**4. Numerical simulation of compression test with DEM**

Evaluation of the actual compressibility properties via soil compression tests is important for employment of subsequent numerical analysis of stress and strain state of ground subjected by supplement loading (e.g. loads transmitted via foundations from a superstructure, inter‐ action of structure and soil strata, etc.). The confined compression (oedometer) test is approved as a relatively fast and simple laboratory test. It is performed under different conditions, loading paths and durability. Test conditions depend on physical changes in multiphase system of soil, generally related with reorganisation of soil grains, that of initial change of skeleton in cohesive soils and velocity of water filtration for saturated soils. One must note that in some cases the duration of testing procedure for prediction of long‐term soil behaviour and in other specific cases is very long [25], thus sometimes taking into account the time and test cost ratio it is not worth even to start the test. On the other hand, one cannot qualitatively explain the variation of soil compression test results, basing on some processing of already known testing and analysis data separately or in concern with view analysis. It is obvious that having not identified the actual physical mechanism for soil grain reorganisation during compression process and its peculiarities, one cannot explain the observed scatter of results under disposal. This mechanism cannot be recorded by applying usual techniques of testing and view analysis but can be simulated applying the relevant DEM techniques (initiated by [27–29]): that of the mathematical models of processes and discrete models for soil grains [1].

The above‐mentioned circumstances, as well as the permanently reducing computational costs, the development of numerical techniques and software in the field of multi‐scale analysis (including the particle strata mechanics), initiated a fast development and the applications numerical analysis in the field of the soil behaviour by means of the DEM. Such approach, combined with an experimental analysis for validation and calibration of the mathematical models, is definitely a promising one, allowing to reduce the price and quantity of laboratory tests and a reasonless conservatism in determining the values of mechanical properties of soils in near future.

Numerical simulation via DEM was provided using DEMMAT code [30]. This original program called DEMMAT has been written in Compaq Visual FORTRAN language. The quality of implementation is handled by a physically observable behaviour of interactions: particle–particle, particle–wall, particle–bottom and/or top plate (porous stone), and by the validation with the results obtained from physical experiments. The application of DEM to a system involves the following basic steps [30]:


Analysing soil compression curve given in **Figure 8**, it comes obvious that soil density or void ratio for low stress values does not change. Void ratio change is obtained only when soil is loaded with high stress values. Such interpretation of the compression curve is not reliable

**1.** In the contact place of porous stone and soil sample, contact settlements occur at the low stress due to not perfect soil surface. Contact settlements ensure good porous stone and

**2.** When testing clay soils with large sand or gravel particles, sample surface imperfections occur during soil sample preparation on the sample side, in a contact with the oedometer ring surface. Due to these surface imperfections, the soil sample expands in the horizontal direction during the loading process, and it continues until a sufficient contact with the oedometer ring. This can be considered as an explanation of the appearance of additional

If the soil sample has loading, unloading and reloading steps, **Figure 8** given compression curve is suitable only for the reloading step. Other authors present soil compression curves with vertical loading from 5 to 10 kPa [22–26]. In this case, it is not necessary to show what

Evaluation of the actual compressibility properties via soil compression tests is important for employment of subsequent numerical analysis of stress and strain state of ground subjected by supplement loading (e.g. loads transmitted via foundations from a superstructure, inter‐ action of structure and soil strata, etc.). The confined compression (oedometer) test is approved as a relatively fast and simple laboratory test. It is performed under different conditions, loading paths and durability. Test conditions depend on physical changes in multiphase system of soil, generally related with reorganisation of soil grains, that of initial change of skeleton in cohesive soils and velocity of water filtration for saturated soils. One must note that in some cases the duration of testing procedure for prediction of long‐term soil behaviour and in other specific cases is very long [25], thus sometimes taking into account the time and test cost ratio it is not worth even to start the test. On the other hand, one cannot qualitatively explain the variation of soil compression test results, basing on some processing of already known testing and analysis data separately or in concern with view analysis. It is obvious that having not identified the actual physical mechanism for soil grain reorganisation during compression process and its peculiarities, one cannot explain the observed scatter of results under disposal. This mechanism cannot be recorded by applying usual techniques of testing and view analysis but can be simulated applying the relevant DEM techniques (initiated by [27–29]): that of the mathematical models of processes and discrete models for soil grains [1]. The above‐mentioned circumstances, as well as the permanently reducing computational costs, the development of numerical techniques and software in the field of multi‐scale analysis

happens with the soil compression curve when vertical stress is from 0 to 5 or 10 kPa.

**4. Numerical simulation of compression test with DEM**

due to two reasons:

252 Modeling and Simulation in Engineering Sciences

sample settlement.

soil sample contact between each other.


**Figure 9.** Numerical granulometric composition curve.

More detailed information about used models and parameters in DEM simulation is in references [1, 30].

Numerical DEM simulations are performed with the same granulometric curve as obtained in experimental testing for the Baltic Sea sand. The used numerical granulometric curve with mean experimentally determined particle shape is given in **Figure 9**.

In this study, recalculation of time period is based on reference [31]:

$$T\_H = 2.87 \left( \frac{\frac{V\_i \rho}{2}}{\frac{R\_{\text{min}}}{2} \cdot \frac{E\_p}{2\left(1 - \nu^2\right)} \cdot \nu\_y} \right)^{0.2} \cdot \tag{1}$$

where *Ep*—modelled particle deformation modulus, MPa; *v*—loading velocity, m/s2 ; *vij*—initial particle velocity, m/s; *ρ*—particle density, kg/m3 ; *Rmin*—smallest modelled particle radius, m.

Seeking to increase the calculation accuracy, it is necessary to re‐calculate the time period, thereby obtaining the real‐time period for computation:

$$
\Delta t = \frac{T\_H}{10}.\tag{2}
$$

Particles position and contact forces change according to *Δt* are given in **Figure 10**.

**Figure 10.** Particles positions and contacts recalculation at time *t* and *t* + d*t* [32].

The test process and parameters for simulations are presented in **Table 3**. The actual Young's modulus *Eoed* = 200 GPa for oedometer volume parts is employed for simulations with Poisson's ratio *υ* = 0.3 and density *ρ* = 7850 kg/m<sup>3</sup> , and simulated oedometer height *H* = 0.00484 m and diameter *D* = 0.0102 m. During simulations reached maximum strain was 1.76% (as in the experimental testing). Accepted simulated particles Poisson's ratio *υ* = 0.17, oedometer walls Poisson's ratio *υ* = 0.3.


\* Note: Literature overview values correspond references sequence number.

**Table 3.** Test model data.

Numerical DEM simulations are performed with the same granulometric curve as obtained in experimental testing for the Baltic Sea sand. The used numerical granulometric curve with

( )

n

2 2.87 .

*<sup>R</sup> <sup>E</sup> <sup>v</sup>*

× × - è ø

Seeking to increase the calculation accuracy, it is necessary to re‐calculate the time period,

The test process and parameters for simulations are presented in **Table 3**. The actual Young's modulus *Eoed* = 200 GPa for oedometer volume parts is employed for simulations with Poisson's

diameter *D* = 0.0102 m. During simulations reached maximum strain was 1.76% (as in the experimental testing). Accepted simulated particles Poisson's ratio *υ* = 0.17, oedometer walls

*i*

æ ö ç ÷

r

*V*

2 2 1

Δ . 10

Particles position and contact forces change according to *Δt* are given in **Figure 10**.

where *Ep*—modelled particle deformation modulus, MPa; *v*—loading velocity, m/s2

*min p*

2

*ij*

0.2

(1)

; *vij*—initial

; *Rmin*—smallest modelled particle radius, m.

*TH <sup>t</sup>* <sup>=</sup> (2)

, and simulated oedometer height *H* = 0.00484 m and

mean experimentally determined particle shape is given in **Figure 9**.

In this study, recalculation of time period is based on reference [31]:

*H*

=

*T*

thereby obtaining the real‐time period for computation:

**Figure 10.** Particles positions and contacts recalculation at time *t* and *t* + d*t* [32].

ratio *υ* = 0.3 and density *ρ* = 7850 kg/m<sup>3</sup>

Poisson's ratio *υ* = 0.3.

particle velocity, m/s; *ρ*—particle density, kg/m3

254 Modeling and Simulation in Engineering Sciences

**Figure 11.** Modelled oedometer compression test separation into quarters [1].

All DEM numerical simulation calculations ran on cluster due to faster calculation process. In this case, it is possible to separate modelled oedometer into four quarters where each quarter is calculated by separate computer (**Figure 11**). In DEM simulations, parallel calculations of clusters are widely applied. Using these clusters, it is possible to calculate much bigger simulations in the same period of time, as with a single computer. Nevertheless, applications of clusters in DEM simulations do not provide enough calculation capacity. More detailed explanation of calculations with DEM is presented in Refs. [1, 30].

Used modelled particles shapes in numerical simulations have three shapes: ideal sphere, particle recreated from two spheres and particle recreated from three spheres (**Figure 12**). Recreation of particles shapes is based on experimental testing results obtained from mor‐ phology parameters determination part.

**Figure 12.** Recreation of particles shapes.

Providing DEM numerical simulations with different recreated particles shapes, it is possible to obtain particle shape influence for compression results. The analysis of influence of simulated particles shape on compression results is presented in **Figure 13**.

**Figure 13.** Comparison of compression results with different particle shape: 1—particle recreated from sphere; 2—par‐ ticle recreated from two spheres; 3—particle recreated from three different sizes spheres.

Analyzing **Figure 13**, it is evident that the compression curve which is obtained from the simulations with ideal sphere particles has a smooth curve. With increasingly complex particle shapes, stress jumps arise in the numerical simulation. These stress jumps appear due to faster particles repositioning than porous stone compression velocity. To increase porous stone velocity is not recommended, because it is possible to have not a static but dynamic modelling effect.
