Introduction
The following will demonstrate the possibilities for simulating the interaction of wind, earthquakes, and soil-structure interaction using the example of a high-rise building.
Model Description
This technical article considers a fictional 20-story high-rise building with a twisted design. The floor slabs, columns, and core for bracing are made of reinforced concrete. The exterior surfaces are clad with glass. The subsurface with uneven layering is considered through borehole profiles. This consists of sand, gravel, and weathered rock from the terrain surface to the bottom of the examined terrain section. Loads considered include dead weight, live loads on floor slabs at 2 kN/m², wind loads in one direction from RWIND 3, and earthquake loads from the response spectrum method. The model can be downloaded from the link below.
Soil-Structure Interaction
In this example, the subsoil is simulated using the stiffness modulus method. From the three input borehole profiles, the stiffness corresponding to the reaction of the present soil to the applied base pressure is determined for each element of the foundation slab. Here, the influence of the chosen consideration of the soil is first seen in the file size and thus also in performance. The greatest contribution here is the calculation of the subsoil using the two-dimensional method compared to the calculation as a 3D volume body. However, direct consideration of soil layering from the borehole profiles without generating volume bodies further reduces the storage requirement of the model and leads to improved performance. Further information on input and available options is available in the online manual at the link below:
The following image compares the settlements under dead weight (Top) with those of the characteristic load combination with live load (Middle) and accompanying wind impact (Bottom). It shows a stronger settlement under the reinforced concrete building core, which decreases towards the edge of the foundation slab. Comparing the settlements resulting from the combination with wind (Bottom) to the settlement without (Middle), the wind load in the positive x-direction expectedly leads to reduced settlement on the left and increased settlement on the right side.
Comparing the coefficients of elastic support, it appears that the two characteristic load combinations do not differ. This is because they were automatically imported using the combination wizard from the corresponding quasi-permanent combination. This not only saves computation time but should also more closely resemble soil behavior due to the sluggish soil reaction. More information on adopting elastic support can be found at the manual link below.
Wind Simulation
The following animation shows the results of the wind simulation from RWIND. As seen here, the structure is flowed around in the X direction.
The torsional wind load resulting from the twisted design also leads to a twisting of the high-rise around its vertical axis. This is shown in the image below for the characteristic load combination with leading wind load (top in isometric view and bottom in plan view).
Earthquake
Since the modal analysis, as the basis for earthquake design using the response spectrum method, does not account for nonlinearities, special attention must be paid to the assumed supports in this case. The subsoil can typically not take tensile forces, especially in the case of shallow foundations, as planned here. This behavior is also represented by the stiffness modulus method. The results of the modal analysis are exemplified in the following image for the first eigenmode.
For a simplified earthquake design, there are various approaches. For example, the German national annex of Eurocode 8 refers to comparing the ratio of wind load to earthquake load. If the wind load is more than 1.5 times greater than the earthquake load, a separate approach can be omitted. In this example, this can be determined from the sum of the support forces of characteristic load combination 9 (self-weight and wind in X) and the acceleration in the X direction derived from the response spectrum of the first eigenmode. However, the resulting ratio is greater, as shown in the following equation. The application of this limit value for a 70 m high-rise would be questionable in any case.
A good reference value for the permissible fundamental eigenperiod is given by ASCE 7. According to formula 12.8-8, a permissible eigenperiod of 2.13 s is obtained for this example. However, since the first eigenperiod determined by modal analysis is 2.24 s, a simplified proof cannot be provided here.
Nevertheless, a load case was considered here, which simplifies the horizontal acceleration of the first eigenform in each mass point as a factor of the earthquake acceleration. Additionally, the plateau value of 1.67 m/s² is applied. More correctly, this would be set corresponding to the eigenform instead of uniformly in each mass point. However, this consideration simplifies checking the resulting base pressures and excludes gapping. The load case settings and resulting contact pressure are shown in the following images.
As seen here, only with the application of the plateau acceleration does gapping occur in the foundation base. Hence, the surface support would fail under the load of self-weight and horizontal impact from an earthquake.