12.1 Introduction

As the discussion in Chapter 6，finite element method is a powerful tool for geotechnical problem analysis.The normal procedure of the analysis can be demonstrated as 3 steps：（1）build mechanical models，including geometry，constitutive model of soils and rocks and initial boundary conditions；（2）determine the parameters of soils and rocks；（3）get the stress and deformation field.It can be called forward analysis.

However，the determination of parameters of soils and rocks usually has uncertainty，making challenges for prediction of geotechnical performance.Because of the limitation of time and cost，the geological survey before the construction may not be comprehensive enough to reveal real condition of the whole construction field.On the other hand，the results of laboratory tests may fail to fully represent the in situ soils and the complicated soil stratum conditions because of disturbance caused by sampling.Also，some parameters，like the small strain stiffness（Section 7.5.1），are difficult be determined via conventional tests.All of these factors lead FEM prediction to fail to match the observed response.

In this regard，observational method（Terzaghi and Peck，1943；Peck，1969b），a framework wherein construction and design procedures and details are adjusted based upon observations and measurements made as construction proceeds，was usually used to optimize the design parameters.In this framework，the excavation⁃induced response has been measured and the more reasonable soil（rock）parameters are supposed to be back⁃figured based on the observation，allowing more reliable prediction for following construction activities.The procedure is so⁃called back analysis.

Because braced excavations are generally carried out in stages，back⁃analysis to update key soil parameters（such as the normalized undrained shear strength and the normalized initial tangent modulus in an excavation in clays）is generally realized in multiple stages；before the first excavation stage，the wall and ground responses are predicted with field tests and／or laboratory data.After the first stage excavation is completed and wall and／or ground responses are measured，the key soil parameters can be updated with the observed responses to refine the knowledge of the soil parameters.With the updated soil parameters，the wall and／or ground responses in the subsequent excavation stages may be predicted with improved fidelity.This process can be repeated stage by stage until the final excavation depth is reached.

Figure 12.1 diagrams an example reported by Finno（2005）.Before the optimization，the computed wall lateral displacements by using initial parameters were significantly larger than the observation at every construction stage.The maximum computed displacements were about twice the measured ones and the displacement profiles result in significant and unrealistic movements at the bottom.It indicates that the tests overestimate the soil stiffness properties.To optimize the soil stiffness parameters，back analysis was carried out.When parameters optimized based on Stage 1 observations were used，the improvement of the fit between the computed and measured response at every stage is significant.At Stage 5，the maximum computed displacement exceeds the measured data by only about 15%.Analyses were also made wherein parameters were recalibrated at every stage until the final construction stage and the fit between the computed and measured displacement is further improved.

Figure 12.1 Optimizing analysis via updating parameters（Finno，2005）

While back analysis is necessary，note that it cannot replace laboratory and filed tests，the back⁃figured soil parameters should be regarded as the equivalent soil parameters，not the real soil parameters.It only helps to update the design parameters to provide references for following construction activities.

Generally，back analysis methods used in excavation issues are not specialized.This chapter will only make introduction to some selected methods.