Centrifuge modeling of preloading consolidation and dynamic compaction in treating dredged soil

Accepted Manuscript Centrifuge modeling of preloading consolidation and dynamic compaction in treating dredged soil

Shi-Jin Feng, Feng-Lei Du, H.X. Chen, Jian-Zhi Mao PII: DOI: Reference:

S0013-7952(16)30574-9 doi: 10.1016/j.enggeo.2017.06.005 ENGEO 4584

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

30 October 2016 3 May 2017 10 June 2017

Please cite this article as: Shi-Jin Feng, Feng-Lei Du, H.X. Chen, Jian-Zhi Mao , Centrifuge modeling of preloading consolidation and dynamic compaction in treating dredged soil. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Engeo(2017), doi: 10.1016/j.enggeo.2017.06.005

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ACCEPTED MANUSCRIPT Centrifuge modeling of preloading consolidation and dynamic compaction in treating dredged soil Shi-Jin Feng1, * , Feng-Lei Du1, H. X. Chen1, Jian-Zhi Mao1

* Corresponding author Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education,

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Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

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Email address: [email protected] (Shi-Jin Feng)

ACCEPTED MANUSCRIPT Abstract: Preloading consolidation with drains (PCD) and dynamic compaction (DC) are often combined to improve the ground condition. A novel method of modeling PCD and DC in centrifuge is developed in this study. 3D printing technique is used to greatly improve the manufacturing precision and simulation ability of sand drains. A loading container, which allows adding sand in it stage by stage, is well designed to achieve uniform surface loading.

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Based on strong magnet and reliable mechanical principle, a novel device for modeling

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dynamic compaction is developed, which can realize continuous tamping in centrifuge to a

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certain extent. An example test using dredged soil sampled from Putian Port, Fujian Province, China, was conducted to validate the performance of the method, including self- weight

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consolidation, four-stage preloading with drains, and dynamic compaction. The present method performed well to simulate the whole process of pretreating the dredged soil. The

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surface settlement, changes in excess pore pressure and effective stress, number of drops, crater depth, improvement depth by DC were reasonably predicted. Significant surface

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settlement and crater depth were observed during the preloading consolidation and dynamic compaction, respectively, indicating that the compressibility of the dredged soil was rather

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large. Spacing of sand drains behaved to be more effective than the length. The vertical distributions of water content, excess pore pressure, and effective stress revealed that the

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degree of consolidation decreased with depth, since the drainage condition in the upper part was better. The present method will contribute to a better understanding of PCD and DC, and is promising to be used for the design and evaluation of the current ground improvement methods.

Keywords: Sand drain, 3D printing, Stage loading, CPT, Bearing capacity, Land reclamation

ACCEPTED MANUSCRIPT 1

Introduction Preloading consolidation with drains (PCD) and dynamic compaction (DC) are often

combined to improve the ground condition. For example, dredged soil is widely used in land reclamation, but the ground has little or even no bearing capacity at the early stage, which has to be treated to avoid excess settlement and instability. PCD is extensively used to form the

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basic bearing capacity of the dredged soil ground (Stamatopoulos et al., 2005; Zhou et al.,

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2005; Chu et al., 2009; Fang and Yin, 2006; Wang et al., 2009; Liang and Xu, 2012; Vukadin,

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2013). However, due to the low permeability, PCD costs considerable time to meet the required degree of consolidation as well as ground bearing capacity (Cascone and Biondi,

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2013). Considering construction duration and costs, DC is often adopted as a supplementary reinforcement method. The combination of PCD and DC has been used in various areas

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(Zhou et al., 2003, 2009; Wang et al., 2009; Liang and Xu, 2012; Vukadin, 2013). Due to varying site conditions, rational design of PCD and DC is always not an easy work.

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Therefore, it is very essential to develop a method which can well investigate the mechanism and governing influence factors of the PCD and DC techniques.

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In history, sand drains were extensively used as vertical drains (Carrillo, 1942; Barron, 1948) and prefabricated vertical drains were then introduced to improve the drainage effect

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(e.g., Kjellman, 1952; Hansbo, 1979; Atkinson and Eldred, 1981; Fellenius and Castonguay, 1985; Long and Covo, 1994). The DC method was initiated in the 1970s (Menard and Broise, 1975), which has proven to be effective for various soil types and conditions, especially sandy materials and granular materials (Mayne et al., 1984; Feng et al., 2013, 2014, 2015). Prudence is required if it is used for saturated clay and fine-grained soils (Lukas, 1980), since the method may fail and end up with ‘stuck hammer ’ or ‘rubbery soil’ (Zhou et al., 2003; Deng and Xu, 2010). The DC method can succeed in treating saturated soft clay only if vertical drains are adopted (e.g., Zheng et al., 2000) and operational parameters (e.g., energy

ACCEPTED MANUSCRIPT level) are well designed (Poran and Rodriguez, 1992; Chow et al., 1994; Miao et al., 2006). In-situ pilot tests are very meaningful for the rational design of PCD and DC, but it costs too much to carry out the tests in a large area with highly heterogeneous ground condition. Centrifuge modeling is a powerful tool and has greatly contributed to the progress of geotechnical researches (Fox et al., 2005; Zhang and Wong, 2007; Choy et al., 2014; Wang

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and Zhang, 2015; Ng et al., 2015; Zhou and Tang, 2015). Some efforts have also been made

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to simulate PCD or DC in centrifuge (e.g., Merrifield and Davies, 2000; Sharma and Bolton,

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2001; Chen et al., 2009). However, several important problems still need to be solved. The first problem is how to accurately simulate the vertical drains. Woolen yarn and

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twisted multifilament polyester string were once adopted to simulate sand drains in centrifuge modeling (Sharma and Bolton, 1996, 2001; Chen et al., 2009). Lu (2006) used wool with a

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diameter of 2 mm to simulate plastic drainage plate. The above methods can simulate vertical drains to a certain extent but the simulation ability is limited by the relatively low

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manufacturing precision. The second problem is how to achieve stage preloading. Generally, there are three kinds of methods to achieve stage loading in centrifuge modeling; namely,

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directly adding sand cushion after stopping the centrifuge (Zhang et al., 2007), progressively increasing centrifugal acceleration (Chen et al., 2009), using manipulator. The first one

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cannot guarantee uniform surface loading. The second one increases the scaling factor with increasing centrifugal acceleration, and consequently changes the model size. The third one is the most accurate way, but it is seldom used due to high costs and complex operating system. Hence, a more applicable stage loading method is needed. The third problem is how to simulate DC in centrifuge. In practice, automatic tripping device and manual assistance facilitate continuous tamping. However, it is extremely difficult to achieve this in the rapid-rotating centrifuge if the mechanisms of the existing devices are adopted. Research on this problem is quite limited. Thus, a novel DC device is highly desired to solve the problem.

ACCEPTED MANUSCRIPT This paper aims to develop a novel method of modeling preloading consolidation and dynamic compaction in centrifuge. Firstly, the framework of the method is introduced. Then the principles and physical descriptions of the PCD and DC devices are described. Finally, three groups of tests were conducted using dredged soil taken from Putian Port in Fujian Province to validate the performance of the present method. Cone penetration tests (CPT)

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were performed to evaluate the treatment effect before and after the DC. The results of

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surface settlement, water content, pore pressure, total stress, effective stress, crater depth and

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cone penetration resistance were also comprehensively analyzed and discussed. This study will contribute to a better understanding of PCD and DC, and is promising to be used for the

Framework of the method

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design and evaluation of the current ground improvement methods.

This study includes two test devices (i.e., PCD and DC), which are extensively used in

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land reclamation. For the sake of saving costs and recycling resource, seabed sediments distributed in coastal area are used as the main filling material in land reclamation. However,

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dredged soil ground has little or even no bearing capacity at the early stage, thus pretreatment is very essential. Usually, it takes about 3 months for self- weight consolidation (Fig. 1a).

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Drainage system, such as a network of sand drains or plastic drainage plates, is then established before preloading (Fig. 1c). Although PCD is the main treatment method, it is rather time consuming to meet the required degree of consolidation. In order to obtain sufficient bearing capacity and mitigate the risk of differential settlement as well as seismic subsidence, dynamic compaction is often adopted for further reinforcement (Fig. 1e), and the drainage system is kept in the ground to accelerate the dissipation of excess pore pressure caused by the dynamic compaction. As shown in Fig. 1, centrifuge modeling with three stages is designed according to

ACCEPTED MANUSCRIPT engineering practice. Firstly, dredged soil sampled from construction site is smashed to the initial condition (Fig. 1b). Secondly, sand drains are inserted into the dredged soil as drainage path and loading is added on the surface stage by stage (Fig. 1d). Finally, dynamic compaction is conducted (Fig. 1f).

Preloading consolidation device

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Drainage path and loading are the main difficulties in modeling preloading consolidation

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in centrifuge. Drainage path plays an important role in treating soft soil, which greatly speeds up the consolidation progress. The most widely used drains include sand drains and plastic

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drainage plates. The typical diameter range of sand drain is from 20 to 30 cm, while plastic drainage plate is generally 0.4 cm thick which is difficult to scale down in centrifuge

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modeling. Hence, sand drains are adopted in this study. In order to precisely simulate sand drains, 3D printing technique is adopted. According to the existing conditions in our

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laboratory, a loading container, which allows adding sand in it stage by stage, is well

in the following part.

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designed to achieve uniform surface loading. The design ideas will be concretely introduced

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3.1 3D-printed sand drain

Since the sand drains used in the centrifuge test have to be tiny but precise, 3D printing technique is introduced to produce the skeleton of the sand drain (Fig. 2a). The skeleton includes cap, clamping ring, longitudinal rib and cone. The cap is a little larger in diameter to keep the sand drain from sinking into the soil. The inner diameter of the sand drain enclosed by the clamping ring and longitudinal rib is 5 mm. The cone angle is 60, which facilitates the installation of sand drains. Fig. 2(b) shows the configuration of the sand drain. The manufactured skeleton is filled with fine sand. A layer of non-woven fabrics is covered on the

ACCEPTED MANUSCRIPT skeleton to prevent the fine sand from flowing out. The sand drains are recommended to be steeped in water for at least 1 hour to facilitate the installation.

3.2 Stage preloading device The stage loading device consists of three components: loading container, steel frame,

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and storage tank, as illustrated in Fig. 3. The centrifuge strongbox is connected with the steel

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frame by high-strength bolts. During the preloading consolidation, pore water is drained out

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and accumulated on the surface. The storage tanks placed on both sides of the strongbox are designed to collect the water. The tanks are coated with filter screen, preventing fine-grained

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soils from flowing into the tank. The first stage loading is realized by adding sand cushion. The latter stage loading is completed by the loading container with a mass of 8.75 kg, which

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is a thin trunk made of five iron sheets of 2 mm in thickness. The effective preloading area is 0.227 m2 . The loading container exerts pressure on the soil by self-weight and realizes

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various loading levels through filling sand in it. Once the loading level is designed, the mass of the filled sand can be determined. The filled sand must be flattened to ensure the applied

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load is uniform. After removing the loading container, unloading can be easily achieved.

friction.

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Moreover, a 3 mm gap between the container and the strongbox is designed to reduce the

3.3 Data-acquisition device A reflection platform is installed at the bottom of the loading container to measure the surface settlement (Fig. 3). The platform is made of two aluminum cylinders connected by an iron rod. The lower cylinder is welded to the bottom of the loading container, while the upper one serves as laser screen. During the preloading consolidation, a laser displacement meter with 0.01 mm precision placed above can measure the surface settlement of the soil. Sensors

ACCEPTED MANUSCRIPT are buried in the modeling soil for measuring total stress and pore pressure.

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Dynamic compaction device It is challenging to simulate DC in rapid-rotating centrifuge. The most difficult work is

to achieve the unhooking process. Since electromagnet crane has been widely applied in steel

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manufacturing industry, it provides inspiration to design a novel DC device based on the

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strong magnet. The device consists of three parts: supporting module, tamping module and

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monitoring module, which will be introduced in detail in the following part.

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4.1 Supporting module

The supporting module contains steel frame and movable support plate (Fig. 4). The

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steel frame is the working platform on which the tamping module and the monitoring module are working. It is firmly fixed on the top of the strongbox by grooves and bolts. The support

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plate can move on the steel frame. Moreover, the tamping module is supported by the support plate and can also move on it. By adjusting the locations of the support plate and the tamping

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4.2 Tamping module

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module, the tamping module can cover a large area.

The tamping module is the core of the whole system, which consists of transparent sliding tube, hammer, magnet, shaft, clamping ring, tube connector, gearbox, electromotor. The electromotor provides power to drive the shaft up and down, and it can change the rotation speed through a frequency controller located in the control room. The magnet is fixed at the end of the shaft by bolts (Fig. 5). In rapid-rotating centrifuge, the hammer is influenced by the gravitational force and the centrifugal force at the same time. In the DC process, the existence of the gravitational force

ACCEPTED MANUSCRIPT tends to make the hammer move along a parabolic curve and deviate from the designed tamping point. To solve the problem, a transparent sliding tube is adopted, which is composed of a plexiglass tube and an inner steel tube. The dimensions of the transparent sliding tube are shown in Fig. 5, which can guarantee the shaft, magnet and hammer moving in a confined area. Since the plexiglass tube is transparent, it is convenient to monitor the whole tamping

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process. The inner steel tube is pressed into the plexiglass tube. It has thread and can connect

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with the outside thread tube connector (20 cm in length), which ensures that the transparent

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sliding tube is freely adjusted until it touches the soil surface. With the clamping ring twisted on the inner thread steel tube in the opposite direction, the transparent sliding tube can be

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firmly fixed.

The magnet of 32 mm in diameter attached to the bottom of the shaft can provide a

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maximum attraction of 250 N, which means that the hammer would never drop down if the mass is less than 500 g (within 50 g centrifugal field). Fig. 6 shows the structure of the model

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hammer, which is a combination of aluminum sleeve and iron cylinder. The height, external diameter and thickness of the aluminum sleeve are 50, 41 and 1 mm, respectively, which can

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effectively avoid overturning. The reason to use aluminum sleeve is that aluminum is relatively smooth, and the friction between the sleeve and the plexiglass tube can be further

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reduced by smearing lubricating oil. With the iron cylinder glued with the sleeve, the model hammer can be attached by the magnet, and also hammers with different masses can be produced by changing the thickness of the iron cylinder. Table 1 shows the design parameters of the hammers of two energy levels with a scaling factor of 50. The operation procedures of the tamping module are shown in Fig. 7. In Step 1, the hammer is attached by the magnet and elevated by the shaft. In Step 2, when the hammer touches the inner steel tube, the shaft continues to elevate and the hammer is separated from the magnet since the diameter of the hammer (41 mm in Fig. 5) is larger than the inner

ACCEPTED MANUSCRIPT diameter of the inner steel tube (34 mm in Fig. 5). In Step 3, after the hammer is separated from the magnet, the hammer drops under the effect of centrifugal force. In Step 4, the shaft drops to attach the hammer. When the shaft is close to the hammer, the dropping speed is controlled to a relative small value to avoid intense impact with the hammer. After the

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hammer is attached, the operation is repeated from Step 1 to Step 4.

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4.3 Monitoring module

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Since dynamic compaction is carried out in the high-speed rotating centrifuge bucket, a HD camera (Fig. 4) is used to monitor the tamping process and provide information for

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post-analysis. With real-time video displaying and saved in computer, the operation of the DC

scale analysis.

Test setup and test procedures

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process can be monitored and recorded. Moreover, crater depth can be determined by image

5.1 Test material

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Dredged soil sampled from the construction site of Putian Port, Fujian Province, China, was tested in this study. The properties of the tested material are summarized in Table 2,

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indicating that the dredged soil had poor engineering properties with high water content and large void ratio. The water content reached 85.47% and the degree of saturation was 96.8%. The content of silt and clay was as large as 92.7%. According to ASTM (2006), the tested dredged soil can be classified as lean clay. With low permeability, there is no doubt that it is hard to consolidate such dredged soil.

5.2 Test setup The centrifuge used in this research had an arm radius (i.e., the distance from the center

ACCEPTED MANUSCRIPT of rotation to the specimen platform) of 3 m and allowed a total capacity of 150 g.t. In this study, a model scale of 1/50 was used with a nominal centrifugal acceleration of 50 g. Three groups of tests (T1-T3) were conducted. The test plan is summarized in Table 3. Different arrangements of sand drains and energy levels were designed for T1-T3. The test setup of T1 group is shown in Fig. 8 as an example. The strongbox had an inner

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size of 600×400×500 mm containing the dredged soil with an original height of 400 mm.

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Working in the 50 g centrifugal field, it simulated a prototype space of 30×20×20 m. Sand

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drains of 200 mm in length and 80 mm spacing were evenly arranged in the dredged soil. As shown in Fig. 8a, the sensors intended to measure total stress (S1-S3) as well as pore pressure

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(P1-P3) were laid at three layers at different depth (Layer 1-Layer 3). The depths of Layer 1-Layer 3 were 50, 100 and 150 mm, respectively. Four tamping points (DC1-DC4) after

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preloading were designed (Fig. 8b). Three CPT points before DC were placed at J1-J3, and another three CPT points (J4-J6) were arranged to evaluate the treatment effect after DC (Fig.

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8b). Similar with T1, the depths of Layer 1-Layer 3 were 50, 150 and 250 mm for T2, and

5.3 Test procedures

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those of T3 were the same with T1.

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Fig. 9 shows the procedures of a typical test. Firstly, the model of dredged soil was prepared in laboratory (Fig. 9a). Enough attention should be paid at this stage to accurately install the sensors and make the conditions of different test groups as similar as possible. Secondly, sand cushion, sand drains as well as preloading were applied (Fig. 9b). The three test groups shared the same preloading conditions, the preloading parameters are summarized in Table 4. The PCD treatment lasted about 1160 min in the rotating centrifuge with 50 g acceleration, which simulated 5.5 years in prototype. In each test group, water content profiles were measured at three locations after PCD (see Z1-Z3 in Fig. 8b as an example).

ACCEPTED MANUSCRIPT Thirdly, when the preloading was completed, the loading container was removed (Fig. 9c). The first three steps aimed to form basic bearing capacity. Afterwards, CPT was conducted to assess the bearing capacity before DC (Fig. 9d). DC was then conducted to further improve the ground condition (Fig. 9e). Finally, CPT was carried out to evaluate the improvement effect of DC (Fig. 9f). It should be noted that continuous tamping can only take place at the

Interpretation of test results

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same DC point, the centrifuge must be stopped when changing to the next tamping point.

6.1 Surface settlement and water content

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Significant surface settlement was observed during the preloading consolidation (Fig. 10). Firstly, the settlement experienced an almost vertical growth due to the increased

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centrifugal acceleration from 0 to 50 g. Large void vanished and a large amount of water was drained out. Initial ground stress started to build up. Secondly, settlement slightly increased

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during the self-weight consolidation, the settlement rates of T1-T3 at this stage were 0.74, 1.08, 1.08 mm/d in prototype (see Table 5), respectively, implying that the water was difficult

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to drain out without treatment measures. After installing the sand drains and applying the 1st stage loading, the settlement sharply increased, and the settlement rates of T1- T3 after

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applying the stage loading were summarized in Table 5. Finally, with four-stage loading and sand drains, the surface settlement gradually grew and ended with 93.84, 88.63 and 80.56 mm for T1, T2 and T3, respectively. The settlement rates of T1-T3 at the end of the tests were all less than 1 mm/d in prototype, which was miniscule (Stamatopoulos et al., 2013). Considering the thickness of the sand cushion decreased by approximately 20 mm after the tests, the surface settlements of the dredged soil were 73.84, 68.63 and 60.56 mm for T1, T2 and T3, respectively. The corresponding prototype settlements were 3.69, 3.43 and 3.03 m, respectively, which evidenced the large compressibility of the dredged soil and revealed the

ACCEPTED MANUSCRIPT treatment effects of different sand drain arrangements. Two methods were adopted to verify the measured surface settlement. The first one was the average strain of the soil. Take T1 group as an example, the average strain of the dredged soil was 3.69/(0.1550)=49.2%. 0.15 m was the length of the sand drains buried in the dredged soil (see Fig. 8), and 50 was the scaling factor. The reason to choose 0.15 m for

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calculation will be explained in Section 6.2. Similarly, the average strains for T2 and T3 were

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27.4% and 40.4%, respectively. The three values were within or close to the range in the

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drained reclamation works in Hong Kong (35%-42%) which was reported by Kwong (1997). The second method was 1D compression prediction using a compression index (Cc)

equation:

Cc p lg 2 H 1  e0 p1

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S

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compatible with the soil type. The surface settlement can be predicted by the following

(1)

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where S is the settlement of the dredged soil (m); e0 is the void ratio corresponding to p1 (kPa); p2 is the stress considering surcharge and self-weight of dredged soil (kPa); H is the

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thickness of the compressed dredged soil (m). The typical range of Cc of marine mud was 0.4-1.0 (Kwong, 1997). The initial void ratio was 2.34 (Table 2) and p1 was taken as 1 kPa

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here. Take T1 as an example. H was 7.5 m (0.1550 m) in prototype. p2 can be determined considering the surcharge and the average self-weight of dredged soil; namely, 144.5+54.1 kPa. The changes in unit weight of soil and buried depth of sand drains in the dredged soil during the preloading consolidation were not considered here for simplicity. In this way, the computed settlement of dredged soil was 2.06-5.16 m. Similarly, the computed settlement ranges of T2 and T3 were 3.55-8.87 m and 2.06-5.16 m, respectively. The measured settlements were within or very close to the respective computed value. Therefore, the analysis results of both methods indicate that the measured settlement values were

ACCEPTED MANUSCRIPT reasonable. Due to consolidation parameters of the dredged soil (e.g., permeability a nd coefficient of consolidation) were lacking, it is quite difficult to predict the settlement rate by analytical solution. Nevertheless, the shape of settlement curves was reasonable compared with the reported results of field measurements (e.g., Stamatopoulos and Kotzias, 1985; Arulrajah,

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2005; Chu et al., 2009; Stamatopoulos et al., 2013). Generally, the settlement rate at the early

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stage of preloading is relatively large, such as 2-10 mm/d (Arulrajah, 2005; Chu et al., 2009;

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Stamatopoulos et al., 2013) which varies with drainage condition and soil properties, while the settlement rate at the end of preloading is miniscule (less than 1 mm/d). Hence the

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measured settlement rate in this study (Table 5) was also reasonable. It should be noted that the total settlement in this study was much larger than that in some embankment construction

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works (e.g., Stamatopoulos et al., 2005, 2013), indicating that dredged soil has much larger compressibility and should be well treated before utilization.

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The variation of water content with depth after preloading consolidation is shown in Fig. 11. The surface water content of T1 fell from 88.7% to 52.4%. Those of T2 and T3 were

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53.2% and 58.8%, respectively. Overall, the water contents with depth of T1, T2, T3 were the lowest, medium, and the largest, respectively. In each test group, the water content generally

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increased with depth, indicating that the degree of consolidation decreased with depth. The largest water content of T1 occurred at depth of 150 mm, reaching 77.1%, while it reduced to 70.1% at depth of 200 mm, which may be caused by the preferential flow effect. Therefore, both surface displacement and water content indicated that the initial state of ground before DC varied with different arrangements of sand drains, T1 was the best, T2 took the second place, and T3 was the worst.

ACCEPTED MANUSCRIPT 6.2 Pore pressure, total stress, and effective stress The measured pore pressure and total stress of T1 group are shown in Fig. 12 as an example. The effective stress and excess pore pressure were then obtained and shown in Fig. 13. It is noteworthy that the effect of settlement of dredged soil was considered when calculating the excess pore pressure. The halt and restart of centrifuge when applying stage

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loading or cleaning the storage tank resulted in saw-tooth curves (Figs. 12 and 13). If the

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consolidation time during the saw-tooth period was excluded, the corrected consolidation

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time was 890 min, which was 4.2 years in prototype.

Both the excess pore pressure and the effective stress experienced a sharp growth with

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the centrifuge acceleration increasing to 50 g (Fig. 13). The self- weight consolidation stage lasted about 52 min, and the excess pore pressure and the effective stress were quite stable,

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also indicating that it was hard to drain out the water in the dredged soil without any measures. Sharp increase of excess pore pressure occurred when the sand drains and stage

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loading were imposed to the dredged soil. However, the effective stress did not change much, indicating that the surcharge was mainly sustained by the excess pore pressure at this stage.

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During the stable preloading stage, the excess pore pressure at Layer 1 (EP1) dissipated significantly and decreased by about 33 kPa; that at Layer 2 (EP2) decreased by 25 kPa; and

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that at Layer 3 (EP3) did not change much. Correspondingly, the increment of effective stress at Layer 1 (ES1) was the largest and that at Layer 3 (ES3) was miniscule. Hence, the sand drains were effective within the insertion depth while the drainage condition was bad even at the bottom of the sand drains (see Layer 3 in Fig. 8). This is the reason why adopting length of the sand drains buried in the dredged soil to calculate the average strain of the dredged soil in Section 6.1. Field measurements in the land reclamation work in Singapore revealed that the excess pore pressure can decrease by as large as 37 kPa for 1260 days (i.e., 3.5 years) but the excess

ACCEPTED MANUSCRIPT pore pressure was still high (e.g., 50 kPa) with 3 m spacing of sand drains (Arulrajah et al., 2004). Since the largest reduction of excess pore pressure was 33 kPa for 4.2 years with 4 m spacing of sand drains in T1 group. The dissipation rate of excess pore pressure in this study was reasonable. It is noteworthy that the excess pore pressure can completely dissipate within a much shorter period (e.g., 140 days) during some embankment construction works (e.g.,

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Stamatopoulos et al., 2013). Thus, the consolidation process in dredged soil is much more

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difficult and the drainage system and preloading scheme should be well designed.

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The pore pressure, total stress, and effective stress at different layers for T1, T2 and T3 are summarized in Table 6. Because of the breakdown of sensors, it failed to record the pore

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pressure at Layer 3 for T2 and T3. The final effective stress overall decreased with depth for T1-T3, further confirming that the degree of consolidation decreased with depth. Similar

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phenomenon was also observed in the land reclamation work in Singapore (Arulrajah, 2005), where decreasing trend of effective stress was observed in the upper 11 m. The reason is that

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the drainage condition in the upper part was better.

The final effective stresses at Layer 1 for T1, T2 and T3 were 35.7, 31.6 and 35.0 kPa,

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respectively (Table 6). The buried depth of sensors at Layer 3 of T1 (150 mm) was the same as that at Layer 2 of T2 (Table 6). But the final effective stress of T1 (16.6 kPa) was much

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larger than that of T2 (5.7 kPa), indicating that the drainage condition of T1 was much better than that of T2. The results were consistent with those of surface settlement and water content. Considering the fact that the sand drain length of T2 (300 mm) was much larger than that of T1 (200 mm), the spacing of sand drains behaved more effectively for drainage than the sand drain length.

6.3 Crater depth Crater depth is the most direct index for evaluating the effectiveness of DC. Prior to DC,

ACCEPTED MANUSCRIPT various soil conditions had been formed by PCD. Fig. 14 presents the photos taken by the HD camera during the tests. H1 and H2 were measured by Photoshop. The cumulative crater depth and crater depth per drop of T1-T3 are shown in Fig. 15. Table 7 summarizes the measured final cumulative crater depth and the equivalent value in 1 g gravitational field. As shown in Fig. 14, the hammer gradually tamped into the soil. The end of the sliding

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tube touched the ground surface before the DC. However, when the DC test ended, an

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obvious gap was observed between the tube and the ground, which indicated that DC could

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cause ground settlement around the tamping point. The phenomenon was consistent with the results of field measurements in dredged soil (Feng et al., 2010). Additionally, a large amount

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of water was detected in T3, which was an evident indicator of poor pretreatment. The water cushion in T3 prevented the hammer from tamping the soil directly and effectively, with most

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DC energy wasted. Therefore, when DC is carried out to treat dredged fills, great efforts should be made to design the drainage system. Sand drains or plastic drainage plates with

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reasonable length and spacing should be adopted to form the basic bearing capacity for DC operation. Horizontal drainage system, such as sand cushion, blind ditch and pipes, are also

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expected to avoid water accumulation in the field. Under the energy level of 1200 kN m in T1 group, the crater depths of the first drop

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from DC1 to DC4 were 12.6, 14.6, 13.4 and 14.2 mm, respectively, with an average value of 13.7 mm (Fig. 15a). The corresponding crater depth in 1 g gravitational field was 0.69 m, which indicated that the compressibility of the dredged soil after pretreatment was still large. Additionally, the crater depth per drop gradually decreased with subsequent drops (Fig. 15a). Convergence sign emerged at the 6th drop. As shown in Table 7, the final cumulative crater depths were almost the same for DC2-DC4 (1.90 to 1.95 m). Under the energy level of 1600 kNm in T2 group, the first drops also created the largest crater depth (Fig. 15b). The average crater depth of the first drops of DC1-DC4 reached 17.4

ACCEPTED MANUSCRIPT mm, which was larger than that in T1 group. However, discrepancy was observed from the follow-up drops. Compared with T1, the crater depth per drop was tremendous in T2. The average cumulative crater depth of DC1-DC4 reached 46.5 mm by only 4 drops, which almost reached the capability of the DC device (i.e., 50 mm). The sand cushion and high energy level were the two main factors for this phenomenon. The earlier DC was exerted on

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the sand cushion directly rather than the dredged soil. However, under the higher energy level

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in T2, sand cushion was punctured completely, and the hammer directly impacted the

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dredged soil. Despite the basic bearing capacity formed during the pretreatment, failure deformation occurred due to the high energy dynamic compaction.

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In T3, the DC energy level was designed to be 1200 kNm, and the sand drain arrangement was not the optimal both in length and spacing compared with those of T1 and

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T2 (Table 3). The crater depths of T3 are shown in Fig. 15c. The average crater depth of the first drops at all the four compaction points was 19.7 mm, being the largest among the three

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test groups. After six drops at each point, the cumulative crater depth reached the capability

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of the DC device (i.e., 50 mm), and the compaction test was then ended. As aforementioned, crater depth converged in T1, while those of T2 and T3 failed to converge, both ending up with the hammer caught in the soil. However, the failure reasons

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for T2 and T3 were different. The significant increase in the energy level resulted in the ultra-depth of T2, while poorly pretreated soil was the main reason for T3. As shown in Table 7, the average final cumulative crater depths in prototype for T1-T3 were 1.88, 2.32 and 2.50 m, respectively, which reflected the great compressibility of the dredged soil. However, in engineering practice, such tamping pit is dangerous, because it not only causes inconvenience for operation, but also leads to ground collapse. Sand or gravel fill is recommended to supplement inside in order to continue DC operation. Since crater depth converged in T1, the results in T1 were compared with those of field

ACCEPTED MANUSCRIPT measurements for verifying the present method, including drop number, cumulative crater depth, and crater depth per drop. The results of DC work in a port in Nanjing, China, reported by Hu et al. (2004) were adopted for the following reasons. First, Nanjing and Putian are both located in the east part of China. Second, the compacted soil in Hu et al. (2004) was saturated soft clay with sand cushion above it, similar with the material in this study. Third, 1500 kNm

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was adopted in Hu et al. (2004), slightly larger than the 1200 kNm in T1. The cumulative

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crater depth in Hu et al. (2004) reached 1.4-1.75 m after 7 drops and 5-6 drops were the

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optimal drop number, which match the results in T1 (1.75-1.95 m after 8 drops and 6 drops were the optimal drop number) reasonably well. The crater depth of the first drop was 40-50

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cm in Hu et al. (2004), which was slightly smaller than the results in T1 (63-73 cm). The difference is mainly due to the different soil properties. Moreover, the subsequent crater

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depth per drop after the first drop gradually decreased, which also agreed with the trend in

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the dynamic compaction.

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T1. The comparison reveals that the present method can well simulate the crater depth during

6.4 Cone penetration test

Cone penetration tests were carried out at 6 points in each test group (three points before

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DC, and another three points after DC). Unfortunately, the measured values were not available for T2 and T3, and the sleeve friction for T1 was also not available. The reason is that the cone penetrometer broke down during the test. Nevertheless, the cone resistance data can still reflect the treatment effect of DC to a certain extent. The results of T1 are shown in Fig. 16, each test lasted about 140 s and the penetration depth was 254 mm. Great variance was observed at the early stage because of electromagnetic interference and impact effect between the cone and the soil. As shown in Fig. 16a, the cone resistance trended to be stable at depth of about 40 mm and gradually decreased with the penetration process, which

ACCEPTED MANUSCRIPT revealed decreasing soil strength with depth. The test results after DC are shown in Fig. 16b. Comparison of the average cone resistance between Fig. 16a and Fig. 16b indicated that the ground condition was effectively improved by DC especially at depth shallower than 120 mm (6 m in prototype). Therefore, the combination of PCD and DC is applicable in treating dredged soil ground.

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The improvement depth was adopted as the index to further validate the performance of

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DC in this study. Several researchers have calibrated the original equation proposed by

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Menard and Broise (1975) to fit data from DC sites with various conditions as follow: dmax  n WH t

(2)

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where dmax is the improvement depth (m); W is the tamper mass (ton); Ht is the drop height of tamper (m); n is empirical coefficient accounting for influence factors such as soil type and

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DC procedure. Mayne et al. (1984) and Lukas (1986) suggested that n may vary between 0.3 and 0.8, and the mean value 0.55 was adopted here. In T1 group, W and Ht were 15.31 tons

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and 8.0 m, respectively (Table 1). dmax was 6.09 m according to Eq. (2), slightly larger than

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the observed value (i.e., 6 m). Moreover, Hu et al. (2004) also reported that the improvement depth in their in-situ DC work was 6-7 m. Therefore, the present method can well simulate

7

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the dynamic compaction in terms of improvement depth.

Limitations of the proposed method Although the developed devices for modeling preloading consolidation and dynamic

compaction performed well in the test, there is still room for further improvement, especially in automation. Considering the manufacturing costs, fully automatic stage loading was not achieved. Adoption of electromagnetic switch and water is a possible option to achieve fully automatic stage loading in the future. By controlling the electromagnetic switch, water can be added into the loading container to realize various loading levels. Similarly, the tamping

ACCEPTED MANUSCRIPT module was manually moved to the next tamping point in this study. Moreover, electromagnet can be used as a key unit to flexibly elevate and release hammer in the future.

8

Summary and conclusions A novel method of modeling preloading consolidation and dynamic compaction in

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centrifuge is developed in this study. 3D printing technique is used to greatly improve the

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manufacturing precision and simulation ability of sand drains. A loading container, which

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allows adding sand in it stage by stage, is well designed to achieve uniform surface loading. Based on strong magnet and reliable mechanical principle, a novel device for modeling

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dynamic compaction is developed, which can realize continuous tamping in centrifuge to a certain extent.

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An example test using dredged soil sampled from Putian Port, Fujian Province, China, was conducted to validate the performance of the method, including self- weight

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consolidation, four-stage preloading with sand drains, and dynamic compaction. The dredged soil was characterized by high water content, large void ratio, and low permeability. Some

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major conclusions can be drawn as follows: (1) The present method performed well to simulate the whole process of pretreating the

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dredged soil. Surface settlement, changes in excess pore pressure and effective stress, number of drops, crater depth, improvement depth by DC were reasonably predicted. (2) Significant surface settlement and crater depth were observed during the preloading consolidation and dynamic compaction, respectively, indicating that the compressibility of the dredged soil was rather large. (3) Length and spacing are two important designed parameters of sand drains, and spacing behaved to be more effective in the tests. Sand drains with reasonable length and spacing should be adopted to form the basic bearing capacity for DC operation. Appropriate

ACCEPTED MANUSCRIPT energy level should also be designed for DC. High energy level must be accompanied by proper design of PCD.The distributions of water content, excess pore pressure, effective stress revealed that the degree of consolidation decreased with depth, since the drainage condition in the upper part was better. (4) The method contributes to a better understanding of PCD and DC and is helpful for

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the rational design of them in engineering practice.

Acknowledgments

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The authors would like to thank S.F. Lu, L. Wang, and Y. Sheng for their assistance during the whole experiment. The majority of the work described in this paper was supported by the

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National Natural Science Foundation of China under Grant Nos. 41572265 and 41602288, the Program for New Century Excellent Talents in University under Grant No.

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NCET-13-0421, and the Program for Young Talented Scholars awarded by the Organisation Department of the CPC Central Committee. The authors would like to acknowledge all these

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References

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sources of financial support and express the most sincere gratitude.

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ACCEPTED MANUSCRIPT Atkinson, M.S., Eldred, P.J.L., 1981. Consolidation of soil using vertical drains. Geotechnique 31 (1), 33-43. Barron, R.A., 1948. Consolidation of fine-grained soils by drain wells. Trans. ASCE 113, 718-754. Carrillo, N., 1942. Simple two and three dimensional case in the theory of consolidation of

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soils. Journal of Mathematics and Physics 21 (1), 1-5.

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Cascone, E., Biondi, G., 2013. A case study on soil settlements induced by preloading and

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vertical drains. Geotextiles and Geomembranes 38, 51-67.

Chen, J.F., Yu, S.B., Han, J., 2009. Numerical modeling of a reinforced embankment based

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on centrifuge test dimensions. In: Characterization, Modeling, and Performance of Geomaterials, GeoHunan International Conference, ASCE pp. 68-77.

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Chow, Y.K., Yong, D.M., Yong, K.Y., Lee, S.L., 1994. Dynamic compaction of loose granular soils: Effect of print spacing. Engineering Geology 120 (7), 1115-1133.

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Choy, C.K., Standing, J.R., Mair, R.J., 2014. Centrifuge modelling of diaphragm wall construction adjacent to piled foundations. Geotechnical Testing Journal 37 (4), 1-18.

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Chu, J., Bo, M.W., Arulrajah, A., 2009. Soil improvement works for an offshore land reclamation. Proceedings of the Institution of Civil Engineers-Geotechnical Engineering

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162 (1), 21-32.

Deng, A., Xu, S.L., 2010. Consolidating dredge soil by combining vacuum and dynamic compaction effort. Geotechnical Special Publication 207, 113-118. Fang, Z., Yin, J.H., 2006. Physical modeling of consolidation of Hong Kong marine clay with prefabricated vertical drains. Canadian Geotechnical Journal 43 (6), 638-652. Fellenius, B.H., Castonguay, N.G., 1985. The efficiency of band shaped drains a full scale laboratory study. Report to National Research Council of Canada and the Industrial Research Assistance Programme.

ACCEPTED MANUSCRIPT Feng, S.J., Shui, W.H., Gao, L.Y., He, L.J., Tan, K., 2010. Field studies of the effectiveness of dynamic compaction in coastal reclamation areas. Bulletin of Engineering Geology and the Environment 69 (1), 129-136. Feng, S.J., Tan, K., Shui, W.H., Zhang, Y., 2013. Densification of desert sands by high energy dynamic compaction. Engineering Geology 157, 48-54.

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Feng, S.J., Lu, S.F., Shi, Z.M., Shui, W.H., 2014. Densification of loosely deposited soft soils

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using the combined consolidation method. Engineering Geology 181, 169-179.

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Feng, S.J., Du, F.L., Shi, Z.M., Shui, W.H., Tan, K. 2015. Field study on the reinforcement of collapsible loess using dynamic compaction. Engineering Geology 185, 105-115.

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Fox, P.J., Lee, J., Qiu, T. 2005. Model for large strain consolidation by centrifuge. International Journal of Geomechanics 5 (4), 267-275.

Engineering 12 (5), 16-25.

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Hansbo, S., 1979. Consolidation of clay by band shaped prefabricated drains. Ground

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Hu, X.W., Zhang, W., Wang, J., 2004. Experimental study on dynamic compaction to improve saturated soft c1ay covered with hydraulic fill sand. Rock and Soil Mechanics

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25 (5), 818-823. (in Chinese)

Kjellman, W., 1952. Consolidation of clayey soils by atmospheric pressure. In: Proceedings

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of a Conference on Soil Stabilization, Massachusetts Institute of Technology, Boston, pp. 258-263.

Liang, R.Y., Xu, S.L., 2012. High vacuum densification method for soft soil improvement. In: Geo-Congress 2012: State of the Art and Practice in Geotechnical Engineering, ASCE pp. 1928-1937. Long, R.P., Covo, A., 1994. Equivalent diameter of vertical drains with an oblong cross section. Journal of Geotechnical Engineering, ASCE 120 (9), 1625-1630. Lu, G.S., 2006. Centrifuge experiment to improve soft foundation through plastic wick drain.

ACCEPTED MANUSCRIPT Journal of Southwest University of Science and Technology 21 (4), 42-46. (in Chinese) Lukas, R.G., 1980. Densification of loose deposits by pounding. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 106, 435-446. Lukas, R.G., 1986. Dynamic compaction for highway construction. Vol. 1 Design and construction

guidelines

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No.

FHWA/RD-86/133

Federal

Highway

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Administration, Washington, DC, pp 204-219.

U.S.

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Kwong, J.S.M., 1997. A review of some drained reclamation works in Hong Kong.

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Geotechnical Engineering Office, Civil Engineering Department.

Mayne, P.W., Jones, J.S., Dumas, J.C., 1984. Ground response to dynamic compaction.

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Journal of Geotechnical Engineering, ASCE 110 (6), 757-774.

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Menard, L., Broise, Y., 1975. Theoretical and practical aspects of dynamic consolidation.

Merrifield, C.M., Davies, M.C.R., 2000. A study of low-energy dynamic compaction: field

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trials and centrifuge modelling. Geotechnique 50 (6), 675-681. Miao, L.C., Chen, G., Hong, Z.S., 2006. Application of dynamic compaction in highway: a

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case study. Geotechnical and Geological Engineering 24, 91-99. Ng, C.W.W., Hong, Y., Soomro, M.A., 2015. Effects of piggyback twin tunnelling on a pile

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group: 3D centrifuge tests and numerical modelling. Geotechnique 65 (1), 38-51. Poran, C.J., Rodriguez, J.A., 1992. Design of dynamic compaction. Canadian Geotechnical Journal 29 (5), 796-802. Sharma, J.S., Bolton, M.D., 1996. Centrifuge modeling of an embankment on soft clay reinforced with a geogrid. Geotextiles and Geomembranes 14 (1), 1-17. Sharma, J.S., Bolton, M.D., 2001. Centrifugal and numerical modeling of reinforced embankments on soft clay installed with wick drains. Geotextiles and Geomembranes 19 (1), 23-44.

ACCEPTED MANUSCRIPT Stamatopoulos A.C., Kotzias P.C., 1985. Soil improvement by preloading. J. Wiley & Sons Publications. Stamatopoulos, C., Petridis, P., Bassanou, M., Stamatopoulos, A., 2005. Increase in horizontal stress induced by preloading. Ground Improvement 9 (2), 47-58. Stamatopoulos, C., Petridis, P., Bassanou, M., Allkja, S., Loukatos, N., Small, A., 2013.

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Improvement of dynamic soil properties induced by preloading verified by a field test.

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Engineering Geology 163, 101-112.

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Impact Compaction technique on Brežice test sites. Engineering Geology 160, 69-80.

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Wang, S., Chan, D., Lam, K.C., 2009. Experimental study of the effect of fines content on dynamic compaction grouting in completely decomposed granite of Hong Kong.

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Construction and Building Materials 23 (3), 1249-1264. Wang, L., Zhang, G., 2015. In-flight simulation of pile installation in slopes in centrifuge

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model tests. Geotechnical Testing Journal 38 (1), 50-60. Zhang, L., Luo, Q., Zhou, C., Pei, F.Y., 2007. Comparative research on reinforcement of thick

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soft clay ground based on centrifugal model tests. Chinese Journal of Geotechnical Engineering 29 (7), 982-987. (in Chinese)

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Zhang, L.M., Wong, E.Y., 2007. Centrifuge modeling of large-diameter bored pile groups with defects. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 133 (9), 1091-1101.

Zheng, Y.L., Lu, X., Li, X.Z., Feng, Y.X., 2000. Research on theory and technology of improving soft clay with DCM. Chinese Journal of Geotechnical Engineering, ASCE 22 (1), 18-22. (in Chinese) Zhou, J., Chao, Y., Jia, M.C., Huang, M.S., 2003. In-situ test study on soft soils improvement by the DCM combined with dewatering. Chinese Journal of Rock Mechanics and

ACCEPTED MANUSCRIPT Engineering 24 (3), 376-380. (in Chinese) Zhou, J., Zhang, J., Yao, H., 2005. Study on technique of low-energy dynamic consolidation method combined with dewatering used to treat soft roadbed. Chinese Journal of Rock Mechanics and Engineering 26, 198-207. (in Chinese) Zhou, Y.G., Chen, Y.M., Shamoto, Y., 2009. Verification of the soil- type specific correlation

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between liquefaction resistance and shear-wave velocity of sand by dynamic centrifuge

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test. Journal of Geotechnical and Geoenvironmental Engineering, ASCE 136 (1),

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165-177.

Zhou, J., Tang, Y., 2015. Centrifuge experimental study of thaw settlement characteristics of

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mucky clay after artificial ground freezing. Engineering Geology 190, 98-108.

ACCEPTED MANUSCRIPT Captions of Tables and Figures Table Captions Table 1 Design parameters of the hammer (scaling factor: 50). Table 2 Properties of the tested dredged soil. Table 3 Test plan. DC: dynamic compaction. Table 4 Stage preloading parameters. Table 5 Settlement rate during preloading consolidation.

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Table 6 Pore pressure (PP), total stress (TS), and effective stress (ES) at different stages. Initial value: the value before preloading.

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Table 7 Final cumulative crater depth.

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Figure Captions

Fig. 1. Framework of the method: (a), (c), (e) engineering practice; (b), (d), (f) centrifuge modeling.

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Fig. 2. Sand drain: (a) skeleton; (b) configuration of the sand drain. Fig. 3. Schematic diagram of the preloading device.

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Fig. 4. Schematic diagram of the DC device.

Fig. 5. Dimensions of the transparent sliding tube. Fig. 6. Dimensions of the hammer.

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Fig. 7. Operation procedures of the tamping module. Fig. 8. Centrifuge test setup of T1 group: (a) sectional layout; (b) plane layout. Fig. 9. Test procedures.

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Fig. 10. Surface settlement during the preloading consolidation. Fig. 11. Variation of average water content with depth after the preloading consolidation. Fig. 12. Pore pressure (a) and total stress (b) during the preloading consolidation. Fig. 13. Excess pore pressure and effective stress in T1 group during the preloading consolidation. Fig. 14. Photos during the dynamic compaction: (a) T1; (b) T2; (c) T3. Fig. 15. Crater depth: (a) T1; (b) T2; (c) T3. Fig. 16. Results of cone penetration test: (a) before the dynamic compaction; (b) after the dynamic compaction.

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(

(

(

Self-weight a) consolidation

Dynamic e) compaction

c)

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Preloading

(

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(

d)

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b)

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Fig. 1. Framework of the method: (a), (c), (e) engineering practice; (b), (d), (f)

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centrifuge modeling.

( f)

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(a)

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(b)

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Fig. 2. Sand drain: (a) skeleton; (b) configuration of the sand drain.

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Fig. 3. Schematic diagram of the preloading device.

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Fig. 4. Schematic diagram of the DC device.

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Fig. 5. Dimensions of the transparent sliding tube.

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Fig. 6. Dimensions of the hammer.

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Fig. 7. Operation procedures of the tamping module.

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(a)

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(b)

Fig. 8. Centrifuge test setup of T1 group: (a) sectional layout; (b) plane layout.

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(b) Preloading

(c) Unloading

(f) CPT after DC (e) Dynamic compaction

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(d) CPT before DC

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Fig. 9. Test procedures.

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Beginning of self-weight consolidation: t1 ≈ 600 s

T1 T2 T3

3rd stage loading : t4 ≈ 5520 s 4th stage loading : t5 ≈ 6600 s

40

60

End of preloading: t6 ≈ 70600 s

1st stage loading: t2 ≈ 3720 s

80

100 0

1

2

3

4

5

6

7

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Time (104 s)

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Surface settlement (mm)

2nd stage loading : t3 ≈ 4620 s

20

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Fig. 10. Surface settlement during the preloading consolidation.

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Sampling depth (mm)

0

T1 T2 T3

50

100

150

50

55

60

65

70

75

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200 80

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Water content (%)

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Fig. 11. Variation of average water content with depth after the preloading consolidation.

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(a)

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(b)

Fig. 12. Pore pressure (a) and total stress (b) during the preloading consolidation.

ACCEPTED MANUSCRIPT Excess pore pressure EP1 EP2 EP3

100 80

Effective stress ES1 ES2 ES3

Stable preloading

60 40

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4 stages of loading Self-weight consolidation

Centrifuge acceleration

0 0

1

2

3

4

5 4

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Time (10 s)

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20

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Stress or pore pressure (kPa)

120

6

7

Fig. 13. Excess pore pressure and effective stress in T1 group during the preloading

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consolidation.

ACCEPTED MANUSCRIPT

No.1_DC1_T

H1

HMeasured

No.8_DC1_T

No.3_DC1_T

H1 H

HMeasured values H1=3.00 cm H2=5.01 cm

values H1=1.60 cm H2=5.01 cm

Measured values H1=3.64 cm H2=5.01 cm

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H1

H

Measured values H1=3.43 cm H2=4.43 cm

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No.3_DC2_T 2

H H

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Measured values H1=1.51 cm H2=4.43 cm

H

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No.1_DC2_T 2

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(a)

No.4_DC2_T

2 Measured values H1=4.32 cm H2=4.43 cm

H H

No.1_DC2_T

H

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Measured values H1=2.73 cm H2=6.36 cm

H

No.6_DC2_T

No.3_DC2_T

3

Measured values H1=4.81 cm H2=6.36 cm

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3

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(b)

H H

3 Measured values H1=6.37 cm H2=6.36 cm

(c)

Fig. 14. Photos during the dynamic compaction: (a) T1; (b) T2; (c) T3.

H H

ACCEPTED MANUSCRIPT (a)

Number of drops 1

2

3

4

5

6

7

8 T1： cumulative crater depth DC1 DC2 DC3 DC4

10

T1： crater depth per drop DC1 DC2 DC3 DC4

20

30

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Crater depth (mm)

0

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40

Number of drops 1

2

3

4

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T2： cumulative crater depth DC1 DC2 DC3 DC4

20

30

T2： crater depth per drop DC1 DC2 DC3 DC4

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Crater depth (mm)

10

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(b)

40

(c)

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50

Number of drops

1

2

3

4

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0

Crater depth (mm)

10 20 30 40 50

Fig. 15. Crater depth: (a) T1; (b) T2; (c) T3.

5

6 T3： cumulative crater depth DC1 DC2 DC3 DC4 T3： crater depth per drop DC1 DC2 DC3 DC4

ACCEPTED MANUSCRIPT 25

(a)

15

10 J1 J2 J3 Average

5

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Cone resistance (kN)

20

0 0

40

80

120

160

200

240

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Depth (mm)

25

(b)

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15

10

J4 J5 J6 Average

5

0 0

40

80

120

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Cone resistance(kN)

20

160

200

240

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Depth (mm)

Fig. 16. Results of cone penetration test: (a) before the dynamic compaction; (b) after

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the dynamic compaction.

ACCEPTED MANUSCRIPT Table 1 Design parameters of the hammer (scaling factor: 50). 1200

1600

Prototype (m)

8.0

8.0

Model (cm)

16.0

16.0

Prototype (ton)

15.31

20.41

Model (g)

122.45 2.05

2.05

Hammer mass

Hammer diameter

163.27

41.0

41.0

50.0

50.0

16.96

16.96

Iron cylinder mass (g)

105.49

146.31

Iron cylinder thickness (mm)

11.23

15.57

Prototype (m)

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Tamping height

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DC energy level (kNm)

Sleeve height (mm)

model hammer

Sleeve mass (g)

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Configuration of

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Model (mm)

density Dry density Water

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Bulk

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Table 2 Properties of the tested dredged soil. Specific Void ratio

(g/cm3 )

(g/cm3 )

content (%)

gravity

1.47

0.80

85.47

2.65

of Liquid limit Plastic limit Liquidity

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Degree

2.34 Content of

saturation (%)

(%)

(%)

index

silt and clay

96.8

39.56

20.20

3.37

92.7%

ACCEPTED MANUSCRIPT Table 3 Test plan. DC: dynamic compaction. Preloading parameters Sand drain

DC

Sand

drain

length spacing (mm)

Total loading

Energy

in prototype (kPa) level (kNm)

200

80

144.5

T2

300

100

144.5

T3

200

100

144.5

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T1

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(mm) 1200 1600 1200

ACCEPTED MANUSCRIPT Table 4 Stage preloading parameters.

Prototype Loading

Model Time

(day)

Time

nt mass (kg)

Self-weight 90.0

1st stage loading

25.5

25.0

2nd stage loading

34.0

3rd stage loading

42.5

4th stage loading

42.5

0.0

51.8

14.4

25.0

15.8

14.4

30.0

20.0

17.3

1050

20.0

1060

MA

NU

12.0

SC

RI

0.0 consolidation

(min)

PT

(kPa)

Equivale

ED

Table 5 Settlement rate during preloading consolidation. T1 group Prot

Mod

EP T

Stage

AC C

consolidation

0.00

Mod

0.00

Mod

el (mm/s)

043

otype el (mm/s)

(mm/d) 0.00

1.08

062 6.48

Prot

otype

(mm/d) 0.74

T3 group

Prot

otype

el (mm/s)

Self-weight

T2 group

0.00

(mm/d) 0.00

1.08

062 6.48

0.00

4.32

1st stage loading 375 0.00

375 6.48

0.00

250 4.32

0.00

3.24

2nd stage loading 375 3rd stage loading

0.00

250 4.32

0.00

187 7.56

0.00

3.24

ACCEPTED MANUSCRIPT 250

438

0.00

7.02

187

0.00

4.32

0.00

3.24

th

4 stage loading 406

250

0.00

2.43

188

0.00

2.7

0.00

2.16

st

End of the 1 year 156

0.00

2.43

125

0.00

End of the 2nd year 125

0.00

1.62

RI

141

0.00

0.00

1.22

AC C

EP T

NU

ED

039

0.00

0.68

0.00

031

0.00

1.76

102 0.00

1.08

062 1.35

078

MA

070

End of preloading

1.35

078

End of the 4th year

0.00

SC

End of the 3rd year 094

2.16

PT

141

0.00

0.81

047 0.54

0.00 031

0.54

ACCEPTED MANUSCRIPT Table 6 Pore pressure (PP), total stress (TS), and effective stress (ES) at different stages. Initial value: the value before preloading. Layer 1 T

1

2

T 3

5

5

T 1

5

T 2

1

PP (kPa)

8.3

Peak value

52.0

Initial

1

4

1

AC C

Final

value

Initial

ES (kPa)

value Final value

1

48.6

3.9

1.1

56.8 1

45.4

02.2 1

30.5

RI

2

1 73.0

9 8.8

83.8

82.5

—

—

—

—

—

—

1

9

1

1

1

50

81.5

0.6

09.3

00

1

2

7

2

2

03.0

38.4

5.1

3

8

1

9

T

3.5

74.9

76.8

2

50

1

1

8

1

2

T

1

6

4.7

02.0

1

3

00

6.3

48.0

1

8

1

9

1

70.9

6

85.3

5.5

5.6

72.3

1

4

2.0

Peak value

13.8

50

5.9

34.3 1

EP T

value

1 45.7

12.9

2 2.1

ED

value

(kPa)

0.4 1

Final

TS

3

MA

value

2

00

NU

Initial

0

T 1

1

SC

0

T 3

Depth (mm) 0

Layer 3

PT

T

Layer 2

81.0 2

25.9 1

64.7

6.4 3

04.6 1

98.1

20.3 2

71.4

1

1

1

1

8

5

1

3.7

5.2

1.8

5.2

.8

.9

5.3

3

3

3

2

5

2

1

5.7

1.6

5.0

5.0

.7

6.3

6.6

2

1 94.8

—

—

—

—

ACCEPTED MANUSCRIPT

Table 7 Final cumulative crater depth. Test group

T1 (1200 kNm)

T2 (1600 kNm)

T3 (1200 kNm)

Tamping

8

4

6

counts

el (mm)

Prot otype

Mod el (mm)

Prot otype

Mod

PT

point

Mod

el (mm)

RI

Tamping

(m)

otype (m)

35.0

1.75

52.0

2.60

50.3

2.52

DC2

38.9

1.95

48.6

2.43

48.7

2.44

DC3

37.8

1.90

45.4

2.27

50.8

2.54

DC4

38.5

1.93

39.8

1.99

50.1

2.51

Average

37.6

1.88

46.5

2.32

50.0

2.50

AC C

EP T

ED

MA

DC1

NU

SC

(m)

Prot

ACCEPTED MANUSCRIPT Highlights 

A novel method of modeling preloading consolidation and dynamic compaction in centrifuge is developed.



3D printing technique is used to greatly improve the manufacturing precision and simulation ability of sand drains.



A loading container, which allows adding sand in it stage by sta ge, is well designed to

A novel device for modeling dynamic compaction is developed, which can realize continuous tamping in centrifuge to a certain extent.

EP T

ED

MA

NU

SC

Spacing of sand drains behaved to be more effective than the length.

AC C



RI



PT

achieve uniform surface loading.