###### Abstract  
U-shape steel sheet piles are widely used in deep and large excavation engineering due to their excellent soil-retaining and water-stopping performances. To achieve deformation control in excavations, an experimental investigation on the deformation characteristics of a strutted U-shape sheet pile flexible retaining structure was conducted. Single-layer and double-layer strutted retaining structure excavation indoor model tests in sand, where U-shape sheet piles were formed by 3D printing, were successfully accomplished. Deformation was monitored in real time during the test. The results show that the lateral displacement mode of the retaining structure transformed with the change in excavation from the \"cantilever\" to the \"bulge\" and finally developed into an intricate \"recurve bow\". The average maximum lateral displacement was 0.756% of the excavation depth. With a maximum settlement of 0.375% of the excavation depth on average, the distribution of ground settlement behind walls changed from \"exponential\" to \"triangular\" before ultimately transforming into \"trough\" or \"trapezoid\" mode. The maximum settlement to maximum lateral displacement ratio (\(s_{max}/\delta_{max}\)) on average was 0.54; the maximum settlement deformation rate was always less than the maximum lateral displacement deformation rate. deep excavations; strutted flexible retaining structure; U-shape sheet pile; deformation; model test +
Footnote †: journal: Applied  
a subdivision of deep inward deformation, as shown in Figure 1d. [PERSON] [4] studied numerous excavations in China and concluded that the deformation behavior of retaining structures could be divided into four modes: cantilever, convex, composite, and kick-in deformation modes. The kick-in mode is a type of convex deformation, as illustrated in Figure 1e. [PERSON] [2] found that the distribution of excavation ground settlement after walls in sand and stiff to very hard clays presents a triangular pattern, with an impact range of 2 \(Z\) and 3 \(Z\) (\(Z\) represents the excavation depth). Moreover, the distribution of excavation ground settlement in soft to medium clays follows a trapezoidal pattern, with the maximum settlement occurring within a horizontal distance of 0-0.75 \(Z\) and an impact range of 2 \(Z\). [PERSON] [5] analyzed the measured data from 10 excavations in Taipei's soft clay area and concluded that the characteristics of ground surface settlement could be divided into spandrel and concave profiles. Furthermore, [PERSON] [6] improved [PERSON]'s prediction method and proposed a primary and secondary influence zone. [PERSON] [7] investigated the deformation of excavations using data from deep excavation engineering. [PERSON], [PERSON], and [PERSON] [8; 9; 10; 11] analyzed the deformation behavior of retaining structures and ground surface settlement in numerous deep and large excavations in Shanghai's soft clay area and summarized the relationship between deformation behavior and factors such as excavation depth and retaining system stiffness. [PERSON] et al. [12] proposed an excavation method that could control the deformation of retaining structures and ensure construction safety through centrifugal testing. In addition, [PERSON] and [PERSON] [13; 14] used indoor excavation model tests to determine the deformation characteristics of cantilever and strutted pipe pile retaining structures and then compared and analyzed the results. [PERSON] [15] and [PERSON] [16] used finite element analysis on steel sheet pile cofferdams to investigate the distribution of internal force and the deformation of flexible retaining structures of steel sheet piles, as well as their variation patterns. [PERSON] [17] used the FLAC3D finite difference method (FDM) to simulate four excavation schemes and study the deformation of the main retaining structure. In summary, most studies have focused on traditional retaining structure deformation characteristics.