and Nimityongskul, 2003) and ferrocement bins (Adhikarinayake et al., 2006).
* Corresponding author. Agricultural and Food Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721 302, India. Tel.: þ 91 3222 283164; fax: þ 91 3222 282244. E-mail address: [email protected] (L.E. Jayachandran). https://doi.org/10.1016/j.jspr.2019.06.011 0022-474X/© 2019 Elsevier Ltd. All rights reserved.
Design and development of improved grain storage structures call for sound knowledge about their structural safety and functional efficacy. The stresses developed in silos during filling and discharge of granular material is highly complex. The dynamics of these handling and storage operations are often described by theoretical (Janssen, 1895; Reimbert and Reimbert, 1987; Walker and Blanchard, 1967), analytical (ACI, 1997; BIS, 1974; CEN, 2007) jcik and experimental techniques (Horabik and Molenda, 2017; Wo et al., 2017). While the experimental assays are the most reliable method, it involves huge expenses in establishing model/full-scale silos, instrumentation setup and associated geometric imperfections due to the installation of sensors. Hence, several silo researchers relied on the classic theories and design codes for this purpose. These theories and codes were developed for explaining the static state of stored grains and utilize an overpressure coefficient to account for dynamic stresses generated during filling and discharge stages. Janssen’s theory and Reimbert’s theory are the two most popular theories in structural analysis of grain silos. Significant differences have been encountered in their results, especially when the material parameters approach a theoretical
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limiting values. Most studies suggest that Janssen’s theory has an upper hand over Reimbert’s theory under critical limiting cases (Manbeck et al., 1995). Stipulated guidelines are recommended by the Bureau of Indian Standards (BIS, 1974) for the design of reinforced concrete silos of variable planforms, intended for food grain storage. The Indian Standard (IS) code provides the values of material properties such as bulk density, angle of internal friction, angle of wall friction and pressure ratio under conditions of grain filling as well as discharge. The computations are based on the stored material properties estimating three different types of loads in the silo system (horizontal, vertical and frictional loads). The advent of numerical techniques such as the Finite Element Method (FEM) and Discrete Element Method (DEM) opened up new avenues for understanding the complex interactions between the stored grains and silo walls. Studies have established FEM as more definitive for predicting silo stresses while DEM was more accurate in representing the granular flows (Rotter et al., 1998). In spite of its intricate nature, the application of DEM was limited owing to the high computational time and difficulty in modeling nonspherical particles. Over the last few decades, FEM has evolved as a promising technique for the prediction of the structural behavior of grain silos and the stored material. Characterized by a high versatility, FEM has been established as an economic way of analyzing silo stresses. Besides, FEM could successfully address a wide range of complex silo phenomena which is otherwise impossible using conventional theories. These include incidences such as eccentric discharge (Łapko, 2010; Vidal et al., 2008), progressive and en masse filling (Gallego et al., 2010), variable planforms (Goodey et al., 2017), flexible walled silos (Guines et al., 2001), geometric imperfections due to stiffeners and ties (Chen et al., 2001), flat and inclined silo bottoms (Goodey and Brown, 2004), and flat and hopper bottoms (Guaita et al., 2003; Zheng and Yu, 2015). Only a handful of literature is available related to the design of concrete grain silos. With the scientific community realizing the effect of grain properties on the loads generated in silos, experimental works have been undertaken to determine the mechanical properties of commonly stored food grains (Moya et al., 2002, 2006). However, the innate properties of biological materials seldom acquire a constant value and differ with the type of cultivar, grain moisture content, and grain maturity. Hence, the sensitivity of the FEM model developed on different mechanical properties of stored grains needs to be validated. The current study investigates the structural performance of a bamboo reinforced concrete (BRC) silo designed for storage of rough rice, by the application of FEM. A comparison has been made between the FEM results and the analytical techniques/classic theories habitually used for the stress analysis in grain silos. The study also explores the margin by which the simulation results are offset, upon varying the material properties of the biological product stored in the silo. The study is expected to aid researchers in developing innovative storage structures using locally available material and employ FEM to check its structural stability. 2. Methodology 2.1. Design of bamboo reinforced concrete silo A BRC silo, with 1000 kg capacity, was designed and developed based on the design procedures prescribed in IS 4995: 1974 (Fig. 1 (a)). The thickness of the silo walls were set at 0.1 m as per the standard guidelines as described in IS 4995 (Part -II): 1974. The silo body was reinforced with bamboo strips, both horizontal and vertical, at a spacing of 18 cm (center to center distance). The material to be stored was transferred manually into the silo. The 3D silo
geometry consisting of the cylindrical bin and bulk rice has been mes, generated using SolidWorks®2015 software (Dassault syste lizy-Villacoublay, France) (Fig. 1 (b)). Ve 2.2. Storage material The granular material considered in this study was rough rice. High amylose, long grain rice variety (IR-36) was selected for this purpose. The rough rice was cleaned and sundried to a moisture content of 12 ± 0.4% (wet basis) before loading. The mechanical properties of rice were determined over a wide range of moisture contents and confining pressures (Moya et al., 2002, 2006). The physical properties of IR-36 have been previously studied and reported over a range of moisture contents (Reddy and Chakraverty, 2004). A range of values were used for Young’s modulus, Poisson’s ratio, cohesiveness, and dilatancy, in order to account for the variations encountered while handling the biological material in bulk. The properties of the stored rice sample were also determined experimentally according to the methods suggested by Moya et al. (2002); (Moya et al., 2006). The experimentally obtained values were well within the range of the previous studies mentioned herein. The cohesion and angle of dilatancy of rough rice were adopted from the values reported by Moya et al. (2006). The properties of rough rice used for the simulation has been tabulated in Table 1. 2.3. Classic theories and design codes The present study has compared the FEM predictions with the classic silo theories (Janssen, 1895; Reimbert and Reimbert, 1987), as well as the design code Indian Standards, IS 4995-1974 (BIS, 1974) based on which the silo has been developed. Janssen’s theory has been widely adopted for developing silo design codes in various countries (DIN 1055-6, ACI 313, EN 1991-4) with slight modifications in the lateral pressure ratio. Reimbert’s theory, on the other hand, was formulated based on the experiments conducted on a small scale silo. The main difference between the two theories is that while Janssen’s equations assume constant pressure ratio (k) throughout the silo body, Reimbert’s theory considers a variation of k value with the silo height, which is closer to reality. 2.4. Assessment of stresses in silo-grain system using finite element method FEM has been employed to detect the stress profiles generated in the silo system, taking into consideration, the properties pertaining to both silo structure and stored material. Simulations were conducted in the Static Structural module of ANSYS® academic software program (Version 18.0, ANSYS Inc., Pennsylvania, USA). The simulations have been confined to the cylindrical bin portion, which is directly in contact with the stored grain. This has been done to reproduce a reasonable silo wall and grain interaction involving a simplified model based simulation. 2.4.1. Silo geometry and meshing The silo geometry considered for the simulation comprises of the grain containing cylindrical bin as shown in Fig. 1(b). The 3D silo body was generated with embedded bamboo reinforcements. The rough rice was represented as layers of equal thickness (20 cm), establishing the provision for progressive filling of grains. Gallego et al. (2015) described progressive filling to be more reliable than en masse filling in case of grain silo simulations. The storage system was divided into tetrahedral mesh on the concrete containment and bulk material. The tetrahedron mesh is known for its capability to adjust to complex body shapes,
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Fig. 1. a) Design of the bamboo reinforced concrete silo and b) the 3D representation of the silo model for simulation.
Table 1 Material properties of rough rice. Material properties
Value
Range of values
Grain specific weight, r (kN/m3) Grain elastic modulus, E (kPa) Angle of internal friction, i ( ) Wall friction coefficient, m Angle of dilatancy, j ( ) Cohesion, c (kPa) Poisson’s ratio, n
5.75 6475 42 0.38 15 0.0175 0.1515
e 6,000e1,0000 32e42 e 9e27 0.011e0.027 0.12e0.24
including the curvature. Mesh size optimization is highly essential for reducing the computational time while ensuring minimal space discretization errors. Mesh independence study was carried out to find the optimum mesh size for the model considered. The mesh size was fixed at 30 mm (12449 elements) after an extensive mesh sensitivity analysis ensuring a reasonable computational time without compromising on the accuracy of the results obtained. This has been considered as an indication of the mesh independence of the stress values (Alfaifi et al., 2014). 2.4.2. Selection of ANSYS elements The stored material and silo body were represented using ANSYS elements SOLID185 and SHELL281, respectively. While SOLID185 is suitable for simulation of deformation in incompressible and elastoplastic material, SHELL281 was used to analyze moderately thick containment structures for nonlinear applications. Bamboo strips were assigned BEAM188, with capabilities of warping under restrained or unrestrained conditions. The contact behavior between the grain and the concrete walls were embodied using the combination of TARGET170 and CONTACT173 (Gallego et al., 2010). 2.4.3. Material model The complex behavior of the stored rough rice was captured by the linear elastic model with the Mohr-Coulomb failure criterion. This model is characterized by five parameters, viz, Young’s modulus (E), Poisson’s ratio (n), cohesiveness (c), dilatancy (j) and
angle of internal friction (i). This model has been widely used by several silo research community (Masson and Martinez, 2000; Vidal et al., 2005). The BRC silo has been modeled using a simple linear elastic model described by two parameters, viz., E and n. While the material parameters for concrete (E ¼ 30,000 kPa, n ¼ 0.18) were inbuilt in the software, the properties of bamboo strips (E ¼ 24.46 kPa, n ¼ 0.4) were adopted from literature (Agarwal et al., 2014). 2.4.4. Boundary conditions Two boundary conditions (B.C) were used to solve the grain filling process. B.C 1 The silo bottom has been fixed and corresponding nodes restrained; B.C 2 Full weight of the bulk material layers acting in a downward direction. The progressive filling (“filling layer by layer”) has been adopted in this study to ensure reasonable results Gallego et al. (2015). For this, “element birth and death” procedure was employed to subsequently activate individual grain layers. The process involved activating the bottom grain layer first, ensuring that the remaining layers stayed inactive. In the second step, the second layer was activated; the remaining layers inactive. The procedure was continued until the top most layer was activated. Seven time steps and ten sub steps were employed to achieve this. 3. Results 3.1. Variation of lateral pressure along the silo wall Fig. 2 illustrates the variation in the wall stresses with the depth of silo. These stresses have been compared with analytical results, including the design code (IS 4995-1974) and classic theories. The FE prediction values were less in magnitude compared to analytical results, but the stress distribution pattern remained similar in both cases. The FE predictions differed from the outcomes of Janssen’s theory by 56% at the silo base. Significant variations were observed between the FEM results and the IS code.
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silo base were observed. Above the height of 0.4 m, the stresses remained uniform within the grain layers. At 0.2 m and 0.4 m, the pressure magnitudes reduced significantly towards the walls. 3.5. Effect of grain properties on the FEM predictions Among the material model parameters, only E and n had any effect on the wall stresses in the silo. With an increase in E value from 6000 kPa to 10000 kPa, the lateral pressure increased by up to 70% in the upper half of the silo body. However, towards the silo base, there was no effect of changing E values. The peak pressures at lower 1/4th of the silo were almost equal. However, less than 20% variation in axial pressure was encountered within the same range of E. The increasing Poisson’s ratio exhibited an increase of axial pressure by up to 18% towards the lower half of the silo. Poisson’s ratio had a limited effect on the dynamic pressures in comparison to the static pressures. The plasticity parameters such as i, c, and j showed no significant effect on the silo wall stresses. 4. Discussion
Fig. 2. Variation of the lateral pressure (Pa) along the silo wall during the progressive filling of rough rice in the bamboo reinforced concrete silo.
3.2. Variation of axial pressure along the silo wall Fig. 3 depicts the change in the vertical stresses along the silo wall depth. It could be observed that both classic theories over predicted the vertical stresses developed, by a substantial amount, while the IS code predicted the stress values close to the FEM results. While the maximum pressure predicted by the IS code was 1247 Pa the corresponding value of FEM was 2250 Pa. Reimbert’s and Janssen’s theory predicted peak stress values of 6222 Pa and 7020 Pa, respectively. The predicted values could effectively capture the sharp increase in the compressive stress at the lower portion of the silo. At the silo base, the vertical wall pressure increased by up to 60% in comparison with the pressures at lower silo depths. 3.3. Vertical pressures acting across the silo base At the silo base, the vertical compressive loads due to the stored material acts symmetric with respect to the central axis of the silo. The vertical pressure was higher at the silo center and dropped with an increase in proximity to the silo walls (Fig. 4). The magnitude of silo bottom pressures predicted by FEM was substantially higher than the pressures acting on silo walls. 3.4. Vertical stresses on the stored grain layers at different heights The stresses acting on the grain layers have been depicted in Fig. 5. Stresses due to grain consolidation were less in magnitude than that acting on walls. Peak stress levels appeared at the lowest grain layer, with a gradual reduction towards the wall surface. This trend existed up to 1/4th of the silo height from base. Higher compressive stresses in the grain layer, up to a height of 0.4 m from
Structural analysis is an inevitable aspect for designing a storage structure for bulk grains, which is inextricably linked with the description of different wall pressures. Design and development of grain silos take into account two different kinds of non-uniform wall stresses, viz., a) Stresses due to the grain-silo wall interactions b) Wind loads (mainly applicable for empty silos) (Juan et al., 2006). In the present study, FEM results showed close agreement with Janssen’s theory, in predicting the lateral wall pressures due to stored grains. Close agreement between lateral pressures predicted by FEM and Janssen’s theory has been previously reported in case of concrete wheat silos of 3 m diameter (Zhang et al., 1989). The difference in lateral pressure values predicted by FEM and European experimental standard (CEN, 2007) has been shown to reach up to 40% in case of steel silos (diameter 6m) (Juan et al., 2006). According to the aforementioned studies, the difference between the analytical techniques and FEM results is high in case of silos with less height and diminishes in slender silos. Stress over prediction by the Indian Standards (IS) code, as observed in the present study could result in the additional cost of fabrication of silos. The design code by the IS suggests a value of 0.5 for both the wall friction coefficient as well as pressure ratio, which is a rarely encountered value in reality. A brief surge in lateral pressure was observed at the silo bottom in the stress profile, which has often been reported in different types of flat bottom silos (Sanad et al., 2001; Vidal et al., 2005). However, the analytical approaches do not account for such local peaks/patch loads. This could be an indication of the insufficiency of the classic theories and standard codes for designing small and medium scale silos to be used at farm levels. Towards the silo bottom, the gravity force of the bulk solid surpasses the friction force along the wall leading to a considerable surge in the axial pressure accompanied by an increase in bulk density (Gao et al., 2018). This has been effectively demonstrated in the FEM results, which is otherwise overlooked in analytical results. FEM is thus a powerful technique for visualizing even minor changes induced by the grain-wall interactions in the storage structure. Pattern of stress profile at the silo base was in line with the fact that maximum grain weight is borne by the silo floor in comparison to silo walls (Thompson, 1982). For instance, during filling of wheat in a silo (H/D ¼ 3), 83% of the total grain weight was supported by silo base while 17% was transferred to silo wall (Schwab et al., 1994). In a silo with smaller H/D ratio, the percentage of the load carried by the floor increases further. It needs to be pointed out that all the
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Fig. 3. Variation of the axial (vertical) pressure (Pa) along the silo wall during progressive filling of the rough rice in the bamboo reinforced concrete silo.
Fig. 4. Variation of the normal pressure (Pa) at the silo bottom during the progressive filling of the rough rice in the bamboo reinforced concrete silo.
analytical methods propose a uniform pressure across the silo bottom, but FEM could represent the heterogeneity on the pressure distribution pattern. Heterogeneity in stress distribution could be a consequence of the arching effect of stored rough rice (Gallego et al., 2010). Similar vertical pressure patterns across the silo radius have been experimentally observed by several researchers (Bovey, 1904; Dale and Robinson, 1954). The contribution of the restrained node on the silo floor to the peak bottom pressures cannot be overlooked (Juan et al., 2006). Stored grains are subjected to compression due to the cumulative effect of several forces such as gravity loads, internal friction as well as forces due to contact with silo walls, resulting in grain rearrangement with increasing grain depth (Moya et al., 2006). In this study, stresses observed in different layers of grains suggested substantial compaction of grains and an increase in bulk density as a result of grain rearrangement (Gao et al., 2018). Higher stresses at the lower grain layers could be explained by two concepts, viz, 1) Possible grain deformation at the lower portion of the silo resulting in grain rearrangement 2) Changes in the direction of principle stresses at the silo base reducing the pressures close to the silo wall (Haque, 2011). The observation was also supported by the findings of Gao et al. (2018) hinting at a reduction in grain bulk density with
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Fig. 5. Variation of the vertical pressure (Pa) at different grain layers from above the silo base, during filling of rough rice in subsequent layers.
increase in silo radius. Our results also highlight the importance of storing rough rice grains in smaller heap heights, in order to minimize the grain damage due to pressure build up (Cheng et al., 2016). The robustness of the FEM results depends on the material properties used in the constitutive model employed for describing the nonlinear grain behavior. The modulus of elasticity of rough rice has been reported to be in the range of 6000 kPa -10000 kPa under the confining pressures of up to 30 kPa (Du et al., 2017). Ayuga et al. (2001b) had emphasized the significant effect of E on the pressures developed during the progressive filling of silos. Change in n values from 0.2 to 0.4 increased the silo wall pressures by up to 90% in a silo containing wheat grains (Ayuga et al., 2001b). However, the magnitude of change in this study was less than this observation. It could be due to the difference in the material properties or the range of n considered. A variation of up to 6% has been reported by Ayuga et al. (2001a) in the range of dilatancy angle from 0 to 20 . The uncertainties observed in the stress distribution pattern between analytical and predicted results could be a result of several intricacies associated with the simulation process. One or more of the following factors could be among the reasons for this. Possible existence of shear zones has been reported throughout jcik and Tejchman, 2009). These shear forces the silo height (Wo could contribute to sudden fluctuations or deviation in the normal pressure curves generated through the FEM prediction. An in-depth study has to be conducted on the internal shear zones along the silo walls to validate this theory. Compression of continuum solids have also been associated with mobilization of friction throughout the silo wall leading to
significant slip phenomena, the underlying reason for which is still unknown. This has to be addressed in future simulation studies. Use of inappropriate contact stiffness factors could also result in “chattering”. Too high a contact stiffness factor, on the other hand, could lead to numerical issues in convergence. This study has attempted to annotate the calculation and analysis of the stress profiles in a grain silo, which is inevitable while designing a storage structure for food grains. The approach employed in this study can be applied for designing different storage structures for a wide variety of stored commodities including cereals and millets. FEM could effectively resolve the models developed for simulating the complexities arising out of the sharp corners or variable grain compaction with increasing grain depth. The FE approach could also account for the heterogeneities in stress distribution which is seldom addressed by the classic theories. 5. Conclusion A 3D model of the grain filling process in a BRC silo has been developed and compared with the classical theories as well as the IS 4995-1974. The study revealed FEM as a powerful alternative tool to analyze the structural performance of farm silos. The study also highlighted the excessive conservativeness of the analytical techniques resulting in over prediction of the silo wall stresses. While the FEM results showed a similar pattern as that of the analytical approaches, the magnitude of pressures were different in each method. Possible reasons for such mismatch have been discussed in
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this paper. FEM could effectively capture the local peak pressure, which tends to develop during the grain filling process, which is otherwise not accounted for in the analytical approaches. Future works need to be undertaken for comparing the FEM results with the experimental observations. However, this may incur high cost in order to establish appropriate instrumentation set up with minimal impact on the silo wall geometry. Acknowledgements This research was supported by the financial assistance from the Ministry of Human Resources Development, Government of India under the megaproject "Sustainable Food Security through Technological Interventions for Production, Processing and Logistics". The first author would like to express gratitude to the Indian Institute of Technology Kharagpur for providing institute fellowship during the research work. References ACI, 1997. Standard 313-97: Standard Practice for Design and Construction of Concrete Silos and Stacking Tubes for Storing Granular Materials. Farmington Hills, Michigan, US. Adhikarinayake, T.B., Palipane, K.B., Müller, J., 2006. Quality change and mass loss of paddy during airtight storage in a ferro-cement bin in sri lanka. J. Stored Prod. Res. 42 (3), 377e390. Agarwal, A., Nanda, B., Maity, D., 2014. Experimental investigation on chemically treated bamboo reinforced concrete beams and columns. Constr. Build. Mater. 71, 610e617. Alfaifi, B., Tang, J., Jiao, Y., Wang, S., Rasco, B., Jiao, S., Sablani, S., 2014. Radio frequency disinfestation treatments for dried fruit: model development and validation. J. Food Eng. 120, 268e276. Ayuga, F., Guaita, M., Aguado, P., 2001a. Sedstructures and environment: static and dynamic silo loads using finite element models. J. Agric. Eng. Res. 78 (3), 299e308. Ayuga, F., Guaita, M., Aguado, P., 2001b. Static and dynamic silo loads using finite element models. J. Agric. Eng. Res. 78 (3), 299e308. BIS, 1974. Criteria for Design of Reinforced Concrete Bins for the Storage of Granular and Powdery Materials. Bureau of Indian Standard. Bovey, H.T., 1904. Experiments on grain pressure in deep bins and strength of wooden bins. Eng. News 52 (2), 32e34. CEN, 2007. Eurocode 1: Actions on Structures, Part 4: Silos and Tanks. European Committee for Normalisation, Brussels. Chen, J., Yu, S., Ooi, J., Rotter, J., 2001. Finite-element modeling of filling pressures in a full-scale silo. J. Eng. Mech. 127 (10), 1058e1066. Cheng, X., Yan, X., Hu, M., 2016. The effect of storage pressure on the mechanical properties of paddy grains. J. Stored Prod. Res. 68, 19e24. Dale, A., Robinson, R., 1954. Pressure in deep grain storage structures. Agric. Eng. 35 (8), 570e573. Deepak, K., Prasanta, K., 2017. Reducing postharvest losses during storage of grain crops to strengthen food security in developing countries. Foods 8 (8), 1e22. Du, X., Cheng, X., Gao, M., 2017. Determination of the parameters of modified camclay model for paddy grain. J. Cereal Sci. 76, 1e7. Gallego, E., Rombach, G., Neumann, F., Ayuga, F., 2010. Simulations of granular flow in silos with different finite element programs: ansys vs. Silo. Trans. ASABE 53 (3), 819e829. Gallego, E., Ruiz, A., Aguado, P.J., 2015. Simulation of silo filling and discharge using ansys and comparison with experimental data. Comput. Electron. Agric. 118, 281e289. Gao, M., Cheng, X., Du, X., 2018. Simulation of bulk density distribution of wheat in silos by finite element analysis. J. Stored Prod. Res. 77, 1e8. Goodey, R.J., Brown, C.J., 2004. The influence of the base boundary condition in modelling filling of a metal silo. Comput. Struct. 82 (7e8), 567e579.
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Goodey, R.J., Brown, C.J., Rotter, J.M., 2017. Rectangular steel silos: finite element predictions of filling wall pressures. Eng. Struct. 132, 61e69. Guaita, M., Couto, A., Ayuga, F., 2003. Numerical simulation of wall pressure during discharge of granular material from cylindrical silos with eccentric hoppers. Biosyst. Eng. 85 (1), 101e109. Guines, D., Ragneau, E., Kerour, B., 2001. 3D Finite-element simulation of a square silo with flexible walls. J. Eng. Mech. 127 (10), 1051e1057. Haque, E., 2011. Void fraction as a function of depth and pressure drops of packed beds of porous media formed by granular materials. Trans. ASABE 54 (6), 2239e2243. Hengsadeekul, T., Nimityongskul, P., 2003. Utilization of vetiver grass as construction material for paddy storage. In: Truong, P., Hanping, X. (Eds.), Proceedings of the Third International Conference on Vetiver and Exhibition, 6e9 October 2003, Guangzhou, China. China Agriculture Press, Beijing China. Horabik, J., Molenda, M., 2017. Distribution of static pressure of seeds in a shallow model silo. Int. Agrophys. 31 (2). Janssen, H., 1895. Janssen, ha, and z. Vereins, 1895. dtsch. Eng. 39 (25), 1045. Dtsch. Eng., 39, 1045. Juan, A., Moran, J., Guerra, M., Couto, A., Ayuga, F., Aguado, P., 2006. Establishing stress state of cylindrical metal silos using finite element method: comparison with env 1993. Thin-Walled Struct. 44 (11), 1192e1200. Manbeck, H.B., Puri, V.M., Britton, M.G., 1995. Structural loads in grain storages. Stored Grain Ecosyst. 465e526. Masson, S., Martinez, J., 2000. Effect of particle mechanical properties on silo flow and stresses from distinct element simulations. Powder Technol. 109 (1e3), 164e178. Moya, M., Ayuga, F., Guaita, M., Aguado, P., 2002. Mechanical properties of granular agricultural materials. Trans. ASAE 45 (5), 1569. Moya, M., Guaita, M., Aguado, P., Ayuga, F., 2006. Mechanical properties of granular agricultural materials, part 2. Trans. ASABE 49 (2), 479e489. Omobowale, M., Mijinyawa, Y., Armstrong, P., Igbeka, J., Maghirang, E., 2015. Performance evaluation of termite-mound clay, concrete and steel silos for the storage of maize grains in the humid tropics. J. Stored Prod. Postharvest Res. 6 (7), 56e65. Reddy, B., Chakraverty, A., 2004. Physical properties of raw and parboiled paddy. Biosyst. Eng. 88 (4), 461e466. Reimbert, M.L., Reimbert, A.M., 1987. Silos. Theory and Practice. Vertical Silos, Horizontal Silos (Retaining Walls). Lavoisier Publishing. Rotter, J., Holst, J., Ooi, J., Sanad, A., 1998. Silo Pressure Predictions Using DiscreteElement and Finite-Element Analyses. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, pp. 2685e2712. Sanad, A., Ooi, J., Holst, J., Rotter, J., 2001. Computations of granular flow and pressures in a flat-bottomed silo. J. Eng. Mech. 127 (10), 1033e1043. Schwab, C.V., Ross, I.J., White, G.M., Colliver, D.G., 1994. Wheat loads and vertical pressure distribution in a full-scale bin Part 1 dFilling. Trans. ASAE 37 (5), 1613e1619. Thompson, S.A., 1982. Physical Properties of Wheat and its Relationship to Vertical Wall Loads in Grain Bins. Vidal, P., Guaita, M., Ayuga, F., 2005. Analysis of dynamic discharge pressures in cylindrical slender silos with a flat bottom or with a hopper: comparison with eurocode 1. Biosyst. Eng. 91 (3), 335e348. Vidal, P., Gallego, E., Guaita, M., Ayuga, F., 2008. Finite element analysis under different boundary conditions of the filling of cylindrical steel silos having an eccentric hopper. J. Constr. Steel Res. 64 (4), 480e492. Walker, D., Blanchard, M., 1967. Pressures in experimental coal hoppers. Chem. Eng. Sci. 22 (12), 1713e1745. jcik, M., Tejchman, J., 2009. Modeling of shear localization during confined Wo granular flow in silos within non-local hypoplasticity. Powder Technol. 192 (3), 298e310. jcik, M., Sondej, M., Rejowski, K., Tejchman, J., 2017. Full-scale experiments on Wo wheat flow in steel silo composed of corrugated walls and columns. Powder Technol. 311, 537e555. Zhang, Q., Puri, V., Manbeck, H., 1989. Static and thermal loads in full size grain bins predicted by vectorized fem on supercomputer. Trans. ASAE 32 (2), 685e0690. Zheng, Q.J., Yu, A.B., 2015. Finite element investigation of the flow and stress patterns in conical hopper during discharge. Chem. Eng. Sci. 129, 49e57. Łapko, A., 2010. Pressure of agricultural bulk solids under eccentric discharging of cylindrical concrete silo bin. Int. Agrophys. 24 (1), 51e56.
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Journal of Stored Products Research journal homepage: www.elsevier.com/locate/jspr
Simulation of the stress regime during grain filling in bamboo reinforced concrete silo Lakshmi E. Jayachandran a, *, B. Nitin b, Pavuluri Srinivasa Rao a a b
Agricultural and Food Engineering Department, Indian Institute of Technology Kharagpur, West Bengal, 721302, India Cryogenic Engineering Centre, Indian Institute of Technology Kharagpur, West Bengal, 721302, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 9 August 2018 Received in revised form 4 June 2019 Accepted 19 June 2019 Available online 27 June 2019
Design and development of low-cost farm silos call for a strong understanding of its structural performance and loads. Limited studies address the effect of stored grains on silos. A farm level bamboo reinforced concrete (BRC) silo with a flat bottom has been designed for the storage of rough rice. A fullscale 3D finite element (FE) model of the BRC silo has been developed and the grain filling in progressive layers simulated in the ANSYS® software. The stored grain and silo body interactions have been modeled considering the characteristic properties of both rough rice as well as the BRC, with minimal simplifications. The numerical results have been compared with the outcomes of classical theories (Jannsen’s and Reimbert’s) and design code (IS 4995-1974). While a significant difference was observed between the lateral stress magnitudes predicted by the numerical and analytical methods, the axial wall stresses from FEM approach deviated from the IS code values by 16%. Contrary to the analytical approaches, FEM predicted non-uniform stress distribution due to the bulk grain at the silo bottom. The numerical approach could also identify the localized peak pressures and stress distribution patterns within the grain layers, which is usually beyond the scope of analytical techniques. Possible reasons for fluctuations in stress patterns are discussed in detail. The study unveiled the intricacies involved in the FEM and the analytical outcomes while predicting the stresses in small and medium scale silos intended for use on farms. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Bamboo reinforced concrete silo Filling Finite element Stress
1. Introduction Silos are storage structures which are effective in retaining food grains for long periods, with minimal spoilage. These structures are generally made of steel or concrete and are regarded as an alternative to the conventional bag storage system (Deepak and Prasanta, 2017). The high initial cost involved in the fabrication of these structures is a major hindrance for its adoption by small and medium scale farmers. Several low cost, environmentally sustainable structures have been developed across the globe in the last few decades. A few such structures include termite mount clay silo (Omobowale et al., 2015), vetiver reinforced clay silo (Hengsadeekul and Nimityongskul, 2003) and ferrocement bins (Adhikarinayake et al., 2006).
* Corresponding author. Agricultural and Food Engineering Department, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721 302, India. Tel.: þ 91 3222 283164; fax: þ 91 3222 282244. E-mail address: [email protected] (L.E. Jayachandran). https://doi.org/10.1016/j.jspr.2019.06.011 0022-474X/© 2019 Elsevier Ltd. All rights reserved.
Design and development of improved grain storage structures call for sound knowledge about their structural safety and functional efficacy. The stresses developed in silos during filling and discharge of granular material is highly complex. The dynamics of these handling and storage operations are often described by theoretical (Janssen, 1895; Reimbert and Reimbert, 1987; Walker and Blanchard, 1967), analytical (ACI, 1997; BIS, 1974; CEN, 2007) jcik and experimental techniques (Horabik and Molenda, 2017; Wo et al., 2017). While the experimental assays are the most reliable method, it involves huge expenses in establishing model/full-scale silos, instrumentation setup and associated geometric imperfections due to the installation of sensors. Hence, several silo researchers relied on the classic theories and design codes for this purpose. These theories and codes were developed for explaining the static state of stored grains and utilize an overpressure coefficient to account for dynamic stresses generated during filling and discharge stages. Janssen’s theory and Reimbert’s theory are the two most popular theories in structural analysis of grain silos. Significant differences have been encountered in their results, especially when the material parameters approach a theoretical
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limiting values. Most studies suggest that Janssen’s theory has an upper hand over Reimbert’s theory under critical limiting cases (Manbeck et al., 1995). Stipulated guidelines are recommended by the Bureau of Indian Standards (BIS, 1974) for the design of reinforced concrete silos of variable planforms, intended for food grain storage. The Indian Standard (IS) code provides the values of material properties such as bulk density, angle of internal friction, angle of wall friction and pressure ratio under conditions of grain filling as well as discharge. The computations are based on the stored material properties estimating three different types of loads in the silo system (horizontal, vertical and frictional loads). The advent of numerical techniques such as the Finite Element Method (FEM) and Discrete Element Method (DEM) opened up new avenues for understanding the complex interactions between the stored grains and silo walls. Studies have established FEM as more definitive for predicting silo stresses while DEM was more accurate in representing the granular flows (Rotter et al., 1998). In spite of its intricate nature, the application of DEM was limited owing to the high computational time and difficulty in modeling nonspherical particles. Over the last few decades, FEM has evolved as a promising technique for the prediction of the structural behavior of grain silos and the stored material. Characterized by a high versatility, FEM has been established as an economic way of analyzing silo stresses. Besides, FEM could successfully address a wide range of complex silo phenomena which is otherwise impossible using conventional theories. These include incidences such as eccentric discharge (Łapko, 2010; Vidal et al., 2008), progressive and en masse filling (Gallego et al., 2010), variable planforms (Goodey et al., 2017), flexible walled silos (Guines et al., 2001), geometric imperfections due to stiffeners and ties (Chen et al., 2001), flat and inclined silo bottoms (Goodey and Brown, 2004), and flat and hopper bottoms (Guaita et al., 2003; Zheng and Yu, 2015). Only a handful of literature is available related to the design of concrete grain silos. With the scientific community realizing the effect of grain properties on the loads generated in silos, experimental works have been undertaken to determine the mechanical properties of commonly stored food grains (Moya et al., 2002, 2006). However, the innate properties of biological materials seldom acquire a constant value and differ with the type of cultivar, grain moisture content, and grain maturity. Hence, the sensitivity of the FEM model developed on different mechanical properties of stored grains needs to be validated. The current study investigates the structural performance of a bamboo reinforced concrete (BRC) silo designed for storage of rough rice, by the application of FEM. A comparison has been made between the FEM results and the analytical techniques/classic theories habitually used for the stress analysis in grain silos. The study also explores the margin by which the simulation results are offset, upon varying the material properties of the biological product stored in the silo. The study is expected to aid researchers in developing innovative storage structures using locally available material and employ FEM to check its structural stability. 2. Methodology 2.1. Design of bamboo reinforced concrete silo A BRC silo, with 1000 kg capacity, was designed and developed based on the design procedures prescribed in IS 4995: 1974 (Fig. 1 (a)). The thickness of the silo walls were set at 0.1 m as per the standard guidelines as described in IS 4995 (Part -II): 1974. The silo body was reinforced with bamboo strips, both horizontal and vertical, at a spacing of 18 cm (center to center distance). The material to be stored was transferred manually into the silo. The 3D silo
geometry consisting of the cylindrical bin and bulk rice has been mes, generated using SolidWorks®2015 software (Dassault syste lizy-Villacoublay, France) (Fig. 1 (b)). Ve 2.2. Storage material The granular material considered in this study was rough rice. High amylose, long grain rice variety (IR-36) was selected for this purpose. The rough rice was cleaned and sundried to a moisture content of 12 ± 0.4% (wet basis) before loading. The mechanical properties of rice were determined over a wide range of moisture contents and confining pressures (Moya et al., 2002, 2006). The physical properties of IR-36 have been previously studied and reported over a range of moisture contents (Reddy and Chakraverty, 2004). A range of values were used for Young’s modulus, Poisson’s ratio, cohesiveness, and dilatancy, in order to account for the variations encountered while handling the biological material in bulk. The properties of the stored rice sample were also determined experimentally according to the methods suggested by Moya et al. (2002); (Moya et al., 2006). The experimentally obtained values were well within the range of the previous studies mentioned herein. The cohesion and angle of dilatancy of rough rice were adopted from the values reported by Moya et al. (2006). The properties of rough rice used for the simulation has been tabulated in Table 1. 2.3. Classic theories and design codes The present study has compared the FEM predictions with the classic silo theories (Janssen, 1895; Reimbert and Reimbert, 1987), as well as the design code Indian Standards, IS 4995-1974 (BIS, 1974) based on which the silo has been developed. Janssen’s theory has been widely adopted for developing silo design codes in various countries (DIN 1055-6, ACI 313, EN 1991-4) with slight modifications in the lateral pressure ratio. Reimbert’s theory, on the other hand, was formulated based on the experiments conducted on a small scale silo. The main difference between the two theories is that while Janssen’s equations assume constant pressure ratio (k) throughout the silo body, Reimbert’s theory considers a variation of k value with the silo height, which is closer to reality. 2.4. Assessment of stresses in silo-grain system using finite element method FEM has been employed to detect the stress profiles generated in the silo system, taking into consideration, the properties pertaining to both silo structure and stored material. Simulations were conducted in the Static Structural module of ANSYS® academic software program (Version 18.0, ANSYS Inc., Pennsylvania, USA). The simulations have been confined to the cylindrical bin portion, which is directly in contact with the stored grain. This has been done to reproduce a reasonable silo wall and grain interaction involving a simplified model based simulation. 2.4.1. Silo geometry and meshing The silo geometry considered for the simulation comprises of the grain containing cylindrical bin as shown in Fig. 1(b). The 3D silo body was generated with embedded bamboo reinforcements. The rough rice was represented as layers of equal thickness (20 cm), establishing the provision for progressive filling of grains. Gallego et al. (2015) described progressive filling to be more reliable than en masse filling in case of grain silo simulations. The storage system was divided into tetrahedral mesh on the concrete containment and bulk material. The tetrahedron mesh is known for its capability to adjust to complex body shapes,
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Fig. 1. a) Design of the bamboo reinforced concrete silo and b) the 3D representation of the silo model for simulation.
Table 1 Material properties of rough rice. Material properties
Value
Range of values
Grain specific weight, r (kN/m3) Grain elastic modulus, E (kPa) Angle of internal friction, i ( ) Wall friction coefficient, m Angle of dilatancy, j ( ) Cohesion, c (kPa) Poisson’s ratio, n
5.75 6475 42 0.38 15 0.0175 0.1515
e 6,000e1,0000 32e42 e 9e27 0.011e0.027 0.12e0.24
including the curvature. Mesh size optimization is highly essential for reducing the computational time while ensuring minimal space discretization errors. Mesh independence study was carried out to find the optimum mesh size for the model considered. The mesh size was fixed at 30 mm (12449 elements) after an extensive mesh sensitivity analysis ensuring a reasonable computational time without compromising on the accuracy of the results obtained. This has been considered as an indication of the mesh independence of the stress values (Alfaifi et al., 2014). 2.4.2. Selection of ANSYS elements The stored material and silo body were represented using ANSYS elements SOLID185 and SHELL281, respectively. While SOLID185 is suitable for simulation of deformation in incompressible and elastoplastic material, SHELL281 was used to analyze moderately thick containment structures for nonlinear applications. Bamboo strips were assigned BEAM188, with capabilities of warping under restrained or unrestrained conditions. The contact behavior between the grain and the concrete walls were embodied using the combination of TARGET170 and CONTACT173 (Gallego et al., 2010). 2.4.3. Material model The complex behavior of the stored rough rice was captured by the linear elastic model with the Mohr-Coulomb failure criterion. This model is characterized by five parameters, viz, Young’s modulus (E), Poisson’s ratio (n), cohesiveness (c), dilatancy (j) and
angle of internal friction (i). This model has been widely used by several silo research community (Masson and Martinez, 2000; Vidal et al., 2005). The BRC silo has been modeled using a simple linear elastic model described by two parameters, viz., E and n. While the material parameters for concrete (E ¼ 30,000 kPa, n ¼ 0.18) were inbuilt in the software, the properties of bamboo strips (E ¼ 24.46 kPa, n ¼ 0.4) were adopted from literature (Agarwal et al., 2014). 2.4.4. Boundary conditions Two boundary conditions (B.C) were used to solve the grain filling process. B.C 1 The silo bottom has been fixed and corresponding nodes restrained; B.C 2 Full weight of the bulk material layers acting in a downward direction. The progressive filling (“filling layer by layer”) has been adopted in this study to ensure reasonable results Gallego et al. (2015). For this, “element birth and death” procedure was employed to subsequently activate individual grain layers. The process involved activating the bottom grain layer first, ensuring that the remaining layers stayed inactive. In the second step, the second layer was activated; the remaining layers inactive. The procedure was continued until the top most layer was activated. Seven time steps and ten sub steps were employed to achieve this. 3. Results 3.1. Variation of lateral pressure along the silo wall Fig. 2 illustrates the variation in the wall stresses with the depth of silo. These stresses have been compared with analytical results, including the design code (IS 4995-1974) and classic theories. The FE prediction values were less in magnitude compared to analytical results, but the stress distribution pattern remained similar in both cases. The FE predictions differed from the outcomes of Janssen’s theory by 56% at the silo base. Significant variations were observed between the FEM results and the IS code.
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silo base were observed. Above the height of 0.4 m, the stresses remained uniform within the grain layers. At 0.2 m and 0.4 m, the pressure magnitudes reduced significantly towards the walls. 3.5. Effect of grain properties on the FEM predictions Among the material model parameters, only E and n had any effect on the wall stresses in the silo. With an increase in E value from 6000 kPa to 10000 kPa, the lateral pressure increased by up to 70% in the upper half of the silo body. However, towards the silo base, there was no effect of changing E values. The peak pressures at lower 1/4th of the silo were almost equal. However, less than 20% variation in axial pressure was encountered within the same range of E. The increasing Poisson’s ratio exhibited an increase of axial pressure by up to 18% towards the lower half of the silo. Poisson’s ratio had a limited effect on the dynamic pressures in comparison to the static pressures. The plasticity parameters such as i, c, and j showed no significant effect on the silo wall stresses. 4. Discussion
Fig. 2. Variation of the lateral pressure (Pa) along the silo wall during the progressive filling of rough rice in the bamboo reinforced concrete silo.
3.2. Variation of axial pressure along the silo wall Fig. 3 depicts the change in the vertical stresses along the silo wall depth. It could be observed that both classic theories over predicted the vertical stresses developed, by a substantial amount, while the IS code predicted the stress values close to the FEM results. While the maximum pressure predicted by the IS code was 1247 Pa the corresponding value of FEM was 2250 Pa. Reimbert’s and Janssen’s theory predicted peak stress values of 6222 Pa and 7020 Pa, respectively. The predicted values could effectively capture the sharp increase in the compressive stress at the lower portion of the silo. At the silo base, the vertical wall pressure increased by up to 60% in comparison with the pressures at lower silo depths. 3.3. Vertical pressures acting across the silo base At the silo base, the vertical compressive loads due to the stored material acts symmetric with respect to the central axis of the silo. The vertical pressure was higher at the silo center and dropped with an increase in proximity to the silo walls (Fig. 4). The magnitude of silo bottom pressures predicted by FEM was substantially higher than the pressures acting on silo walls. 3.4. Vertical stresses on the stored grain layers at different heights The stresses acting on the grain layers have been depicted in Fig. 5. Stresses due to grain consolidation were less in magnitude than that acting on walls. Peak stress levels appeared at the lowest grain layer, with a gradual reduction towards the wall surface. This trend existed up to 1/4th of the silo height from base. Higher compressive stresses in the grain layer, up to a height of 0.4 m from
Structural analysis is an inevitable aspect for designing a storage structure for bulk grains, which is inextricably linked with the description of different wall pressures. Design and development of grain silos take into account two different kinds of non-uniform wall stresses, viz., a) Stresses due to the grain-silo wall interactions b) Wind loads (mainly applicable for empty silos) (Juan et al., 2006). In the present study, FEM results showed close agreement with Janssen’s theory, in predicting the lateral wall pressures due to stored grains. Close agreement between lateral pressures predicted by FEM and Janssen’s theory has been previously reported in case of concrete wheat silos of 3 m diameter (Zhang et al., 1989). The difference in lateral pressure values predicted by FEM and European experimental standard (CEN, 2007) has been shown to reach up to 40% in case of steel silos (diameter 6m) (Juan et al., 2006). According to the aforementioned studies, the difference between the analytical techniques and FEM results is high in case of silos with less height and diminishes in slender silos. Stress over prediction by the Indian Standards (IS) code, as observed in the present study could result in the additional cost of fabrication of silos. The design code by the IS suggests a value of 0.5 for both the wall friction coefficient as well as pressure ratio, which is a rarely encountered value in reality. A brief surge in lateral pressure was observed at the silo bottom in the stress profile, which has often been reported in different types of flat bottom silos (Sanad et al., 2001; Vidal et al., 2005). However, the analytical approaches do not account for such local peaks/patch loads. This could be an indication of the insufficiency of the classic theories and standard codes for designing small and medium scale silos to be used at farm levels. Towards the silo bottom, the gravity force of the bulk solid surpasses the friction force along the wall leading to a considerable surge in the axial pressure accompanied by an increase in bulk density (Gao et al., 2018). This has been effectively demonstrated in the FEM results, which is otherwise overlooked in analytical results. FEM is thus a powerful technique for visualizing even minor changes induced by the grain-wall interactions in the storage structure. Pattern of stress profile at the silo base was in line with the fact that maximum grain weight is borne by the silo floor in comparison to silo walls (Thompson, 1982). For instance, during filling of wheat in a silo (H/D ¼ 3), 83% of the total grain weight was supported by silo base while 17% was transferred to silo wall (Schwab et al., 1994). In a silo with smaller H/D ratio, the percentage of the load carried by the floor increases further. It needs to be pointed out that all the
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Fig. 3. Variation of the axial (vertical) pressure (Pa) along the silo wall during progressive filling of the rough rice in the bamboo reinforced concrete silo.
Fig. 4. Variation of the normal pressure (Pa) at the silo bottom during the progressive filling of the rough rice in the bamboo reinforced concrete silo.
analytical methods propose a uniform pressure across the silo bottom, but FEM could represent the heterogeneity on the pressure distribution pattern. Heterogeneity in stress distribution could be a consequence of the arching effect of stored rough rice (Gallego et al., 2010). Similar vertical pressure patterns across the silo radius have been experimentally observed by several researchers (Bovey, 1904; Dale and Robinson, 1954). The contribution of the restrained node on the silo floor to the peak bottom pressures cannot be overlooked (Juan et al., 2006). Stored grains are subjected to compression due to the cumulative effect of several forces such as gravity loads, internal friction as well as forces due to contact with silo walls, resulting in grain rearrangement with increasing grain depth (Moya et al., 2006). In this study, stresses observed in different layers of grains suggested substantial compaction of grains and an increase in bulk density as a result of grain rearrangement (Gao et al., 2018). Higher stresses at the lower grain layers could be explained by two concepts, viz, 1) Possible grain deformation at the lower portion of the silo resulting in grain rearrangement 2) Changes in the direction of principle stresses at the silo base reducing the pressures close to the silo wall (Haque, 2011). The observation was also supported by the findings of Gao et al. (2018) hinting at a reduction in grain bulk density with
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Fig. 5. Variation of the vertical pressure (Pa) at different grain layers from above the silo base, during filling of rough rice in subsequent layers.
increase in silo radius. Our results also highlight the importance of storing rough rice grains in smaller heap heights, in order to minimize the grain damage due to pressure build up (Cheng et al., 2016). The robustness of the FEM results depends on the material properties used in the constitutive model employed for describing the nonlinear grain behavior. The modulus of elasticity of rough rice has been reported to be in the range of 6000 kPa -10000 kPa under the confining pressures of up to 30 kPa (Du et al., 2017). Ayuga et al. (2001b) had emphasized the significant effect of E on the pressures developed during the progressive filling of silos. Change in n values from 0.2 to 0.4 increased the silo wall pressures by up to 90% in a silo containing wheat grains (Ayuga et al., 2001b). However, the magnitude of change in this study was less than this observation. It could be due to the difference in the material properties or the range of n considered. A variation of up to 6% has been reported by Ayuga et al. (2001a) in the range of dilatancy angle from 0 to 20 . The uncertainties observed in the stress distribution pattern between analytical and predicted results could be a result of several intricacies associated with the simulation process. One or more of the following factors could be among the reasons for this. Possible existence of shear zones has been reported throughout jcik and Tejchman, 2009). These shear forces the silo height (Wo could contribute to sudden fluctuations or deviation in the normal pressure curves generated through the FEM prediction. An in-depth study has to be conducted on the internal shear zones along the silo walls to validate this theory. Compression of continuum solids have also been associated with mobilization of friction throughout the silo wall leading to
significant slip phenomena, the underlying reason for which is still unknown. This has to be addressed in future simulation studies. Use of inappropriate contact stiffness factors could also result in “chattering”. Too high a contact stiffness factor, on the other hand, could lead to numerical issues in convergence. This study has attempted to annotate the calculation and analysis of the stress profiles in a grain silo, which is inevitable while designing a storage structure for food grains. The approach employed in this study can be applied for designing different storage structures for a wide variety of stored commodities including cereals and millets. FEM could effectively resolve the models developed for simulating the complexities arising out of the sharp corners or variable grain compaction with increasing grain depth. The FE approach could also account for the heterogeneities in stress distribution which is seldom addressed by the classic theories. 5. Conclusion A 3D model of the grain filling process in a BRC silo has been developed and compared with the classical theories as well as the IS 4995-1974. The study revealed FEM as a powerful alternative tool to analyze the structural performance of farm silos. The study also highlighted the excessive conservativeness of the analytical techniques resulting in over prediction of the silo wall stresses. While the FEM results showed a similar pattern as that of the analytical approaches, the magnitude of pressures were different in each method. Possible reasons for such mismatch have been discussed in
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this paper. FEM could effectively capture the local peak pressure, which tends to develop during the grain filling process, which is otherwise not accounted for in the analytical approaches. Future works need to be undertaken for comparing the FEM results with the experimental observations. However, this may incur high cost in order to establish appropriate instrumentation set up with minimal impact on the silo wall geometry. Acknowledgements This research was supported by the financial assistance from the Ministry of Human Resources Development, Government of India under the megaproject "Sustainable Food Security through Technological Interventions for Production, Processing and Logistics". The first author would like to express gratitude to the Indian Institute of Technology Kharagpur for providing institute fellowship during the research work. References ACI, 1997. Standard 313-97: Standard Practice for Design and Construction of Concrete Silos and Stacking Tubes for Storing Granular Materials. Farmington Hills, Michigan, US. Adhikarinayake, T.B., Palipane, K.B., Müller, J., 2006. Quality change and mass loss of paddy during airtight storage in a ferro-cement bin in sri lanka. J. Stored Prod. Res. 42 (3), 377e390. Agarwal, A., Nanda, B., Maity, D., 2014. Experimental investigation on chemically treated bamboo reinforced concrete beams and columns. Constr. Build. Mater. 71, 610e617. Alfaifi, B., Tang, J., Jiao, Y., Wang, S., Rasco, B., Jiao, S., Sablani, S., 2014. Radio frequency disinfestation treatments for dried fruit: model development and validation. J. Food Eng. 120, 268e276. Ayuga, F., Guaita, M., Aguado, P., 2001a. Sedstructures and environment: static and dynamic silo loads using finite element models. J. Agric. Eng. Res. 78 (3), 299e308. Ayuga, F., Guaita, M., Aguado, P., 2001b. Static and dynamic silo loads using finite element models. J. Agric. Eng. Res. 78 (3), 299e308. BIS, 1974. Criteria for Design of Reinforced Concrete Bins for the Storage of Granular and Powdery Materials. Bureau of Indian Standard. Bovey, H.T., 1904. Experiments on grain pressure in deep bins and strength of wooden bins. Eng. News 52 (2), 32e34. CEN, 2007. Eurocode 1: Actions on Structures, Part 4: Silos and Tanks. European Committee for Normalisation, Brussels. Chen, J., Yu, S., Ooi, J., Rotter, J., 2001. Finite-element modeling of filling pressures in a full-scale silo. J. Eng. Mech. 127 (10), 1058e1066. Cheng, X., Yan, X., Hu, M., 2016. The effect of storage pressure on the mechanical properties of paddy grains. J. Stored Prod. Res. 68, 19e24. Dale, A., Robinson, R., 1954. Pressure in deep grain storage structures. Agric. Eng. 35 (8), 570e573. Deepak, K., Prasanta, K., 2017. Reducing postharvest losses during storage of grain crops to strengthen food security in developing countries. Foods 8 (8), 1e22. Du, X., Cheng, X., Gao, M., 2017. Determination of the parameters of modified camclay model for paddy grain. J. Cereal Sci. 76, 1e7. Gallego, E., Rombach, G., Neumann, F., Ayuga, F., 2010. Simulations of granular flow in silos with different finite element programs: ansys vs. Silo. Trans. ASABE 53 (3), 819e829. Gallego, E., Ruiz, A., Aguado, P.J., 2015. Simulation of silo filling and discharge using ansys and comparison with experimental data. Comput. Electron. Agric. 118, 281e289. Gao, M., Cheng, X., Du, X., 2018. Simulation of bulk density distribution of wheat in silos by finite element analysis. J. Stored Prod. Res. 77, 1e8. Goodey, R.J., Brown, C.J., 2004. The influence of the base boundary condition in modelling filling of a metal silo. Comput. Struct. 82 (7e8), 567e579.
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