1-2 Silo

As mentioned, the height of the new silo is 118 meter and it has a weight of 80000 tons. The silo dimension is 20 meters times 24 meters, and the internal structure is honeycomb and lattice-like. The volume of the concrete used was 18000 cubic meter, further 2700 ton reinforcements were used. The silo is located on 49 concrete piles with 120 centimeter in diameter and 40-45 meters in length. The lengths of the piles are selected as such to reach the bedrock. The tip of piles is considered to penetrate about 5 meters inside the bed-rock. The pile cap thickness is maximum 480 centimeter. Figure 1-2 shows the approximate geometry of the old and the retrofitted silo and Figure 1-3 presents the layout of the piles under the pile caps. The amount of excavated soil to implement the piles and pile caps was about 5000 cubic meter. The plan of the silo is shown in Figure 1-4.

Figure 1-3 The foundation of the retrofitted silo and the position of the piles

Figure 1-2 The old and the new geometry of the silo

1-3 Analysis and Seismic Design

As such structures are unconventional, and their operation is of great importance, the seismic analysis of these structures is highly challenging and sensitive. Based on the ratio of the plan dimension to the height, the silo should be considered as a slender structure with a small frequency and large period. The prominent period of the structure is also dependent on the foundation modeling. If the foundation is simulated as a rigid one with fixed supports, the structure would be stiffer. While if the piles and the surrounding soil are also modeled, the period would be increased. In the case of foundations located on piles, the dynamic interaction, and considering the effect of the piles set, is a substantial issue. As a pioneer work, Dr. John Wolf from ETH Zurich realized the importance of the dynamic interaction of soil and piles and the dynamic effect of piles group, when he was performing the seismic analysis of a nuclear power plant in Brazil. If the number of piles is large and the spaces are small, the dynamic effect of the entire group would reduce the pilegroup stiffness up to 80 percent. Hence, considering this point, the structure foundation was modeled using a high accurate analysis tool (e.g. FEM); as a result the responses are close to the real building. Further, it was decided for modelling of the soil to utilize also the CONE model. Following this procedure, the piles were replaced and modeled with springs and dampers. Figure 1-5 displays the piles‘ position in finite element modeling of the silo. In fact, 49 piles are placed under the two pile caps at both sides of the silo, and as it was mentioned it is essential to consider the dynamic interaction and effect of the whole group as well. Figure 1-6 shows the situation of soil layers.

In the silo dynamic calculations, the finite element model was constructed using 50 centimeter hexahedral elements. Also, the adapting re-meshing based on maximum stresses option was used to obtain the maximum accuracy.

The seismic analysis was done based on the DUZCE acceleration time history, which is displayed in Figure 1-7. The ETABS and ADINA software were used as analysis tools.

If the silo structure was modeled with fixed supports, the first period would be 1.8 second. On the other hand, in the case of considering piles in the simulation, the dynamic interaction effect, and the reducing effect of piles lateral stiffness, the period would reach up to 3 seconds (the structure would be softer). It should be noted that in this project the stiffness of pile cap’s lateral spring, piles, and the soil is 890 MN/m, and vertical stiffness of the replaced springs was calculated to 1800 MN/m.

In the current design, the radiation damping effect was neglected. After analysis, the maximum axial force in piles was equal to 19000 KN, which is due to the dead loads, and the earthquake loads.

As a result of the earthquake analysis, the lateral displacement of the structure in the directions of east west is 17 and north south is 21 centimeter, respectively; both are in an acceptable range of operation. It should be noted that due to the significance of this project and to the necessity of doing a nonlinear dynamic analysis, a similar design and analysis was performed by Exponent Inc. USA, under the supervision of Prof. Brian McDonald from Stanford University and Dr. John Osteraas and Dr. Patxi Uriz from Exponent Ltd., Stanford USA, as well. The obtained results of this team were in great agreement with our results.

Generally, in such structures the stress control and crack width checking are also essential points in addition to deformation control and operation condition. Because of the large weight of the silo, the compressive stresses in concrete may reach up to 50 Mpa, especially in lower stories and cantilever region, the control of which is extremely important as a critical point of the structure. For this reason, in the current design in the case of the probable existence of high stress concentration in the concrete, the factor of safety was increased to 3, in order to assure safety.

Few months after completion of the silo design, we noticed that some old books related to 40 years ago had displayed the stress distribution based on analytical calculations without any advanced computational method or FEM (Figure 1-10). Surprisingly, there is not a large difference between manual results and new computational methods. This subject was a valuable point for us.

Figure 1-4 The story plan of the silo

Figure 1-5 The modeling and position of the piles in FEM modeling of the silo

Figure 1-6 The soil layers and wave propagation pattern

Figure 1-7 DUZCE acceleration time history, used in seismic analysis of the silo

1-4 Hints

By the analysis and design of the silo project we have learned numerous practical and professional lessons. First, it is necessary to consider the dynamic interaction of soil-pile structures. Considering this phenomenon the behavior of simulated structures are much closer to the real one. In this project due to the large number of piles, their high concentration and their long length, soil-pile-structure effects were much more important. Another point of such projects is that it is recommended not to rely only on one method in complex problems and especially in nonlinear dynamic analysis. It is beneficial to use different methods and analyses and then compare the results. Although it may not be time-efficient or cost-effective, covering this part of the process is a vital step in large-scale projects. The different analytical methods can provide different interpretations and results and also various beneficial points, as in the present project the Exponent design group, USA, played a major role in evaluation of our results.

Finally, despite the availability of advanced pieces of software and new methods, analytical methods and hand calculations should not be ignored. We firmly suggest that engineers and designers try to apply simplifications and also implement the simple solutions, especially in complex problems, to obtain an acceptable solution for comparing to advanced methods. Moreover, this manner would facilitate the understanding of structure behavior, and the designer would have a better understanding of force and stress values.

I have presented the silo project to a group of 30 outstanding professors in the field of earthquake, geotechnics, and structure at MIT in Cambridge, USA, which was held at the occasion of Professor Kausel’s invitation in November 2015.

Figure 1-8 A schematic of the structure deformation

Figure 1-9 A schematic of the lateral piles displacement