**1. Introduction**

Japan is a disaster-prone country that is exposed to the threat of various disasters, such as earthquakes, tsunamis, and floods caused by heavy rains. In addition, there are many soft grounds mainly composed of fine particles, such as clay, silt, and sand, especially in urban waterfront areas, which are the cause of great damage due to liquefaction. The phenomenon of liquefaction was first noticed in the 1964 Niigata Earthquake, and more recently in the Great East Japan Earthquake that occurred on 11 March 2011 and caused substantial damage, especially in Urayasu City, Chiba Prefecture [1–3]. There is great concern about damage caused by liquefaction in the event of an earthquake directly beneath the Tokyo metropolitan area or a huge Nankai Trough earthquake that is expected to occur in the future. In modern times, the world must protect its land from various disasters, such as earthquakes, tsunamis, and floods caused by heavy rains. For that purpose, it is necessary to improve the land, that is, the ground, so that it is sustainable against disasters. This concept will directly contribute to the achievement of Goal 11 (Sustainable Cities and Communities) in the Sustainable Development Goals (SDGs).

Various ground-improvement measures are being taken to suppress damage associated with various disaster [4,5]. Ground-improvement measures are indispensable measures for forming sustainable ground in the future. By performing ground-improvement

**Citation:** Nakao, K.; Inazumi, S.; Takaue, T.; Tanaka, S.; Shinoi, T. Evaluation of Discharging Surplus Soils for Relative Stirred Deep Mixing Methods by MPS-CAE Analysis. *Sustainability* **2022**, *14*, 58. https:// doi.org/10.3390/su14010058

Academic Editors: Carlos Morón Fernández, Castorina Silva Vieira and Daniel Ferrández Vega

Received: 17 October 2021 Accepted: 12 December 2021 Published: 22 December 2021

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work, it is possible to prevent the liquefaction phenomenon and suppress its damage. However, it is difficult to perform ground-improvement work while checking the internal conditions of the ground during the construction, and the design and evaluation are based on empirical rules [6–8]. Therefore, the purpose of the present study was to conduct a visible and measurable evaluation of the quality and performance of ground-improvement work by computer simulation.

A simulation analysis of the relative stirred deep mixing method (RS-DMM) [9], a kind of ground-improvement method, was performed in this study using a computer-aided engineering (CAE) analysis based on the moving particle semi-implicit (MPS) method, which is one of the particle-based methods (PBMs) [10,11]. The RS-DMM is a method of penetrating and stirring while rotating the inner and outer wings of the stirring wing in opposite directions and discharging the solidifying material from the tip of the stirring wing [9,12]. In addition, the "displacement reduction type (DRT)" of RS-DMM suppresses displacement during the construction. A series of operations, such as penetration, stirring, and extraction, performed by the DRT and the normal-type (NT) RS-DMM, was reproduced with a 3D model. Then, a visible and measurable evaluation was conducted on the conditions of the inside of the ground during each construction, the quality of the improved body, and the displacement reduction performance.

#### **2. Deep Mixing and Relative Stirred Deep Mixing Methods**
