Numerical Simulation of Mutually Embedded Settlement in Miscellaneous Fill

Research Institute of Geotechnical Engineering, Hohai University, Nanjing 210098, China Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China Engineering Research Center of Dredging Technology of Ministry of Education, Hohai University, Nanjing 210098, China Department of Civil and Architecture Engineering, Jiangsu University of Science and Technology, Zhenjiang, China


Introduction
Urban construction and reconstruction will produce a considerable amount of miscellaneous fill, which is characteristic of a large natural density range, loose structure, large compressive deformation, and low strength. Miscellaneous fill is significantly different from uniform soil in terms of mechanical properties [1][2][3]. In foundations with miscellaneous fill and soft soil, embedding miscellaneous fill particles into soft soil under overlying loads is easy (Figure 1). is phenomenon may decrease pores among miscellaneous fill particles and thereby cause foundation settlement. Settlement analysis and prediction of miscellaneous fill composite foundation have become research hotspots in geotechnical engineering.
Existing studies on settlement of miscellaneous fill foundation currently focus on single aspects. A few methods are available to predict settlement of miscellaneous fill foundation with soft soil layer effectively. erefore, influencing laws of interface friction on mutually embedded settlement of miscellaneous fill and soft soil, as well as basic characteristics of soft soil particle displacement, porosity, and contact in the mutual embedding process, were investigated by particle flow method. On this basis, causes of miscellaneous fill-soft soil mutual embedding and relevant microscopic mechanism were disclosed. Research conclusions provide reasonable theoretical references to predict settlement of miscellaneous fill-soft soil composite foundation.

Model Construction and Implementation Method
Mutual embedding is a phenomenon in which soft soil particles embed into pores of particles under loads. Particle displacement at the occurrence of mutual embedding is relatively high. Miscellaneous fill and soft soil particles produce dislocation on spatial position and lead to discontinuous deformation. Particle flow method is unrestricted by deformation volume and can process mechanical problems of discontinuous media. e particle flow method not only effectively simulates discontinuous phenomena, such as cracking and separation of media, but also reflects the mechanism, process, and outcome of soil deformation. erefore, this method was applied to study the mutual embedding phenomenon in the present study [35,36].

Construction of Models.
e frequent use of cylinder samples in laboratory tests is an axial symmetric problem. In this study, the axial symmetric problem is simplified into a two-axis problem. A two-dimensional plane model was constructed to simulate and analyse formation mechanism and universal law of mutual embedding under the assistance of particle flow PFC2D. e simplified chart of miscellaneous fill particles is shown in Figure 2. Figure 2(a) is the top view of vertically arranged miscellaneous fill particles, and Figure 2(b) is the profile of the plane line. In the profile, the graph diameter is equal to particle diameter. Meanwhile, pore channels, which form vertical particles with equal pore channels, are also available. Channels formed by different sizes of miscellaneous fill particles have different sizes. e relationship between channel size (L) and particle size of miscellaneous fill (R) is determined according to geometric relationship to identify the position relations of miscellaneous fill particles in the model.
In the aforementioned formula, L is the minimum width of miscellaneous fill channel; R is the radius of miscellaneous fill particles.   Advances in Civil Engineering A numerical model for mutual embedding test was constructed based on the aforementioned analysis (Figure 3). e bottom is filled with soft soil particles (ball). Particle size ranges from 0.5 mm to 1 mm, and particles are in uniform distribution. Height of soft soil particles is 8 cm and comprises 7416 balls. e upper layer is filled with miscellaneous fill particles. Particle size is equal to particle size in laboratory tests (15-45 mm). In the numerical test, all miscellaneous fill particles are replaced by the same clump. e number of vertical particles is four, and a single vertical particle is composed of three particles ( Figure 3). Rigid walls are used as boundaries. ese boundaries are kept L/2 away from the interface of miscellaneous fill particles, meeting the distance relationship among different vertical particles. A loading plate (clump) is found on the top of miscellaneous fill particles. Different densities are given to the loading plate to provide different constant loads.
A simulation test on mutual embedding of miscellaneous fill and soft soil was conducted based on the constructed model. Steps of the simulation test are introduced as follows.
(1) Contact model, contact parameters, and gravity are endowed to miscellaneous fill and soft soil particles to balance the model under dead loads. (2) According to the area of loading plate, different densities are provided to the loading plate (in this study, area of the loading plate is 2.74 × 10 −3 m 2 and density is 7.8 × 10 3 kg/m 3 ; other loads can be inferred in the same way). With the gradual application of loads, 25, 50, and 100 kPa were applied in 25, 50, and 100 times, respectively. A total of 500 time steps were circulated under each load. e loading ended at 60,000 time steps. e size of mutually embedded settlement was also recorded every 500 time steps. e mutually embedded settlement was the product of mutually embedding thickness and porosity. e mutually embedding thickness is the difference between the top and the lowest position of soft soil particles in miscellaneous fill channels. e mean of mutually embedding thickness of three channels was chosen as the final mutually embedding thickness.

Parameter Calibration.
e aforementioned numerical model involves two materials (particles and boundary walls) and four contact types (ball-ball contact between soft soil particles, ball-pebble contact between soft soil and miscellaneous fill particles, ball-facet contact between soft soil particles and boundary walls, and pebble-pebble contact

Advances in Civil Engineering
between the loading plate and miscellaneous fill particles). e ball-ball contact model applies the antirolling linear contact model, while the remaining contact models (ballpebble, ball-facet, and pebble-pebble) applied the linear models. In this numerical simulation, the contact parameters are adjusted continuously and compared with laboratory test. When the two results are consistent, the contact parameters are determined, as shown in Table 1.
Taking the interpenetrating displacement of 35 mm particle size as an example, Figure 4 shows the comparison between the numerical simulation results and the experimental parameters under the selected parameters. It can be seen from the figure that the numerical simulation curve is consistent with the experimental curve, indicating that the parameter calibration is effective.

Effects of Microparameters of Particles on Mutually
Embedded Settlement. Numerical test based on particle flow is conducted to reflect macrochanges in materials through the general motion trail of particles, which is restricted by microparameters of particles. Many types of microparameters, including stiffness, friction coefficient, damping, modulus, and strength, are available. In the model, soft soil particles applied the rolling resistance linear contact model, in which changes in stiffness and friction coefficient can significantly influence simulation results. erefore, influences of stiffness and friction coefficient on mutually embedded settlement are analysed in this section.

Effects of Stiffness on Mutually Embedded Settlement.
e simulated relation curves of stiffness and friction coefficient with mutually embedded settlement when particle size is 25 mm and load is 100 kPa are shown in Figure 4. In Figure 5(a), mutually embedded settlement attenuates in the nonlinear pattern with the increase in normal stiffness. Given the same contact friction coefficient, the maximum static friction at contact interface may increase with contact stiffness. Under this circumstance, mutually embedded settlement decreases with the increase in contact stiffness. When the contact stiffness further increases, the maximum static friction force at contact interface becomes higher than the interparticle maximum static friction force and develops a weak surface between soft soil particles. In this case, contact stiffness influences mutually embedded settlement. Figure 5(b) shows that mutually embedded settlement decreases first and then stabilizes with the increase in friction coefficient. A nonlinear relationship exists between mutually embedded settlement and friction coefficient. When the friction coefficient is 0-0.45, mutually embedded settlement drops sharply. When friction coefficient exceeds 0.45, mutually embedded settlement remains constant. In the numerical test, the friction coefficient of soft soil particles is 0.45, which is close to that at the turning point of the relation curves. When soft soil particles are embedded into miscellaneous fill channel, these particles may produce friction effects with miscellaneous fill particles. When contact friction coefficient is lower than the interparticle friction coefficient, the maximum static friction force at the contact surface of soft soil and miscellaneous fill particles is smaller than the interparticle maximum static friction force. At the occurrence of mutual embedding, soft soil particles in miscellaneous fill channel may slide along the contact surface. erefore, the interface sliding friction force increases, and the mutually embedded settlement declines as the contact friction coefficient approaches the interparticle friction coefficient. When contact friction coefficient is higher than interparticle friction coefficient, a weak surface of soft soil particles is observed. At this moment, mutually embedded settlement remains the same with the increase in contact friction coefficient.

Particle Displacement during Mutual Embedding.
e maximum mutually embedded settlement is achieved under 100 kPa and approximately 15,000 time steps. Considering that mutually embedded settlement slightly changes in follow-up time steps, vertical displacements of particles under four time steps (2500, 5000, 10,000, and 15,000) were chosen to study particle displacement characteristics during mutual embedding. Vertical displacements of particles under different time steps are shown in Figure 6, in which particles with an upward vertical displacement higher than zero are expressed in gray. e entire soft soil particles are compressed at 2500 time steps, and only superficial soft soil particles develop displacement. e contact surface displacement between miscellaneous fill and soft soil particles reaches the peak. Particles at the contact surface are still compressed at 5000 time steps, and the vertical displacement of a few particles at miscellaneous fill channel is higher than zero.
is finding implies the occurrence of mutual embedding. e number of soft soil particles with displacement higher than zero is increased at 10,000 time steps, and the displacement at the contact surface is relatively evident. Moreover, the displacement diffuses around. Soft soil particles further move upward at 15,000 time steps, while soft soil particles adhered onto the surface of miscellaneous fill particles are kept compressed. Based on displacements at different time steps, particles at contact surface may squeeze particles in miscellaneous fill channel to produce an upward displacement during the development of downward displacement. Mutual embedding is the consequence of relative movement between soft soil and miscellaneous fill particles.

Pore Characteristics of Particles during Mutual
Embedding. Measuring circles are set in Figure 7 because the model is symmetric. Statistical analysis on porosity of particles in the region of measuring circles was conducted to obtain the porosity contour line of soft soil particles in Figure 8. On this basis, pore characteristics of particles during mutual embedding at 50 kPa were investigated. Considering that the first row of measuring circles may overlap with miscellaneous fill particles after 10,000 time steps in the test, only porosity distributions at 2500 and 7500 time steps were analysed. At 2500 time steps, the space between contour lines is relatively uniform, and porosity is negatively related to depth. e porosities at contact surface and miscellaneous fill channel are similar and slightly lower than those before loading. Particles are also compressed under this circumstance. At 7500 time steps, the upper contour lines are relatively dense, while the lower contour lines are relatively sparse. A high density of contour lines leads to quick changes in porosity. Evidently, particle porosity at miscellaneous fill channel considerably varies, while that at contact surface slightly changes. By comparing porosities at 2500 time steps, changes in porosity are mainly manifested at the upper position. With the increase in time steps, porosity at miscellaneous fill channel sharply increases, while that at contact surface slightly changes. is finding demonstrates that particles in miscellaneous fill channel slide with the occurrence of mutual embedding. Position state of particles at 10,000 time steps is shown in Figure 8(c). Particles at miscellaneous fill channel are sparse, but those at contact surface are dense. erefore, miscellaneous fill particles may squeeze soft soil particles under loads. e loads in the early stage are insufficient to overcome interparticle friction, and particles hardly produce dislocation, thus leading to slight changes in porosity. With the further transmission of loads, particles at the contact surface become tight and squeeze surrounding particles. As a result, particles at miscellaneous fill channel slide upward, and porosity in the miscellaneous fill channel increases accordingly.

Changes of Intraparticle Contact Force during Mutual
Embedding. Intraparticle force chain distribution under different time steps is shown in Figure 9. e force chain is vertically downward in the beginning. At 2500 time steps, the force chain on the contact surface of soft soil and miscellaneous fill particles is concentrated and begin to skew toward two sides. e contact surface with stress concentration develops a slight downward deformation. Moreover, the force chain develops from the initial stress contact point around. With the increase in time steps, the force chain further develops and becomes dense. e force chain below particles begins to develop and transmits approximately vertically downward, accompanied with uniform distribution. is phenomenon is caused by force chain transmission along the skewing direction. Moreover, the skewing depth of force chain at the contact surface significantly increases, while force chain at miscellaneous fill channel is relatively weak, forming a triangular distribution. e mutual embedding phenomenon can be observed at 10,000 time steps, and force chain is fully developed. Force chains at miscellaneous fill channel connect and form an arc distribution that opens upward. e force chain at the upper position of the channel is still weak. erefore, particles at the contact surface initially develop downward deformation, thus causing dislocation of particles at two sides and producing a skewed force chain. e skewed force chain continuously develops, and force chains at miscellaneous fill channel will be connected after reaching a certain extent, forming arch force chains. Particles above the arc force chains move upward due to the weak force chains and are influenced by the dislocation of surrounding particles. Figure 10(b) shows that the soft soil particles have been squeezed into the miscellaneous fill channel, and the thickness of the soft soil particles in each miscellaneous fill channel is not different, which is similar to laboratory the test rule (Figure 10(a)). e results show that the numerical model is reasonable and can reflect the general law of the embedded displacement.

Comparison and Validation
It can be seen from Figure 11 that the growth rate of embedded displacement with load in numerical simulation is slightly slower than that of laboratory test results. Under the load of 50 kPa, the embedded displacement of laboratory test and numerical simulation is approximately equal.

Conclusions
In this study, a two-dimensional numerical simulation of mutually embedded settlement of miscellaneous fill-soft soil composite foundation is conducted by using the particle flow method. Influences of microparameters of particles on mutually embedded settlement are investigated, and influencing laws of controlling factors of mutual embedding phenomenon are discussed. e following major conclusions could be drawn.
(1) Mutually embedded settlement decreases first and then stabilizes with the increase in friction coefficient. is settlement attenuates continuously with the increase in normal stiffness. Mutually embedded settlement continuously decreases when the maximum static friction force on the interface approaches the interparticle maximum static friction force. (2) Mutual embedding phenomenon is the consequence of relative movement between soft soil and miscellaneous fill particles. Under loads, miscellaneous fill particles produce concentrated stress on soft soil particles. Loads in the early stage are insufficient to overcome interparticle friction, and particles hardly produce dislocation, thus leading to slight changes in porosity. With the further transmission of loads, particles at the contact surface become tight and squeeze the surrounding particles. As a result, particles at miscellaneous fill channel slide upward, and porosity in the miscellaneous fill channel increases accordingly. (3) e force chain at the contact surface inclines around, and that at miscellaneous fill channel presents approximately horizontal distribution. Particles on the contact surface move downward, and the lateral pressure on particles at the miscellaneous fill channel continuously increases. e contact force direction continuously changes, and then arch force chains are formed after reaching to a certain extent.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interests regarding the publication of this paper.