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# During analysis of underground structures, the results diverge under loads such as hydraulic pressure.

## Question

During analysis of underground structures, the results diverge under loads such as hydraulic pressure.

In underground structure analysis, the simultaneous loadings need to be substituted for a load combination in the pre-processing mode. The results of individual load cases should not be combined after analysis.

Generally, underground structures are placed on top of the ground, and the ground can resist only the vertical loads due to gravity but cannot resist any horizontal loads. Therefore, the boundary conditions of underground structures are represented using compression-only (Comp. Only Type) Point Spring Support or Elastic Link.

A model with nonlinear boundary conditions such as compression-only Point Spring Support or Elastic Link requires iterative analysis to find the state where all springs are under compression and output the corresponding results. Therefore, if all springs are compressed within the specified number of iterations, the results will converge, but if not, the results will diverge, resulting in unreliable values.

The divergence of the analysis results can be checked through the information displayed on the Message Window during the analysis process.

In the 'Load Combination', the load combination created by 'Add Type' is simply the sum of the multiplied load factors of each 'Load Case'. Therefore, for the load combination result to be reliable, the results of the 'Load Case' that make up the combination must be trustworthy. In this sense, in the figure above, the load combination including Load Cases 4, 6, 7, 9 and 31 can be considered as an unreliable result.

For underground structures that use compression-only boundary conditions, such as point spring supports or elastic links, it is common for the results to diverge when subjected to loads such as positive hydraulic pressure or asymmetric horizontal soil pressure. Therefore, in underground structures, it is common practice to substitute all Load Cases with a single load case (simultaneous loads) in the pre-analysis stage.

For example, if you select 10 load combinations created in 'Load Combination' and move them to Selected Combinations as shown in the figure below, 10 load cases (simultaneous load cases) will be additionally created.

By creating simultaneous load cases as described above and performing analysis using them, the results of the simultaneous load cases converge in most cases while the results of the original Load Cases 5, 7, and 8 still diverge.

In general, for underground structures, the analysis is usually carried out using simultaneous load cases, so it is not necessary to worry about the divergence of the single load's results. Alternatively, it is possible to delete the single load, but it is recommended to keep it for future modifications to the single loads.

For more information, you can learn about the precautions that need to be taken when analyzing underground structures by referring to the 'Check Point for Underground Structure' document, which is  in the 'Technical Materials' > 'Program Technical Materials' section on the technical support website.

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