Numerical modeling for controlled compensation grouting

This article analyzes the numerical modeling of the stress-strain state of a gravity structure sand base during grouting works using the controlled compensation grouting technique. The modeling is performed using the finite element method and physical nonlinear soil models that take into account the Coulomb-Mohr strength condition. The modeling is done in the computational software JuliS as well as the universal software complex PC ZSoil. The goal of the research is to study the impacts of compensation grouting parameters on the elevation value of base slab. A model was created for the grout body as an expanding spheroid whose volume changes as cement grout is fed in the soil. The authors developed a grouting sequence for grouting solutions based on the location of grout body in the grouting pillar. It is more efficient to feed the grout starting from the lower grout body. The grouting solution feed mode is selected depending on the soil strength condition and accounting for the prevention of hydraulic fracture. As a result of the research, the initial subsidence of the soil on the daytime surface above the injection zone was obtained, which requires experimental confirmation and is a matter for discussion.


Introduction
Controlled compensation grouting is a technique used to eliminate the negative consequences of uneven soil settlement under structures.Bases of buildings and structures may deform during construction due to the uneven distribution of the load, which may lead to such negative consequences as cracking and uneven structure subsidence.
Controlled compensation grouting is based on the controlled and even feeding of special grouting solutions into the soil under the structure.These solutions are usually made of polymers or cement mixes.They bind and compact soil to compensate for its settlement and prevent further deformations.
Controlled compensation grouting consists of several stages.Firstly, geotechnical data are analyzed to determine the properties of the soil under the structure constructed.Then the optimal locations for grouting wells are determined and the suitable grouting solution composition is selected.
After that, the solution is fed into the soil through the grouting wells.This process is carried out under strict supervision and control to assure the even distribution of the solution and prevent potential overtension in the soil.
Controlled compensation grouting allows for the even elevation and alignment of the structure base while minimizing the risks of cracking and other damages.This significantly improves the durability and reliability of buildings and reduces the risks and costs associated with their subsequent repairs and reinforcements.
Thus, controlled compensation grouting is an efficient technique for uneven soil settlement mitigation and structure stability and safety assurance [9].

Materials and Methods
The authors developed JulyS, a signature calculations program for the numerical study of compensation base grouting.The program solves a spatial problem.We selected the tetrahedron as a finite element.The program allows for the modeling of expansion in the finite-element mesh by setting the node movements.Thus, we can expand the grouting area to the set volume value.
To analyze it, we developed the JulyS program for the modeling of injecting additional volumes of grouting material in the soil base.The injection is implemented by setting the additional movements for the finite-element mesh nodes.The package is based on the development and description of the shape of the elements modeling the cement grouting in a sand base.Assume that the grouting body is an expanding spheroid (figure 1).The volume of the obtained grouting body changes according to the set grouting volume.To verify the software package, we compared the calculations with the analytical solution of the Lame problem [1], as well as the results of the physical experimentation with cement grout feeding to a sand base by Luca Masini, Ph.D. [2].

Results
Some calculations were carried out for grouting to gaskets located along one vertical axis [8].We studied the correlations between the gasket depth and the surface elevation value under the base slab.We used the distributed load per base surface at 0.4 MPa as the base load [3].The surface was elevated along the vertical axis.The calculation model for this problem is shown in figure 2.
The depth of the compressed base is 40 meters, and the vertical distance between the gaskets, following the available controlled grouting examples, may reach about 1 meter [4][5][6][7].The analysis of different gasket grouting options showed that the most efficient method is the subsequent grouting into the gasket pillar starting from the bottom one.This method proved to be more than 2 times more efficient than the one where grouting starts from the upper gaskets.
The results of modeling for 10 gaskets located on one vertical axis with grouting from the bottom up are shown in figures 3 and 4.  The graph in figure 5 presents the generalized calculation results for all of the grouting pillars with different numbers of gaskets.This graph shows the upper envelope curve, which is a dependency of the total base slab elevation and the grouting volume.The grouting volume value determines the arrangement of gaskets in the grouting pillar.This research was designed for relatively large grouting volumes and movements of the base slab.At the initial grouting stages, as well as for smaller volumes, the calculations showed a small surface settlement in the calculation model where the elevation took place later.This settlement is not important for the significant structure elevation values.However, if we aim to compensate for structure base settlement, which might be tolerated if it does not exceed several millimeters (or even 0 millimeters for landmark structures), this effect may lead to unwanted additional settlements.
This effect was analyzed in the Z-Soil software package.In this case, compensation grouting is modeled with increased finite element volumes by assigning additional deformations to them.To model the compensation grouting, the selected finite elements receive the load function and the initial deformation coefficient Δе0 that records their increase by the set volume (figure 6) [9].We used an area of 20 х 9 meters for the analysis.Grouting was modeled at a depth of 6 meters below the surface.While modeling the compensation grouting of small initial volumes into the base soil, the unwanted settlement value was 2 mm (figure 7).The deformation chart with a distorted scale is shown in figure 8. Figure 9 shows that a settlement area is formed over the expanding area.Having analyzed the horizontal tensions (figure 10), we can conclude that when an area is expanded within the finite-element mesh, horizontal tension stresses are formed over this area that result in soil loosening.This effect is observed both in the Mohr-Coulomb soil model and in the more complex Hardening Soil model.It is uncertain whether this effect can be observed in reality or it is a drawback of the existing numerical models.During the research, we obtained functional dependencies that help determine the elevation value of the base slab using the depth of gasket locations, their number, and the grouting volume.
3. We also found that the most efficient method is the subsequent feeding into the gasket pillar starting with the bottom gasket.This method proved to be more than 2 times more efficient than the one where grouting starts from the upper gaskets.4. We identified the settlement effect at the initial stages of grouting that may have negative impacts on the compensating structure.5. Whether the settlement effect is observed at the initial stages of grouting in reality, or it is a drawback of the existing numerical soil models remains an open problem.

Figure 1 .
Figure 1.The obtained grouting volume shape: acentral axis section, bspatial rendering of the volume half.

Figure 2 .
Figure 2. Calculation model 1 is the area shaped as cylinder half; 2 is the distributed load of 0.4 MPa; 3 is the gasket location; 4 is the gasket axis.

Figure 5 .
Figure 5.The dependency graphs for the base slab elevation and the useful proportion of the grouting volume.

Figure 6 .
Figure 6.Assigning the initial deformation coefficient and its change function depending on the calculation increment.

Figure 7 .
Figure 7.The dependency between surface movement and small-volume grouting.

Figure 9 .
Figure 9. Vertical movements (mm).The settlement zone is located over the expanding volume.