1 Introduction

With the continuing depletion of land mineral resources,the development and utilization of the seabed mineral resources are extremely urgent. At present,the exploitation of deep- sea mineral resources has entered the stage of designing deep-sea mining system. During the period of the 11th Five-Year plan,China focused on strengthening the research on the key technology of pipeline hydraulic transportation system^{[1, 2, 3]} . Whether the mining machine can work normally on the deep-sea sediment is vital for the safe operation of the mining system and the improvement of the mining effciency^[4] . Compared with land soil,deep-sea sediment has higher water content^{[5, 6, 7]} and lower shear strength^{[8, 9]} ,which can easily make the deep-sea mining machine slip and reduce the mining effciency. Therefore,the studies on the traction characteristics of grouser cutting deep-sea sediment and its traction model are very important.

Recently,the traction characteristics of grouser cutting land soil has been widely studied. Based on the traction characteristics of grouser cutting brittle and plastic land soil,Bekker^[10]and Stafford^[11] proposed two traction models. According to the snowfield traction test,Wong^[12] built a traction model of the grouser cutting snowfield. Based on the contact analysis of soil and cutting plate,Nardin et al. ^[13] used the exact mesoscopic soil model to predict the macroscopic characteristic of the soil,and verified its macroscopic characteristics through experiments. Aim- ing at the sandy soil and clay soil with low water content,Aluko and Chandler^[14] studied the traction of different cutting plates,and analyzed the cutting mechanism according to the pas- sive soil pressure theory. Manuwa and Ademosun^[15] studied the traction characteristics of the grouser in the sandy clay with different water content,and confirmed the traction model by the polynomial regression equation. Chandio et al. ^[16] studied the Paddyfield plastic soil,and obtained the traction characteristics of the grousers with different tooth profiles,water content, and ground pressures by introducing the rheological parameter. However,the above studies are all based on the land soil with low water content,which is different from the deep-sea sed- iment with high water content. Based on the physical and mechanical properties of deep-sea sediment,simulative soil was prepared to conduct the traction test of different grousers,and the corresponding traction-displacement models were established by Schulte et al. ^[17] ,Choi et al. ^[18] ,and Xu et al. ^[19] . However,the cutting mechanism of grouser and soil has not been analyzed.

Based on the deep-sea sediment from the pacific mining area,four kinds of bentonites mixed with a certain percentage of water are selected to find the best simulative soil. The traction characteristics of the grouser,who has the best traction performance with the tooth height less than 15 cm,are studied in the traction characteristic test. Combining the analysis of the cutting mechanism of grouser and soil,the traction-displacement model is obtained. According to the traction characteristics of grousers with different tooth widths,tooth heights,and ground pressures,the traction model of grouser with a certain group values of tooth width,tooth height, and ground pressure can be predicted to prevent the mining machine slip for the improvement of the mining effciency.

2 Traction test of grouser 2.1 Preparation of simulative soil

Since the main mineral component of deep-sea sediment is montmorillonite^[20] ,four different bentonites with similar physical properties,e.g.,mineral composition,particle size,and specific surface area,are selected as the raw material to prepare the simulative soil for deep-sea sediment by the X-ray diffractometer,laser diffraction particle size,and surface area analyzer tester. Based on the vane shear strength of deep-sea sediment (6 kPa),four kinds of simulative soils, i.e.,S1,S2,S3,and S4,are prepared by mixing the four kinds of bentonites with a certain percentage of water^[21] . Table 1 lists the water content ω,the wet density ρ,the penetration resistance P_s,the cohesion C,and the internal friction angle ϕ of the simulative soil and deep-sea sediment by the drying method,cutting-ring method,penetration resistance method, and direct shear method. It is seen that the S3 simulative soil has the closest physical and mechanical parameters to the deep-sea sediment,and becomes the best substitution for the deep-sea sediment.

2.2 Test arrangement

Since the mining machine with high grouser walks unsteadily and its grouser adheres easily by sediment,high grouser will exacerbate the disturbance of deep seabed. The grouser height of the deep-sea mining machine is generally less than 15 cm^[19] . In this paper,the traction characteristics of the grouser with the height in the range from 0 cm to 15 cm are systematically studied.

Figure 1 shows the traction characteristic test apparatus assembled by ourselves for the mining machine grouser. The simulative soil S3 is prepared to pave in the apparatus,and the grousers with the tooth widths of B = 40mm and B = 100mm are selected to be fixed on the truck. According to the designed ground pressure σ₀ of the mining machine (σ₀ = 5 kPa^[22] ),the constant compressive stress is selected as 0 kPa,5 kPa,and 10 kPa,respectively,by controlling the weight magnitude,and the tooth height H is selected as 2 cm,4 cm,6 cm,8 cm,10 cm, 12 cm,13 cm,and 15 cm,respectively,in each group. The screw rod at the right-side of the apparatus pulls the truck along the rail so as to make the grouser cutting the S3 simulative soil with the constant velocity υ = 1 mm·s−1 by controlling the rotate speed of the motor. The relationship of the traction and time is automatically recorded by the NS-WL1 tension sensor every 0.1 s for the traction-displacement curves. During the test,the mound in front of the grouser is cleaned continually to eliminate the influence of the mound resistance.

3 Traction-displacement curves

Figure 2 shows the traction-displacement curves of the grousers cutting the S3 simulative soil with different tooth widths,tooth heights,and ground pressures. The curves show similar trends,characterized by an obvious hump sign,i.e.,the maximum traction,and soon reduce to the residual traction,which means that the simulative soil has the characteristics of the brittle soil ^[23] (see Fig. 3). The shear deformation process of the brittle soil has obvious character- istics. In the OA stage,i.e.,the linearly elastic deformation stage,the traction F increases linearly with the displacement j to the elastic limit traction F_e,corresponding to the elastic limit displacement je. In the AB stage,i.e.,the strain hardening stage,the traction F increases nonlinearly to the maximum traction F_max,corresponding to the maximum traction displace- ment jm,i.e.,the shear modulus. In the BC stage,i.e.,the strain softening stage,the traction decreases to the residual traction when the displacement increases.

Figure 4 shows the passive soil pressure distribution diagram of Rankine,where σ is the ground pressure,H is the grouser shoe height,and ϕ is the internal friction angle. The traction is obtained by the grouser cutting soil along the direction of motion. At the initial stage,the soil suffers the passive soil pressure,which increases linearly with the displacement until the shear failure occurs and the DBC shear slip band forms at an angel of 45◦ + ϕ/2 to the horizontal direction. Simultaneously,the grouser has the maximum traction and the soil slips along the shear slip band (see Fig. 5). When the displacement j keeps increasing,the grouser will continue cutting the residual soil,leading to the soil under the shear slip band. Therefore,the traction of the grouser is less than the initial maximum traction,and fluctuates to a constant residual traction.

Figure 6 shows the relationship between the maximum traction F_max and the residual trac- tion Fres changing with different grouser tooth heights H under different ground pressures σ and tooth widths B. Obviously,F_max and Fres both increase when σ,B,and H increase. Since the soil suffers shear failure under the grouser cutting,the ground pressure and the shear strength of the soil become larger according to the Mohr-Coulomb law. Meanwhile,the grouser with larger tooth height and tooth width has more cutting soil area. Therefore,the grouser can get larger traction. In general,when the ground pressure is lower than the soil bearing capacity and the tooth height is in the optimum range of good traction performance,the grouser will have larger traction with larger tooth width,tooth height,and ground pressure,which can prevent the mining machine slipping on the deep-sea sediment.

4 Traction model and parameter determination 4.1 Traction model

As shown in Fig. 2,the traction-displacement curves of the grouser cutting the S3 simulative soil are in accord with the brittle soil characteristics,having the maximum traction F_max and the residual traction Fres. When

F rapidly increases with the displacement j,experiencing at the linearly elastic deformation stage and the hardening stage until jm. When

the soil suffers shear slipping,and the grouser continues cutting the residual soil,because the traction of the grouser reduces to the residual traction Fres with stable values. Consider that F_max,jm,and Fres can be determined in the test. Then,the traction-displacement equation can be described. When j increases,F_max decreases to 0 while Fres increases to a constant value. Therefore,

can be introduced into the equation to describe the variation of F_max and Fres. Consider that the soil is brittle. Then,the brittleness index

correlated with the displacement j is introduced into the equation as follows:

Assume that the sensitivity coeffcient Then,Eq. (1) can be transformed to the Wong traction model ^[12] ,i.e.,

Table 2 lists the maximum traction F_max,the sensitivity coeffcient E,and the shear modulus jm with different B,H,and σ according to different traction-displacement curves. Obviously, the values of E fluctuate in the range from 1.264 to 1.348,and jm fluctuates from 8.3 mm to 12.1 mm. Therefore,the average values of Em (1.305) and jm (10.0 mm) can be used as constant traction parameters. Combining the maximum traction of the grouser and Eq. (2),the traction-displacement curves of the grouser cutting the deep-sea simulative soil can be obtained (see Fig. 7).

4.2 Traction calculation

According to the process of the grouser cutting the soil,the traction of the grouser can be divided into two parts,i.e.,the counter-force of the grouser compressing soil and the counter- force of the grouser edge cutting soil. Under the same tooth height and ground pressure,the traction of grouser two-side edge cutting soil with different tooth widths can be considered to be equal. Based on the maximum traction F_max of the grouser with the tooth width

the curves of the maximum traction of the grouser two-side edge Fs and the maximum traction of the 10 mm tooth width increment F changing with H and σ are obtained in Fig. 8. Obviously, Fs and F increase approximately linearly when H increases under constant σ. Therefore,a linear function can be used to fit the curves of Fs and F (see Table 3).

The maximum traction F_max of the certain grouser with a constant tooth width,tooth height,and ground pressure can be predicted according to Table 3. Combining the sensitivity coeffcient E,the shear modulus jm,and Eq. (2),the traction-displacement curve of the grousercutting the simulative soil for the deep-sea sediment can be predicted. Based on the curves,a deep-sea mining machine can be designed against the slipping for a high mining effciency.

5 Conclusions

The investigations conducted in this paper lead to the following conclusions:

(i) The simulative soil is brittle with the maximum traction and residual traction. The traction-displacement curves of the grousers,cutting the simulative soil for deep-sea sediment, have the same changing trend when the tooth width,tooth height,and ground pressure change, and the traction increases when the tooth width,tooth height,and ground pressure increase. When the ground pressure is lower than the soil bearing capacity and the tooth height is in the optimum range of good traction performance,the grouser will have more traction with larger tooth width,tooth height,and ground pressure,which can prevent the mining machine slipping on the deep-sea sediment.

(ii) Based on the passive soil pressure theory of Rankine,the mechanism of the grouser cutting soil is studied. At the initial stage of the grouser cutting soil,the traction increases linearly with the displacement until shear slip occurs in the soil,where the grouser traction reaches its maximum. When the displacement increases,the grouser continues cutting the residual soil,which makes the grouser traction less than the initial maximum traction and fluctuates to a constant residual traction.

(iii) Based on the traction-displacement curves and cutting mechanism of grouser and soil, the Wong traction model is well matched. The sensitivity coeffcient and the shear modulus of the grouser both fluctuate slightly when the tooth width,tooth height,and ground pressure increase. Therefore,the average values can be used as the traction model parameters. According to the grouser with different widths,the relationship of the maximum traction of the grouser with a two-side edge and the 10 mm tooth width increment changing with the tooth height and the ground pressure can be determined. Combining the traction model parameters,the traction-displacement curve with a certain group values of the tooth width,tooth height,and ground pressure can be predicted. Based on it,the slipping of the mining machine can be prevented to improve the mining effciency.