Establishing Of The Blended Cement Hydration And Microstructure Model HYMOSTRUC3D-E And Simulation Of The Autogenous Shrinkage Of Cement Paste

The relationship between the components of raw materials,the properties of the microstructure of cement paste and the performance of cement-based materials can be quantified with the numerical model of cement hydration and microstructure development,which not only provides the theoretical basis for the preparation and application of cement but also reduces the experimental cost.Hence the investigation on the numerical model of cement hydration and microstructure development is increasingly concerned.Up to now the numerical models,such as HYMOSTRUC3D,only deal with the hydration and microstructure development of pure Portland cement.However the interaction between the particles of cementitious materials becomes more important because of the increasing usage of supplementary cementitious materials in cement-based materials.In the meantime the autogenous shrinkage is a crucial problem for the blended cement-based materials with low water-to-binder ratio.The measurement of autogenous shrinkage of cement-based materials is not only time-consuming but also low accuracy.This study aims to propose HYMOSTRUC3D-E model for simulating the hydration and microstructure development of blended cement based on HYMOSTRUC3D model,and a model to simulate the autogenous shrinkage of blended cement paste at the microscale.1.HYMOSTRUC3D-E model for simulating the hydration and microstructure development of blend cementHYMOSTRUC3D-E model contains two main modules:cement hydration module and microstructure development module.The cement hydration module consists of sub-modules including cement hydration,pore solution chemistry and interaction.In the cement hydration sub-module the stoichiometry of the reactions of Portland cement（PC）,BFS and FA particles in blended cement pastes is dealt with.The reaction rates and degrees of reactions of PC（including C₃S,C₂S,C₃A and C₄AF）,BFS and FA are calculated in which the change of water distribution in the pore structure and the change of pore solution chemistry（determined with the interaction sub-module）are considered.Then the evolution of amount and volume of different phases in the cement paste is calculated.In the pore solution chemistry sub-module the volume of free capillary water is calculated at first.Next the concentrations of Na⁺and K⁺in the pore solution are calculated with the method of Taylor^[69].Based on the solubility equilibrim of gyspum and CH and the electrical neutrality of pore solution,the concentrations of Ca²⁺,SO₄^2-and OH^-in the pore solution are calculated.The microstructure development module consists of sub-modules including cement particle growth,CH growth and multi-scale pore structure.In the cement particle growth sub-module,a representative elementary volume（REV）of cement paste is defined.Next,the initial spatial distribution of particles in the fresh paste is simulated by random packing the PC,BFS and FA particles in the REV.Then,by letting these PC,BFS and FA particles grow,the microstructure development（without CH）of blended cement paste is simulated.In the algorithm for particle growth,the thickness of the shell of reaction product depends on the degree of hydration of blended cement obtained in the cement hydration module.A sub-module is proposed to simulate the nucleation and growth of CH particles.Besides,a pore structure sub-module is proposed in the microstructure development module for simulating the evolution of capillary porosity.Specific porosities are assigned to the inner（0.26）and outer products（0.36）.By determining the volume evolution of the inner and outer products in cement paste,the contribution of gel pores to total porosity of cement paste is quantified.In chapter 5 the HYMOSTRUC3D-E model for simulating the hydration process and microstructure development of PC paste,the hydration process,pore solution chemistry and porosity of slag cement pastes,the hydration process,porosity and CH contents of fly ash cement pastes and the chemical shrinkage of PC,slag cement and fly ash cement are validated.By comparing the results of simulations and experiments,the following conclusions can be drawn:（1）Degree of hydrationFor the system with different w/c and different initial content of BFS and FA,the simulated degrees of hydration（or reaction）of PC,BFS and FA are validated with experimental data.In HYMOSTRUC3D-E,the influence of the mineral composition of PC on the hydration of PC is taken into account using the initial penetration rate₀ and the transition thicknessfor different minerals,i.e.C₃S,C₂S,C₃A and C₄AF,in PC particles.In addition,the influence of BFS or/and FA on the hydration of PC and the effect of the w/b on the hydration,or reaction,of PC,BFS,and FA are quantified by further detailing of the reduction factors₁,₂ and₃ of HYMOSTRUC3D,allowing for the changes of the water distribution and changes in pore water chemistry in the system.The effect of the pore solution chemistry on the pozzolanic reaction of BFS and FA is quantified with the pH-factor,allowing for the influence of pH on the reaction rates of BFS and FA particles.With these extensions of the original simulation model,the hydration process of cements with different components,such as different amounts of PC,BFS and FA,and different w/b,could be simulated.（2）Pore structureFor pure Portland cement paste（w/c=0.4）,the simulated capillary pore size distributions at the age from 1 day to 28 days are in good agreement with those obtained using SEM image analysis.The simulated total porosity is larger than the porosity measured using MIP.This is because the small gel pores,i.e.gel pores<4 nm,cannot be measured by MIP,whereas in HYMOSTRUC3D-E all pores are considered.The second reason is that MIP cannot detect the isolated pores,whereas HYMOSTRUC3D-E gives all pores.This difference also occurs in slag cement systems（w/b=0.4 and BFS content from 30%to 70%）,fly ash cement systems（w/b=0.4 initial FA content ranges from 30%to 50%）.（3）Pore solution chemistryFor a pure Portland cement system（w/c=0.4）and slag cement systems（w/b=0.4,BFS content ranges from 30%to 70%）,the simulated concentrations of alkali ions（Na⁺and K⁺）in the pore solution are close to the experimental data.However the simulated concentrations of Ca²⁺and SO₄^2-differ from the experimental data.This is probably because the actual Ca²⁺in pore solution are supersaturated at early age,which cannot be accurately calculated with only the concept of solubility equilibrium.Another possible reason is from inadequate consideration of the solubility equilibria of hydration products containing calcium.In HYMOSTRUC3D-E it is assumed that the concentration of Ca²⁺ions only depends on the solubility equilibria of gypsum and CH.In reality,the concentration of Ca²⁺ions is also affected by the solubility equilibria of other phases in the cement paste,such as AFt,AFm,CSH.The concentrations of Ca²⁺and SO₄^2-are much lower than the concentrations of alkali ions.The relatively low accuracy of the simulated concentrations of Ca²⁺and SO₄^2-will not significantly affect the accuracy of the simulated pH values.Hence the trends of the simulated evolution of the pH of the pore solution and the experimental data are in fairly good agreement.（5）Chemical shrinkageThe chemical shrinkage of PC pastes with w/c=0.3 and 0.4,slag cement paste with w/b=0.31 and fly ash cement paste with w/b=0.33 are simulated with HYMOSTRUC3D-E.For PC pastes,the simulated chemical shrinkage of these cement pastes is in good agreement with the experimental results at early age,i.e.during the first 1 day.At later age,i.e.after 1 day,the simulated chemical shrinkage is larger than the experimental results.The reason for this is in the measurement of chemical shrinkage the transport of water into the cement paste becomes difficult at later age.This difference also occurs in the slag cement paste and the fly ash cement paste.For the same total degree of hydration of cement,both slag cement and fly ash cement show larger chemical shrinkage than pure PC,because the chemical shrinkage of PC for complete hydration is smaller than the chemical shrinkage BFS and FA for complete reaction.（6）Nucleation and growth of CH particlesFor a pure Portland cement system（w/c=0.4）,the cumulative size distribution of CH particles simulated by HYMOSTRUC3D-E is close to the experimental data,at least for small particle sizes,i.e.<3.4μm.For large particle sizes,i.e.>3.4μm,the cumulative size distribution of CH particles simulated by HYMOSTRUC3D-E differs from the experimental data.This is because the pore structure simulated by HYMOSTRUC3D-E does not contain the big pores,i.e.the pores>10μm（limitation due to the size of the REV of cement paste）.In reality these big pores exist in the cement paste,and they provide room for the growth of large CH particles.2.Model for simulating the autogenous shrinkage of cement paste at the microscaleAutogenous shrinkage of cement-based materials（cement pastes,mortars and concretes,etc.）is defined as“the bulk deformation of a closed,isothermal,cementitious material system not subjected to external forces”^[120].Autogenous shrinkage is harmful for concrete structures because it increases cracking risk and potentially reduces service life.In many applications the cement-based materials have low water to binder rations（w/b）to achieve high strength.For these cement-based materials with low w/b,the autogenous shrinkage is commonly significant^{[120,123,124]}.Therefore,the autogenous shrinkage is an important issue.Up to now,the models for simulating the autogneou shrinkage of cement-based materials mainly deal with the autogenous shrinkage at the macroscale.Very few studies concentrate on the imposing of the driving force of autogenous shrinkage on the solid skeleton of cement-based materials at the microscale,and the corresoponding autogneous shrinakge.The second topic of this study is the model for simulating the loading of the driving force of autogneous shrinkage on the solid skeleton of cement paste at the microscale,which is benefical to investigate the microcracking of cement-based materials caused by the autognoue shirnkage.This autogenous shrinkage model consists of input module,self-desiccation module,capillary module and local deformation module.At first a discrete algorithm is proposed to divide the hydration process of cement into several time steps.At each time step,the 3D microstructure,chemical shrinkage and pore solution of cement paste simulated with HYMOSTRUC3-D,and the measured relative humidity are taken as input in the input module.In the self-desiccation module,the distribution of water and“empty capillary pore”in the pore structure of cement paste is simulated.In the capillary pressure module,the capillary pressure in the cement paste is calculated from the measured relative humidity,in which the effect of pore solution chemistry on the capillary pressure is quantified.In addition the location and the direction of capillary pressure are determined in this module.In the local deformation module,a lattice finite element fracture analysis method is used to simulate the impose process of capillary pressure on the capillary pore wall of cement paste,which can be used to obtain the local deformation and autogenous shrinkage of cement paste at each time step.The evolution of autogenous shrinkage of cement paste is calculated from autogenous shrinkage of cement paste at each time step.The proposed model is used to simulate the values of the autogenous shrinkage of Portland cement pastes with water to cement ratios（w/c）of 0.3 and 0.4,and the autogenous shrinkage of slag cement paste（33%slag and w/b=0.31）and fly ash cement paste（27%fly ash and w/c=0.33）.The simulation results are validated by experiments.It is found that the autogenous shrinkage obtained by simulation is smaller than the experiments.This is probably due to insufficient consideration of the saturated pore diameter and the influence of creep.