Analytical solutions are derived to calculate the cutting forces on the blade in both horizontal and vertical directions:

Where Fh is the horizontal cutting force that is aligned with the direction of the cutting blade [N] while Fv is the vertical cutting force [N], α is the cutting angle [-], β is the angle of the shear plane with the direction of the cutting velocity [-], λ is the strengthening factor, which follows the fact that when the cutting velocity increases, the clay gets stronger. c is the cohesive shear stress [Pa] while a is the adhesive shear stress [Pa], hi is the cutting depth [m] and hb is the blade height [m], w is the width of the blade [m], and r is the ratio between adhesion and cohesion [-].

Figure 1 describes the working mechanism in dredging, while in trenching, cutting into clay is also often discussed, for example, in the form of subsea ploughing. Subsea ploughing is a common engineering practice for subsea cable protection. Ploughs are capable of working in a wide range of soils and are capable of operating in water depths up to 1500 metres. An example of a v-shaped plough used to bury pipe is depicted in Figure 2. For the operation of this type of machine, the analytical model to calculate the pulling force Fpull is given in Equation 4, in which cu is the undrained shear strength of a cohesive soil [kPa], Nc is a dimensionless coefficient depending on the plough geometry [-], d the ploughing depth [m], b the ploughing width [m], α the adhesion coefficient defined as (a/c) [-] and la the adhesion length [m] (depending on the plough geometry).

In Equation 3 and 4, the adhesion factor α is an unknown parameter, which reflects one of the fundamental mechanical properties of the clay soil: the ratio between adhesion and cohesion. Without this factor, it becomes almost impossible to calculate the cutting force and pulling force on the mechanical tools.

Literature study on the adhesion factor

In the past, researchers have carried out a series of research activities to investigate the mechanical behaviour of clay with respect to cohesion, adhesion and the relation between them. The adhesion factor is studied based on the two following perspectives: the total shear resistance and the adhesive resistance.

In geotechnical engineering, and in particular foundation engineering, the α-method is a commonly used total shear stress analysis for the capacity of the side resistance of the shaft foundations in cohesive soils. In this method, the side resistance capacity is related to the soil’s undrained shear strength by an empirical coefficient denoted as α, which is, as mentioned earlier, the adhesion factor. With the adhesion factor, the side resistance of a pile foundation in cohesive soil is calculated using Equation 5 (Chen et al., 2011).

Where Qs is the side resistance capacity of the pile foundation [kPa], α the adhesion factor [-], cu the undrained shear strength of the soil [kPa], B the foundation width [m] and t the thickness [m]. Based on Equation 5, Equation 6 is derived to calculate the adhesion factor, where L is the contacting length of pile [m]. It should be noted that the total skin shear resistance consists of both adhesion and friction. Therefore, this empirical coefficient, which is based on the total shear resistance for a given undrained shear strength, is typically higher than the adhesion factor based on the true adhesion of the soil.

Another type of model is based on the ratio between the adhesive resistance and the undrained shear strength. A considerable amount of experimental data has been published supporting this concept. Littleton (1976) measured the adhesion factor, which is around 0.84 for very soft clay. Kooistra et al. (1998) measured for relatively firm river clay that the adhesion factor is around 0.07. Recently, van der Wielen (2014) conducted measurements on soft river clay where he found the adhesion factor to be 0.58.

With the concept that the total shear resistance consisting of the adhesive resistance and the external friction force, Zimnik et al. (2000) further separate the adhesive strength of a soil into:

• an adhesive strength in the normal direction, called the adhesive tensile strength at [Pa]; and
• an adhesive strength in the tangential direction, which is called as the adhesive shear strength a [Pa] as depicted in Figure 3.

When pulling a foreign body from an adhesive soil in normal direction, the adhesive tensile strength at is simply given by Equation 7. On the other hand, when dredging or trenching tools, for example a pipelay trencher, are moving through an adhesive soil, the trencher is subjected to a tangential sliding resistance consisting of an adhesive and a frictional part. This sliding resistance τa [Pa] is described by Stafford and Tanner (1977) and follows the Mohr-Coulomb type expression give in Equation 8.

Where at is the adhesive tensile strength [Pa], F is the required pulling force [N] and As is the effective soil-body contact area [m2], a is the adhesive shear strength [Pa], σ is the normal stress at the contact surface [Pa] and δ the external friction angle [-] of the clay or the soil to the metal blade. Combe and Miedema (2015) investigated the influence of adhesion on cutting processes typically encountered in dredging practice. A custom adhesive test setup was designed and tangential adhesive strength tests were performed. It was concluded that with an increasing cohesive strength of the clay, there is a decrease to zero for the adhesive strength. Futhermore, in addition to the decreasing adhesion there is an increase in the internal friction angle φ.

Experimental study on the adhesion factor

To investigate and analyse the relation between cohesion and adhesion in clayey soils, a series of tests were performed. Both the internal tangential resistance and the external tangential resistance of the soil follow a linear Mohr-Coulomb type expression. Measurements of the tangential resistance at a range of normal stresses σ are used to build up this linear relationship, which can be used to determine:

• the internal shear strength (cohesion) c;
• the internal friction angle φ; • the external shear strength (adhesion) a; and
• the external friction angle δ of the soil as depicted in Figure 4.

The internal shear strength, or often just referred to as the ‘cohesion’, and the internal friction angle φ, are the two properties mostly used to characterise a cohesive soil. For these two properties, the direct shear testing equipment applying to the ASTM-standards is already available. However, this does not apply for external shear strength and external friction angle of soils. Therefore, a dedicated test setup was designed (Figure 5).

In this setup, the cohesive soil is contained in a slotted container with a blade between the two blocks of the cohesive soil. While a normal stress is applied to the top plate and distributed to the clay, the blade is pulled out and the pull-out force is recorded. Dividing this steady-state pull-out force F by the contact area A between the blade and the soil gives the overall tangential resistance τa between the blade and the soil. By conducting this test for a series of normal stresses, a Mohr-Coulomb failure diagram (as in Figure 4) can be created and the external shear strength a and the external friction angle δ can be obtained.

Experimental setup

Machine for the pull-out tests

To enable the measurement of interface shear strength properties, a new experimental setup according to the concept depicted in Figure 5 was designed. The design was a collaboration between Delft University of Technology in the Netherlands and The National Engineering Research Center for Dredging Technology and Equipment located in Shanghai, China. The test equipment was constructed by the Shanghai Leao Test Instrument Company and complies with the Chinese T1129- 2006 and T1130-2006 specifications in the JTG E50-2006 Test Procedure for Geo-synthetics for Highway Engineering. A schematic overview is given in Figure 6.

The experimental rig depicted in Figure 6 is comprised of five main elements: (1) is a pneumatic cylinder capable of applying and maintaining a vertical pressure and (2) indicates the metal container that holds the cohesive soil. The constant speed linear pulling mechanism is made out of a bolted clamping mechanism (3) to ensure the metal blade is securely attached to the rig. (4) is a force sensor and (5) indicates an electrical drive system, consisting of an electrical stepper motor, an encoder and a reduction gearbox to provide a constant pulling speed.

Preparation work and cohesive soil samples

Two types of soils were used in the cohesion-adhesion experiments. Both soils were obtained from real-time dredging projects in China: soil 1 originates from Wuhan and soil 2 originates from Lianyungang. Immediately after dredging, both soils were packed and sent to the research facility where they were stored in a humidified cabinet. Furthermore, part of the two soils were prepared using air-drying, crushing and sieving (1 mm), and then mixed with water to certain water contents to conduct the Atterberg Limit tests. Finally, X-ray diffraction tests were performed by the Shanghai OKanalysis Center to determine the mineralogy of the soils. An overview of the main properties of the soils is presented in Table 1.

The experimental protocol

1. To ensure full saturation, the soil is placed in a large container filled with water for at least 3 days. Subsequently, the soil is put in the metal soil container (see (2) Figure 6), separated in the middle by a plastic film; in this way the soil is split in two halves, which makes for easier blade placement. The container holding the soil is placed on the test equipment and a constant vertical pressure is applied for a predetermined period to ensure the consolidation of the soil up to the desired shear strength.

2. After consolidation, the plastic film and the top half of the consolidated clay are removed from the container. First, both surfaces are rolled to ensure a smooth surface and then the blade is placed in the correct position on the bottom half of the soil. Subsequently, the top half of the soil is put on the top of the blade so that the blade is clamped to the test equipment using the bolted clamping mechanism (see (3) Figure 6).

3. Compression on top of the soil is applied and after the pressure is maintained at a constant value for 30 seconds, the blade pull-out test is commenced. For each consolidated soil sample, five blade pull-out tests are performed at normal pressures ranging from 40 kPa to 200 kPa, at an incremental steps of 40 kPa. Between each two tests, the top half of the consolidated soil and the blade are removed from the test setup. The blade is cleaned to remove any residual soil and the consolidated soil is rolled again to have equally smooth surfaces between tests. The tests are performed at a constant speed of 1 mm/s and recorded for a distance of 100 mm.

4. After the blade pull-out tests, four samples are taken from both the top and bottom half of the consolidated soil to conduct the undrained direct shear tests according to the ASTM-D6528 standard (2007) for undrained direct shear tests. Direct shear tests are performed at four normal pressures and a constant speed of 0.8 mm/min. Furthermore, two samples are taken to determine the water content for each consolidated soil specimen.

Preliminary results of the experiments

The direct shear tests were recorded with a sampling frequency of 6 data points per sheared millimetre. For each test, the internal tangential resistance τc was plotted versus the shearing displacement. An example of these direct shear results for soil 1 is shown in Figure 8.

For both the undrained direct shear and the blade pull-out tests, the average steadystate value for the internal tangential resistance τc and blade pull-out force F were scattered in a Mohr-Coulomb diagram showing normal stress versus shear stress.

Linear regressions were made according to the Mohr-Coulomb failure criterion (Figure 4) to obtain the internal and external shear strength at zero normal stress (cohesion and adhesion), and the internal and external friction angles. Statistical analysis showed a significant linear regression between the normal stress σ and shear stress τ for both the direct shear results and the blade pull-out test results. Examples for showing this linear regression on the pull-out test data for both soil 1 and 2 are illustrated in Figure 10.

The experimentally obtained internal and external shear strength data was analysed and used to create an empirical model shown in Figure 11, where the dimensionless cohesion c* is plotted against the adhesion factor, defined as a/c. The dimensionless cohesion is the nominalised cohesion based on the gravitational force. The filled dots represent data obtained in tests on soil 1 (Wuhan) and the circles represent data obtained in tests on soil 2 (Lianyangang). The black line represents the best exponential fit according to the least-square method.

Preliminary analysis of the results

Efforts have been made on interpreting the adhesion and cohesion of cohesive soils. Actually, the adhesion and cohesion can be interpreted in both the mechanical and non-mechanical manners. From the mechanical perspective, the adhesion and cohesion are generated as a result of the pore water pressure change. This concept is supported and well explained by Mitchell et al. (2005).

The non-mechanical perspective tends to emphasise the impact of the micro-electrochemical reactions that happen inside the clay soil and between the clay soil and the foreign bodies, especially when the clay contains organic compositions. Preliminary results show that although these two types of soil are comprised of different minerals, they still show the same trend that the adhesion factor drops logarithmically to zero with increasing cohesion. It shows that the adhesion factor has a positive correlation with the water content of the clay, which corresponds with the qualitative empirical relation.

In the undrained shear tests of the fully saturated clay, it appears that the external load is transmitted to the pore water, thus increasing the pore pressure. In this way, the effective stress of the solids does not need to change as a result of the frictional forces. Both the internal and external friction remain unchanged. If the cohesive shear strength and the adhesive shear strength of the clay can be seen as constant for a fixed soil type (i.e. soil 1 or soil 2) with fixed water content, then increasing the external compression can hardly affect the apparent shear stress of the soil samples. However, Figure 10, on the contrary, tells that the apparent shear stress increases proportionally to the normal stress. Possible reasons for that might be the local effects on the contacting boundary.

On the contacting surface between the clay sample and the pull-out blade, it is found that in order to ensure the sufficient contact between the soil and the blade, the soil sample is not completely sealed. Therefore, during the pull-out tests, there is inevitably always a small amount of drainage that occurs near the moving blade. That means the load from the upper part of the soil cannot be fully borne by the pore water, so that the local effective stress will increase.

Apart from that, when the blade is being pulled out, in the boundary layer of the soil sample near the blade, a local dilatation in the solid skeleton is expected to occur due to the shearing. Therefore, it is possible that locally the pore volumes will change and most likely increase, considering that the clay samples hold very low porosities and permeability; the surrounding water can hardly flow into the expanded pores and the pore water can hardly flow out of the shrunken pores. Hence, the water under pressure will form up in the boundary layer, which is the part of the clay sample near the blade. For the solid grains in this layer, it means an extra pressure gradient force acting on them, thus locally the effective stress in vertical direction will increase. All these possible reasons lead to an increasing apparent shear resistance against the increasing external compressive load.

Conclusions

An often neglected, while very important mechanical property of clay soils, the adhesion factor has been discussed and studied. The two types of adhesion factor, the ratio between the overall external shear resistance versus the undrained shear strength, and ratio between the actual adhesive resistance versus the undrained shear strength, have been explained. The former is mainly used in the agricultural applications, on which a set of empirical equations have been introduced, and the latter is the term needed in dredging applications, on which the experimental study in the past has been introduced.

T his study shows that the adhesion factor varies heavily with the cohesive strength of the clay, while the cohesive strength relies heavily on the water content. While in dredging operation, the clay encountered can all been seen as fully saturated, thus for the clay in the specific field, the adhesion factor should be seen as constant. The discovered adhesion factor can be brought into Equation 3 and 4 for calculating the cutting forces on clay in dredging and trenching operations. Another discovery lays in the magnitude of the friction. The internal and external friction of clay is frequently neglected since they are considered to be significantly smaller than the cohesion and adhesion. This study found that if the loading process is not fully undrained, then there is an apparent internal and external friction angle which could lead to non-negligible frictional forces. If the two parts are correctly combined, then the cutting force and the specific cutting energy can be calculated in the right order.

The results presented in this article are based on the preliminary post-analysis. It is recommended to conduct further post-analysis on the obtained experimental data to quantitatively obtain all the adhesion factor and friction coefficients of the clay samples. It is also recommended to conduct experiments on more types of soils with different water contents. Only by conducting a large number of tests will it be possible to generate a material database so that a sound empirical relation can be established. In the end, it is expected that with a comprehensive database, a set of empirical equations can be used to calculate the adhesion and external friction coefficient when the clay soil type is known.