## 1 Introduction  
To preserve the environment, and to maintain a balance between accretive populations and rapid urbanization, the construction of utility skyscrapers and underground structures has recently become a demanding sector. Deep excavation is an essential step for constructing these kinds of facilities. Deep excavation can extend to distances exceeding three kilometers [1]. Strutted or braced excavations are effective methods to ensure enough safety because soil movement and wall deformation characteristics are mainly influenced by unsupported wall span lengths [2]. The displacement and ground settlement characteristics of this complex soil-structure interaction system can only be predicted through empirical and semiempirical methods. So, numerical tools have been introduced to deep strutted excavation analysis. By integrating complex nonlinear soil models, numerical tools were used in deep excavation to investigate the passive soil response [3], strut bestressing effect [4], clay layer depth effect on earth pressure, struts, and walls [5], the lateral effective stress effect during the excavation construction process [6], the consolidation effect [7], the excavation geometry effect against basal heave on three-dimensional ground movements [8], the time-dependent behavior of excavation [9], the penetration depth effect of diaphragm wall [10], and the behavior of braced excavation in the sand [11]. These numerical analyses were performed either on the basis of data from case studies or previous studies. Numerical model development and validation, especially the numerical modeling of centrifugal tests, require highly specialized skills. Very few numerical analyses were performed to predict centrifugal results for the static behavior of deep excavation. Excavation effects on piles [12]and basement excavation effects on an existing tunnel [13] are numerically investigated using centrifugal test data.  
Realistic excavation modeling with reliable soil stiffness is still a concerning matter because soil materials usually used in centrifugal modeling differ from field soils [14]. The accuracy of the numerical modeling predominantly depends on the soil character; uncertain soil can generate significant errors in the test results. To minimize error in numerical modeling, the updating of soil parameters with back analysis is usually applied. Back analysis to update the soil parameters for deep excavation is conducted using several approaches, including the Gauss-Newtonian [15], quasi-Newtonian [16], genetic-algorithm [17; 18], differential-evolution [19], self-learning simulation [20], probabilistic maximal-likelihood formulation [21] methods, and Bayesian updating [22]. Most of these analyses use a single response and single objective function. [PERSON] and [PERSON] showed that multiple-point responses can update soil parameters more precisely [23]. Using the Pareto multiobjective optimization technique, [PERSON] et al. updated nine soil parameters in the modified Cam-Clay model [24]. Multiparameter updating using multiple-point responses is a highly complex process, and this analysis is still beyond reach. Back analysis for multiparameter updating using multiple-point responses can be achieved simply through the response-surface method, as there are available software tools for the construction of a response-surface model. The response-surface method has been used as a tool for structural numerical model updating [25] in some aspects, but it has not been used in deep excavation.  
In this paper, an approach is established for smooth multiple-parameter updating using multiple-point responses with the response-surface method. Seven bending strain responses along the depth of a wall from the centrifugal test of strutted deep excavation are used for model updating. A framework is proposed to adopt unknown soil parameters in the numerical modeling of centrifugal tests. A numerical model can be established within an optimal amount of time and with optimal cost using this proposed framework.