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Washout resistance evaluation of fast-setting cement-based grouts considering time-varying viscosity using CFD simulation
Construction and Building Materials 242 (2020) 117959
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Washout resistance evaluation of fast-setting cement-based grouts considering time-varying viscosity using CFD simulation Wei Cui a,b, Qiu-wei Tang a, Hui-fang Song a,⇑ a b
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration, Tianjin University, Tianjin 300350, China
h i g h l i g h t s Evaluate the washout resistance of two new fast-setting cement-based grouts. Investigate the time-varying behavior by experimental tests. Establish a new time dependent and shear-rate related viscosity model in OpenFOAM. Compare the washout resistance and working conditions of the two new grouts.
a r t i c l e
i n f o
Article history: Received 1 July 2019 Received in revised form 19 December 2019 Accepted 24 December 2019
Keywords: Cement-based grouts Fast-setting Washout resistance Time-varying characteristic CFD
a b s t r a c t Fast-setting cement-based grouts are required in certain engineering conditions such as high hydrodynamic pressure or fast water inrush. The rheological properties of the fast-setting grouts evolve rapidly in comparison with those of the conventional ones. Hence, a time-varying viscosity should be considered during the evaluation of washout resistance. In this study, two new cement-based grouts named ‘‘KC-1” and ‘‘KC-2” were proposed for resistance against high-speed and large-mass water inflow. By conducting the experimental tests for rheological properties, it has been presented and discussed the time-varying characteristic of the consistency coefficient in the Herschel-Bulkley constitutive model. Based on the outcome, a time-varying model was developed and established in OpenFOAM, and a computational fluid dynamics (CFD) simulation was implemented to analyze the washout resistance under different water velocities. It was observed that both KC-1 and KC-2 exhibit satisfying washout resistance when the water velocity is no more than 1.0 m/s, showing well maintained integrity and residual rates. In addition, KC-1 performs better washout resistance when the water velocity is higher than 1.0 m/s. However it shows lower workability and injectability due to its higher viscosity. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction With the prosperous hydraulic engineering industry, underground seepage problem broadly emerges in unconsolidated or fractured layers, resulting in foundation deterioration and eventually other adverse incidents. Such problems can be effectively alleviated by forming grout curtains [1,2]. Grouting is a process of injecting pumpable materials into voids and fissures for the purpose of enhancing the impermeability and integrity of soil and rock formations [3,4]. From the observation of previous engineering practices, it is concluded that the selection of proper grouting material is a decisive factor for plugging performance [5,6]. In complex formations with high hydrodynamic pressure and severe leak⇑ Corresponding author. E-mail address: [email protected] (H.-f. Song). https://doi.org/10.1016/j.conbuildmat.2019.117959 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.
age, the grouting capability of conventional grouts is limited, as reflected in a prolonged setting time and a low residual rate. Conventional grouts may fail to block the seepage even if an enlarged amount of grout has been pumped in. Consequently, good plugging performance is hard to achieve by conventional ones [7]. Under these circumstances, in order to strengthen the washout resistance capability, the adoption of new fast-setting grouts is of great value [8]. Generally, fast-setting grouts are modified with admixtures for shorter setting time and higher viscosity. Hence, with the fastsetting nature and well-maintained integrity, the grouts are able to set still in voids and fissures, instead of being torn apart by seepage at early-age. Also, due to their low workability and fluidity, high-pressure grout pumping systems are needed, which challenges the grouting technologies and equipment. To ensure the impermeability of the new grouts, the washout resistance ought to be discussed systematically.
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Experimental test and numerical simulation are two major methods to evaluate the washout resistance of cement-based grouts. Zhang et al. [9] tested the washout resistance of a modified clay grout in a channel of 4 m 0.35 m 1 m indoors. It was found that the grout shows a satisfying water-dilution resistance with a water velocity of 1.2 m/s. Moreover, Khayat et al. [10] made the washout resistance experiment by pouring 500 mL of grout into a beaker containing an equivalent volume of water from a funnel positioned at a predetermined height. The results showed a decreasing washout loss for low fluidity grouts by the usage of viscosity-modifying admixtures (VMA). Also, similar washout resistance experiment was designed by M. Sonebi [11], and it was predicted that the reduction in water-cement ratio (w/c) has a greater influence on reducing washout mass loss than the increase in anti-washout admixture (AWA) concentration. Although accurate and reliable results can be drawn from conventional experiment researches, high cost and difficulty in controlling the experiment procedures are non-negligible obstacles. Given the shortcomings mentioned above, numerical simulation as an alternative methodology for scientific researches and engineering applications is gaining popularity, in which investigations on rheological and mechanical properties of cement-based grouts are of vital importance. Yahia and Khayat [12] used a modified Bingham model which was expressed as a second order polynomial equation to derive the relationship between yield stress and plastic viscosity. In addition, Svermova [13], Celik [14] and Sonebi [15] fitted the rheological properties of cement-based grout mixed with different additives through the same modified Bingham model. Mohammed et al. [16] used a Vipulanandan rheological model to predict the relationships between shear stress and shear strain rate for cement-based grout modified with two types of polymer with w/c of 0.6 and 1.0. Nevertheless, it is generally ignored in the aforementioned literatures the rapid change of rheological properties for fast-setting cement-based grouts. Setting time reduction improves the initial strength of grouts [7], thus contributing to greater dilution and washout resistance against water flows. Given that previous constitutive models are unable to accurately fit the time-varying characteristic of the new grouts, developing a new time-varying viscosity model is urgently needed for CFD simulations. To evaluate the washout resistance, a study has been conducted to address the research gaps outlined above by investigating the time-varying viscosity of two new types of cement-based grouts, namely KC-1 and KC-2. The two new grouts are able to adjust the setting time at will for practical needs while maintaining their integrity and fluidity. OpenFOAM, serving as a CFD solver, was employed for numerical simulations, and the Euler-Euler approach was used for water-grout flow. In the sections below, a summary of the experimental procedures, involving material properties and simulation methods, is firstly introduced, followed by a discussion on the simulation results.
2. Materials 2.1. Admixtures Conventional grouts are formed by adding to plain cement with bentonite, fly ash and water reducer, while the new grouts are composed of cement incorporated with organic polymer chemicals. To be specific, accelerators and flocculants are the two main admixtures. Generally, setting time is affected by the proportion of accelerators through a series of chemical reactions, whilst the yield stress and plastic viscosity are adjusted by flocculants. According to the work of Cheng et al. [7], the viscosity of conventional grouts changes very slowly against time, while the perfor-
mance of the new grouts is effectively controlled by the compound of the additions. Anti-washout admixtures modify the grout properties and help to enhance the cohesion and stability of cement-based systems [4]. Such admixtures, that enhance the water retention capability and the anti-dilution property, make the grouts resist the washout from water flows durably. Based on the method in [17], we improved and proposed two types of cement-based grouts named ‘‘KC-1” and ‘‘KC-2” with different admixtures. To determine the optimal admixture dosages, tests were carried out including measuring the setting time, yield stress, compressive strength, plastic viscosity and fluidity under a constant condition with temperature of 23 ± 2 and humidity no less than 95%. The initial setting time, during which a setting needle sinks to the bottom of a 4 ± 1 mm-thick grout, ranges from 10 to 20 min for KC-1 and from 15 to 30 min for KC-2. It was specified the w/c to 0.5 in the mixtures design. Table 1 summarizes the mix proportions of the investigated grouts. In KC-1, the addition amount of accelerator and flocculant accounted for 5% and 2.05% of the cement mass respectively. The amount of accelerator and flocculant added to KC-2 was 2.5% and 12.5% (7.5% bentonite involved) respectively. 2.2. Rheological properties In this section, the rheological properties of KC-1 and KC-2 at different hydration time were tested using a rotational viscometer. In total, ten samples were prepared and each sample had the volume of 350 mL. The hydration time was 2 min, 5 min, 10 min, 20 min and 30 min, respectively. In a rotational viscometer, a motor is utilized to drive the outer cylinder to rotate. By controlling the rotation speed of the outer cylinder, the grout between the inner and outer cylinders is sheared under different shear rates. The inner cylinder shear torque at the corresponding shear rate is measured by a torsion spring connected to the outer cylinder. By adjusting the magnitude of the shear rate, measured shear stresses were recorded. The rheological properties are fitted with the Herschel-Bulkley model [18–20], which is often used to describe the rheological behavior of concrete and grout. The shear stress is expressed as:
s ¼ s0 þ Kc_ n
ð1Þ
where s0 is the yield stress, K is the grout’s consistency, c_ is the shear rate and n is the flow behavior index. Ruan [21] investigated the viscosity of several materials and found that the yield stress of cement-based grouts turns out to be almost a fixed value as hydration time increases. In this paper, only the time-varying characteristic of the consistency is considered and expressed in the form of an exponential equation by fitting obtained experimental data. Meanwhile, the yield stress and the flow behavior index are used as inputs for numerical simulations. Figs. 1 and 2 show the rheograms of KC-1 and KC-2 at the initial time under different shear rates respectively. By fitting two scatter plots with the Herschel-Bulkley model, the relationships between the shear stress and the shear rate are described clearly. Rheological parameters are listed as follows: s0 = 360 Pa and n = 0.9118 for KC-1; s0 = 50 Pa and n = 0.8751 for KC-2. Additionally, the fluidity Table 1 Mix proportions of the fast-setting cement-based grouts. Mix
KC-1(%)
KC-2(%)
Cement Water Accelerator Flocculant
63.674 31.837 3.184 1.305
60.606 30.303 1.515 7.576
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
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Fig. 1. Rheogram of KC-1 at initial time.
Fig. 2. Rheogram of KC-2 at initial time.
of the fresh cement-based grouts was measured using a slump cone with an upper diameter of 36 mm, a lower diameter of 64 mm and height of 60 mm. The mold was lifted vertically to spread out of the fresh grouts on a horizontal base plate. And the average spread diameter at the end of the flow was measured, shown in Figs. 1 and 2. The spread diameter is 13.87 cm for KC-1 and 14.92 cm for KC-2. Larger spread diameter means higher fluidity and spreading ability. In other words, KC-2 provides better workability and injectability than KC-1. A series of experiments were carried out at the 2nd, 5th, 10th, 20th and 30th minutes before KC-1 and KC-2 reaching their steady states. The experimental data scatters, the fitting curves and the fitting equations of KC-1 and KC-2 are shown in Figs. 3 and 4. Under the premise that the yield stress and the flow behavior index are constant (KC-1: s0 = 360 Pa and n = 0.9118; KC-2: s0 = 50 Pa and n = 0.8751), the consistency coefficient increases with hydration time growing in half an hour. It can be seen that as the hydration time increases, the magnitude of the consistency coefficient of KC-1 changes more rapidly, demonstrating its lower workability once again. The evolution of the consistency coefficient against time due to hydration is depicted in Fig. 5 and obtained by exponential equations for KC-1 and KC-2 as follows:
KKC - 1 ¼ 0:4172e0:0012t
ð2Þ
KKC - 2 ¼ 0:4077e0:0009t
ð3Þ
3. Numerical investigation of grout behavior 3.1. Modification of viscosity model in OpenFOAM CFD work conducted in this study was achieved with opensource software OpenFOAM in Ubuntu 16.04. OpenFOAM is primarily a CFD package written in C++ for the customization and extension of numerical solvers for continuum mechanics problems. It is used to create executables by utilizing classes and templates to manipulate and operate scalar, vectorial and tensorial fields [22]. OpenFOAM provides pre- and post-processing environments. The interface to the pre- and post-processing are built-in OpenFOAM utilities, thereby ensuring consistent data processing across all environments. Programming languages that are object-oriented, such as C++, provide the mechanism, i.e. classes, to declare types and associated operations that are part of the verbal and mathematical languages used in science and engineering. In OpenFOAM, the viscosityModel
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Fig. 3. Rheogram of KC-1 at different times.
Fig. 4. Rheogram of KC-2 at different times.
Fig. 5. Effect of hydration time on consistency coefficient.
is an abstract base class. Among the viscosityModel are inherited subclasses, i.e. incompressible viscosity models, which are available to be re-used, designed and bug-fixed for specific tasks. In
order to achieve the simulation results, a new class including time-varying parameters for non-Newtonian fluid’s viscosity is essential. In this paper, a new time dependent and shear-rate
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
related viscosity model named timeSlurry was coded and compiled as the exponential equations shown in Fig. 5. The dependency of yield stress obeys the following equations:
sKC - 1 ¼ 360 þ 0:4172e0:0012t c_ 0:9118
ð4Þ
sKC - 2 ¼ 50 þ 0:4077e0:0009t c_ 0:8751
ð5Þ
CFD is widely employed to simulate the details of fluid flows. In this study, the Euler-Euler approach, in which the fluid volume is discretized into several small control volumes, was used for the water-grout flow [23–26]. A flow field is characterized by balance in mass, momentum, and total energy governed by the continuity equation, the Navier-Stokes equations, and the total energy equation. The continuity equation is given by:
ð6Þ
ð7Þ
! where p is pressure, s is viscous stress tensor and F refers to interfacial forces. The viscous stress tensor s is defined according to the Newtonian formulation.
s ¼ 2lS S ¼
1 ! !T rt þ rt 2
ð8Þ ð9Þ
where S is the rate of strain tensor and l is the coefficient of dynamics viscosity. In our study, s is expressed by Eqs. (4) and (5) mentioned above. The total energy equation is given by:
@ 1 1 q e þ t2 þ r q! t e þ t2 @t 2 2 ! ! ! ! ¼ r ðkrT Þ þ r p t þ s t þ t F þ Q
ð10Þ
where T is temperature and e is the internal energy per unit mass. The two phases (water and grout) interact through the drag and lift forces acting between them, as well as through heat and mass transfer. Owing to the presence of more than one phase, the simulation in a two-phase system is more complex compared with that in single phase flow. In the Euler-Euler approach, the complicated mixture, where the interactions between each other need to be interpolated, is solved on the basis of the Volume of Fluid (VOF) method, assuming that the fluid acts as a continuum throughout the domain. In VOF method, the interface between the phases is tracked by the volume fraction of phase k, ak. The volume fraction equation is the continuity equation of phase k divided by the density of that phase, and its discretization is crucial for obtaining a sharp interface.
1 @ðqk ak Þ ! þ r qk ak t k ¼ 0 @t qk
np X
ak ¼ 1
ð12Þ
where np is the total number of phases. The fluid properties, such as density and viscosity, are calculated by their volume weighted average.
Ueff ¼
np X
ak Uk
ð11Þ
The benefit of using volume fractions is that only a scalar convective equation needs to be solved to propagate the volume fractions, and hence interface or topological changes are tracked with time in the computational domain. The volume fraction equation indicates whether a chosen phase is present inside the control
ð13Þ
k¼1
In this study, VOF is implemented between the phases to capture the free interface of the grout. To do this, the transport equations are solved for mixture properties, assuming that all field variables are shared between the phases.
@C ! þ t rC ¼ 0 @t
! where q is density and t is velocity. The momentum equation is given in the form:
! ! @ðq t Þ !! þ r ðq t t Þ ¼ rp þ r s þ F @t
volume. If ak = 1, the control volume is completely filled with the chosen phase; if ak = 0, the control volume is filled with a different phase. A value between 0 and 1 indicates that the interface between phases is present inside the control volume. The sum of the volume fractions for each phase must be one, which is described as follows:
k¼1
3.2. Numerical model
@q ! þ r ðq t Þ ¼ 0 @t
5
ð14Þ
Then an advection equation for the fraction function is solved. This is given by Eq. (15) where Cf denotes the volume fraction flux. The advection can be made much more accurate by reconstructing the function in each cell before finding the fluxes. n Cnþ1 i;j;k ¼ Ci;j;k ðC fe C fw þ C fn C fs þ C ft C fb Þ
ð15Þ
The flow chart of the simulation is covered in Fig. 6. In this study, a transient simulation was conducted with the consideration of the gravity effect and the assumption that no mass transfers between phases. CFD method is usually performed in four steps [27]. Firstly, numerical model describing the flow domain is established by means of abstraction and simplification. Secondly, a numerical discretization method is selected for governing equations, such as finite difference method, finite element method and finite volume method. The third step is to create the numerical network and define the initial and boundary conditions. Finally, post-processing is performed to visualize the results. Details of computational geometry, grid and boundary conditions will be discussed below in section 3.4. 3.3. Numerical validation In order to verify the reliability of CFD, the fluidity test of the new cement-based grouts was simulated, and the results were compared between the experimental tests and the numerical simulations. Firstly, a circular truncated cone filling with grout was modeled. The yield stress, the consistency coefficient and the flow behavior index of fresh grout at the initial moment were used as input parameters in OpenFOAM. Fig. 7 shows the shapes of KC-1 and KC-2 at the end of the flow. The diffusion radius given by numerical simulation is 6.91 cm for KC-1 and 7.42 cm for KC-2, respectively. The errors with the true values are both around 0.5%. Therefore, it is validated that the calculation result for the fluidity is in good accordance with the experimental result. 3.4. Geometry and boundary conditions As shown in Fig. 8, the 3-D pipe for washout resistance test is devided into four functional sections: the water-inlet section, the grout-inlet section, the test section and the outflow section. Detailed dimensions of the geometry are referred to in the figure, which were discretized into finite elements with the size of 0.01 m.
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Fig. 6. Flow chart of simulation.
There are two inlet boundaries, namely velocity boundaries, for inflow water and grout respectively, and one outlet boundary for both of them. For the initial condition (t = 0 s), the whole domain
is filled up with still water. From then on grout is injected by specifying the inflow speed of 0.1 m/s from the top portion along the –z direction for the first 30 s. Grouting stops at the 30th second, and
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
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Fig. 7. Spread radius at the end of the flow.
Fig. 8. Geometry and mesh.
the grout-inlet boundary changes into a symmetrical boundary in the next 570 s (t = 30–600 s). The magnitude of inlet water velocity stays zero until the grouting stops. Then it changes into a gradient, i.e. 0.1 m/s, 0.5 m/s, 1.0 m/s, 1.5 m/s and 2.0 m/s, along the x direction in each set of the numerical simulations. After the injection is completed (t = 30 s), the washout resistance within the last 570 s is under observation. 4. Results and discussions The main purpose of the current study was to explore the washout resistance of KC-1 and KC-2 under different water velocities. Detailed comprehension of the washout resistance can help with the prediction of its behavior in engineering. Therefore, in this section, the grout injection velocity of 0.1 m/s was designated as a representative case. First presented is the shape evolution combined with moving distance. Then the variation of volume amount combined with final residual rate is discussed. Both are investigated to characterize the washout resistance. 4.1. Shape evolution and moving distance Figs. 9 and 10 show the typical shape evolution of KC-1 and KC2 in x-y plane at different time intervals, which evaluates the washout resistance intuitively. Grout with more scattered shape indicates the process of a worse washout resistance. In addition,
moving distance of grout was measured (Fig. 11), i.e. the displacement of the centroid from t = 30 s to t = 600 s. It is presented in Fig. 11 the comparison between KC-1 and KC-2 at different water velocities. With moving distance of 0.02 m and 0.03 m for KC-1 and KC-2, it can be observed that the influence of low water velocity (t = 0. 1 m/s) on grout shape can almost be ignored. The initial grout shape basically kept well until the 600th second with slight changes in the shape of the upstream grout due to the direct damage by water flows. In this occasion, washout resistance was adequately possessed by the two new grouts. With the water velocity up to 0.5 m/s, the grout continued to move downstream. However, the stability of both KC-1 and KC-2 was still well maintained. As the velocity reached 1.0 m/s, the centroids of KC-1 and KC-2 moved downwards by 0.14 m and 0.18 m. When the velocity increased on this basis, the grout gradually scattered apart and the shape was severely affected accompanied by a large deviation from the original position. The grout failing to solidify in the upper part of the accumulation layer was more washed away by velocity over 1.5 m/s. Compared with the previous cases of water velocity below 1.0 m/s, the grout no longer deposited effectively and the shape at the 600th second changed significantly. As the velocity increased to 2.0 m/s, it is reasonable to predict that almost all of the grout will be washed out of the pipe if the observation continues. In general, KC-1 performs better washout resistance than KC-2, and the difference is more significant when the water velocity is
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Fig. 9. Shape evolution of KC-1.
Fig. 10. Shape evolution of KC-2.
higher than 1.0 m/s, which can be concluded easily from the enlarged vertical distance between the two curves as shown in Fig. 11. 4.2. Volume amount and final residual rate A key indicator for evaluating washout resistance is the volume amount (V) of grout remaining in the pipe with the accumulation of time steps (Figs. 12 and 13). The curve, that indicates the injection amount, reaches peak at 30 s (Vmax) and keeps unchanged after grouting completed. Residual rate (g) is another quantitative characteristic, which is defined as:
g ¼ Vfinal =Vmax
ð16Þ
where Vfinal refers to the volume amount of grout remaining at the 600th second of each simulation. Through the residual rate, the volume amount of the remaining grout can be expressed clearly. When the velocity reached 0.1 m/s, the integrity of the grout was well preserved with the residual rates both more than 90%. In consequence, the velocity of water through the pipe was slowed down significantly, indicating good plugging performance. Both the final residual rates were above 85% when the velocity reached 0.5 m/s, accompanied by relatively gentle slopes in the descent of residual rate. When the velocity reached 1.0 m/s, part of the grout
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
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Fig. 11. Moving distance of KC-1 and KC-2.
Fig. 12. Volume amount of KC-1.
was washed out of the pipe by the water flow with the edge diluting slightly. But the residual rates of 75% and 71% respectively were at least in line with the requirements, with a little washout volume loss. As the velocity increased to 2.0 m/s, the remaining volume amount of the grout was the least. In this occasion, only 54% of KC-1 and 45% of KC-2 stayed in the pipe. By horizontal comparison, KC-1 always kept more amount in the pipe, showing a higher residual rate than KC-2 on the whole. Similarly, the difference is more significant with the increase of the water velocity, especially after 1.0 m/s. 4.3. Washout resistance evaluation Fig. 11, showing the moving distance versus water velocity, reveals that the moving distance increases slowly when the water
velocity is lower than 1.0 m/s. The distance between the final position and the original position is short as demonstrated. When the water velocity exceeds 1.0 m/s, the increasing trend begins to accelerate. Another observation is that, by examining the trend of final shape variation at 600 s as shown in Fig. 9, the diffusion size of KC-1 increases firstly (with velocity no more than 0.5 m/s) and then shows a noticeable decrease in width (with velocity over 0.5 m/s). The same phenomenon applies to KC-2, which is attributed to the fact that the grout has not fully diffused while part of them is taken away. Analysis of volume amount in Figs. 12 and 13 indicates that washout resistance of grout is getting worse as the velocity increases. The grout withstands washout effectively when the velocity is no more than 1.0 m/s, with the residual rates of 70% guaranteed. KC-1 and KC-2 totally lose efficacy as the velocity reaches 2.0 m/s.
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Fig. 13. Volume amount of KC-2.
Another point to note is that, considering the better maintained integrity and the more satisfying residual rate, KC-1 is a more leading grout to be used in high hydrodynamic pressure conditions. However, its high viscosity (as depicted in Fig. 5) gives rise to low fluidity and low workability, which means a high-pressure grout pumping system is essential when grouting. The washout resistance of KC-2 is sufficient in seepage control for foundation under general water inlet conditions. With the cooperation of solid materials, KC-2 can block the rest of the small leakage channels, which is superior to conventional cement grouts. 5. Conclusions Firstly, the rheological properties of the fast-setting cementbased grouts were analyzed as the focus in this paper. Then, a CFD approach was chosen to study the washout resistance. The shape evolution combined with moving distance and the variation of volume amount combined with final residual rate were obtained under different water velocities. The following conclusions were summarized based on the investigations. (1) The rheological properties of KC-1 and KC-2 are determined based on the Herschel-Bulkley model. The variation of the consistency coefficient with hydration time in the equation is considered, which is described by exponential equations. KC-1 has a larger consistency coefficient and a faster growth rate, as is reflected in the fact that its flow behavior index n is larger than that of KC-2. (2) When injected at 0.1 m/s, the grout maintains integrity and effectively resists the washout against the water flow at no more than 1.0 m/s, obtaining a residual rate above 70%. The grout is washed away by the water flow over 1.0 m/s, with no longer capability to deposit at the bottom of the pipe. Some supplementary measures are needed to ensure the success of grouting in this occasion. For example, filling the pores with an appropriate amount of gravel graded aggregate can be conducted. (3) KC-1 performs better washout resistance especially in high hydrodynamic pressure conditions attributing to its shorter setting time and better long-term durability, but overall it
presents a lower fluidity than KC-2. That is to say, KC-1 is not enough to achieve a satisfactory injectability, which should be equipped with a high-pressure grout pumping system to compensate for the lack of the low workability. Although the washout resistance of KC-2 is worse than KC1, the performance is also sufficient in low flow rates. The high fluidity of KC-2 makes for excellent workability which is suitable for general water inlet conditions. CRediT authorship contribution statement Wei Cui: Conceptualization, Methodology, Writing - review & editing, Supervision. Qiu-wei Tang: Formal analysis, Investigation, Writing - original draft, Visualization. Hui-fang Song: Validation, Funding acquisition. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This research was supported by the Joint Fund of Natural Science Foundation of China and Yalong River Hydropower Development Co., Ltd. (Grant no. U1765106). References [1] H. Dong, J. Chen, X. Li, Delineation of leakage pathways in an earth and rockfill dam using multi-tracer tests, Eng. Geol. 212 (2016) 136–145. [2] J. Warner, Practical Handbook of Grouting: Soil, Rock and Structures, 2004. [3] D. Bruce, D. Stare, T. Dreese, D. Bruce, Contemporary drilling and grouting methods, in: Spec. Constr. Tech. Dam Levee Remediat., 2012, pp. 15–106. [4] C.A. Anagnostopoulos, Laboratory study of an injected granular soil with polymer grouts, Tunn. Undergr. Sp. Technol. 20 (2005) 525–533. ˇ erny´, Technology of Remediation of [5] M. Kociánová, R. Drochytka, V. C Embankment Dams by Optimal Grout, in: Procedia Eng., 2016, pp. 257–264. [6] F. Jorne, F.M.A. Henriques, Evaluation of the grout injectability and types of resistance to grout flow, Constr. Build. Mater. 122 (2016) 171–183. [7] P. Cheng, L. Li, J. Tang, D. Wang, Application of time-varying viscous grout in gravel-foundation anti-seepage treatment, J. Hydrodyn. 23 (2011) 391–397.
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[17] W. Cui, J. Huang, H. Song, M. Xiao, Development of two new anti-washout grouting materials using multi-way ANOVA in conjunction with grey relational analysis, Constr. Build. Mater. 156 (2017) 184–198. [18] C. Atzeni, L. Massidda, U. Sanna, Comparison between rheological models for portland cement pastes, Cem. Concr. Res. 15 (1985) 511–519. [19] V.H. Nguyen, S. Remond, J.L. Gallias, Influence of cement grouts composition on the rheological behaviour, Cem. Concr. Res. 41 (2011) 292–300. [20] A. Papo, Rheological models for cement pastes, Mater. Struct. 21 (1988) 41–46. [21] W.J. Ruan, Research on diffusion of grouting and basic properties of grouts, Chin. J. Geotech. Eng. 27 (2005) 69–73. [22] H.G. Weller, G. Tabor, H. Jasak, C. Fureby, A tensorial approach to computational continuum mechanics using object-oriented techniques, Comput. Phys. 12 (1998) 620. [23] K. Hejranfar, K. Fattah-Hesary, Assessment of a central difference finite volume scheme for modeling of cavitating flows using preconditioned multiphase Euler equations, J. Hydrodyn. 23 (2011) 302–313. [24] L.F.L.R. Silva, P.L.C. Lage, Development and implementation of a polydispersed multiphase flow model in OpenFOAM, Comput. Chem. Eng. 35 (2011) 2653– 2666. [25] J. Jung, R.W. Lyczkowski, C.B. Panchal, A. Hassanein, Multiphase hemodynamic simulation of pulsatile flow in a coronary artery, J. Biomech. 39 (2006) 2064– 2073. [26] D. Gidaspow, Book review – Multiphase flow and fluidization: continuum and kinetic theory descriptions, Powder Technol. 83 (1995) 287. [27] C. Karakurt, A.O. Çelik, C. Yılmazer, V. Kiriççi, E. Özyasßar, CFD simulations of self-compacting concrete with discrete phase modeling, Constr. Build. Mater. 186 (2018) 20–30.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Washout resistance evaluation of fast-setting cement-based grouts considering time-varying viscosity using CFD simulation Wei Cui a,b, Qiu-wei Tang a, Hui-fang Song a,⇑ a b
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration, Tianjin University, Tianjin 300350, China
h i g h l i g h t s Evaluate the washout resistance of two new fast-setting cement-based grouts. Investigate the time-varying behavior by experimental tests. Establish a new time dependent and shear-rate related viscosity model in OpenFOAM. Compare the washout resistance and working conditions of the two new grouts.
a r t i c l e
i n f o
Article history: Received 1 July 2019 Received in revised form 19 December 2019 Accepted 24 December 2019
Keywords: Cement-based grouts Fast-setting Washout resistance Time-varying characteristic CFD
a b s t r a c t Fast-setting cement-based grouts are required in certain engineering conditions such as high hydrodynamic pressure or fast water inrush. The rheological properties of the fast-setting grouts evolve rapidly in comparison with those of the conventional ones. Hence, a time-varying viscosity should be considered during the evaluation of washout resistance. In this study, two new cement-based grouts named ‘‘KC-1” and ‘‘KC-2” were proposed for resistance against high-speed and large-mass water inflow. By conducting the experimental tests for rheological properties, it has been presented and discussed the time-varying characteristic of the consistency coefficient in the Herschel-Bulkley constitutive model. Based on the outcome, a time-varying model was developed and established in OpenFOAM, and a computational fluid dynamics (CFD) simulation was implemented to analyze the washout resistance under different water velocities. It was observed that both KC-1 and KC-2 exhibit satisfying washout resistance when the water velocity is no more than 1.0 m/s, showing well maintained integrity and residual rates. In addition, KC-1 performs better washout resistance when the water velocity is higher than 1.0 m/s. However it shows lower workability and injectability due to its higher viscosity. Ó 2020 Elsevier Ltd. All rights reserved.
1. Introduction With the prosperous hydraulic engineering industry, underground seepage problem broadly emerges in unconsolidated or fractured layers, resulting in foundation deterioration and eventually other adverse incidents. Such problems can be effectively alleviated by forming grout curtains [1,2]. Grouting is a process of injecting pumpable materials into voids and fissures for the purpose of enhancing the impermeability and integrity of soil and rock formations [3,4]. From the observation of previous engineering practices, it is concluded that the selection of proper grouting material is a decisive factor for plugging performance [5,6]. In complex formations with high hydrodynamic pressure and severe leak⇑ Corresponding author. E-mail address: [email protected] (H.-f. Song). https://doi.org/10.1016/j.conbuildmat.2019.117959 0950-0618/Ó 2020 Elsevier Ltd. All rights reserved.
age, the grouting capability of conventional grouts is limited, as reflected in a prolonged setting time and a low residual rate. Conventional grouts may fail to block the seepage even if an enlarged amount of grout has been pumped in. Consequently, good plugging performance is hard to achieve by conventional ones [7]. Under these circumstances, in order to strengthen the washout resistance capability, the adoption of new fast-setting grouts is of great value [8]. Generally, fast-setting grouts are modified with admixtures for shorter setting time and higher viscosity. Hence, with the fastsetting nature and well-maintained integrity, the grouts are able to set still in voids and fissures, instead of being torn apart by seepage at early-age. Also, due to their low workability and fluidity, high-pressure grout pumping systems are needed, which challenges the grouting technologies and equipment. To ensure the impermeability of the new grouts, the washout resistance ought to be discussed systematically.
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Experimental test and numerical simulation are two major methods to evaluate the washout resistance of cement-based grouts. Zhang et al. [9] tested the washout resistance of a modified clay grout in a channel of 4 m 0.35 m 1 m indoors. It was found that the grout shows a satisfying water-dilution resistance with a water velocity of 1.2 m/s. Moreover, Khayat et al. [10] made the washout resistance experiment by pouring 500 mL of grout into a beaker containing an equivalent volume of water from a funnel positioned at a predetermined height. The results showed a decreasing washout loss for low fluidity grouts by the usage of viscosity-modifying admixtures (VMA). Also, similar washout resistance experiment was designed by M. Sonebi [11], and it was predicted that the reduction in water-cement ratio (w/c) has a greater influence on reducing washout mass loss than the increase in anti-washout admixture (AWA) concentration. Although accurate and reliable results can be drawn from conventional experiment researches, high cost and difficulty in controlling the experiment procedures are non-negligible obstacles. Given the shortcomings mentioned above, numerical simulation as an alternative methodology for scientific researches and engineering applications is gaining popularity, in which investigations on rheological and mechanical properties of cement-based grouts are of vital importance. Yahia and Khayat [12] used a modified Bingham model which was expressed as a second order polynomial equation to derive the relationship between yield stress and plastic viscosity. In addition, Svermova [13], Celik [14] and Sonebi [15] fitted the rheological properties of cement-based grout mixed with different additives through the same modified Bingham model. Mohammed et al. [16] used a Vipulanandan rheological model to predict the relationships between shear stress and shear strain rate for cement-based grout modified with two types of polymer with w/c of 0.6 and 1.0. Nevertheless, it is generally ignored in the aforementioned literatures the rapid change of rheological properties for fast-setting cement-based grouts. Setting time reduction improves the initial strength of grouts [7], thus contributing to greater dilution and washout resistance against water flows. Given that previous constitutive models are unable to accurately fit the time-varying characteristic of the new grouts, developing a new time-varying viscosity model is urgently needed for CFD simulations. To evaluate the washout resistance, a study has been conducted to address the research gaps outlined above by investigating the time-varying viscosity of two new types of cement-based grouts, namely KC-1 and KC-2. The two new grouts are able to adjust the setting time at will for practical needs while maintaining their integrity and fluidity. OpenFOAM, serving as a CFD solver, was employed for numerical simulations, and the Euler-Euler approach was used for water-grout flow. In the sections below, a summary of the experimental procedures, involving material properties and simulation methods, is firstly introduced, followed by a discussion on the simulation results.
2. Materials 2.1. Admixtures Conventional grouts are formed by adding to plain cement with bentonite, fly ash and water reducer, while the new grouts are composed of cement incorporated with organic polymer chemicals. To be specific, accelerators and flocculants are the two main admixtures. Generally, setting time is affected by the proportion of accelerators through a series of chemical reactions, whilst the yield stress and plastic viscosity are adjusted by flocculants. According to the work of Cheng et al. [7], the viscosity of conventional grouts changes very slowly against time, while the perfor-
mance of the new grouts is effectively controlled by the compound of the additions. Anti-washout admixtures modify the grout properties and help to enhance the cohesion and stability of cement-based systems [4]. Such admixtures, that enhance the water retention capability and the anti-dilution property, make the grouts resist the washout from water flows durably. Based on the method in [17], we improved and proposed two types of cement-based grouts named ‘‘KC-1” and ‘‘KC-2” with different admixtures. To determine the optimal admixture dosages, tests were carried out including measuring the setting time, yield stress, compressive strength, plastic viscosity and fluidity under a constant condition with temperature of 23 ± 2 and humidity no less than 95%. The initial setting time, during which a setting needle sinks to the bottom of a 4 ± 1 mm-thick grout, ranges from 10 to 20 min for KC-1 and from 15 to 30 min for KC-2. It was specified the w/c to 0.5 in the mixtures design. Table 1 summarizes the mix proportions of the investigated grouts. In KC-1, the addition amount of accelerator and flocculant accounted for 5% and 2.05% of the cement mass respectively. The amount of accelerator and flocculant added to KC-2 was 2.5% and 12.5% (7.5% bentonite involved) respectively. 2.2. Rheological properties In this section, the rheological properties of KC-1 and KC-2 at different hydration time were tested using a rotational viscometer. In total, ten samples were prepared and each sample had the volume of 350 mL. The hydration time was 2 min, 5 min, 10 min, 20 min and 30 min, respectively. In a rotational viscometer, a motor is utilized to drive the outer cylinder to rotate. By controlling the rotation speed of the outer cylinder, the grout between the inner and outer cylinders is sheared under different shear rates. The inner cylinder shear torque at the corresponding shear rate is measured by a torsion spring connected to the outer cylinder. By adjusting the magnitude of the shear rate, measured shear stresses were recorded. The rheological properties are fitted with the Herschel-Bulkley model [18–20], which is often used to describe the rheological behavior of concrete and grout. The shear stress is expressed as:
s ¼ s0 þ Kc_ n
ð1Þ
where s0 is the yield stress, K is the grout’s consistency, c_ is the shear rate and n is the flow behavior index. Ruan [21] investigated the viscosity of several materials and found that the yield stress of cement-based grouts turns out to be almost a fixed value as hydration time increases. In this paper, only the time-varying characteristic of the consistency is considered and expressed in the form of an exponential equation by fitting obtained experimental data. Meanwhile, the yield stress and the flow behavior index are used as inputs for numerical simulations. Figs. 1 and 2 show the rheograms of KC-1 and KC-2 at the initial time under different shear rates respectively. By fitting two scatter plots with the Herschel-Bulkley model, the relationships between the shear stress and the shear rate are described clearly. Rheological parameters are listed as follows: s0 = 360 Pa and n = 0.9118 for KC-1; s0 = 50 Pa and n = 0.8751 for KC-2. Additionally, the fluidity Table 1 Mix proportions of the fast-setting cement-based grouts. Mix
KC-1(%)
KC-2(%)
Cement Water Accelerator Flocculant
63.674 31.837 3.184 1.305
60.606 30.303 1.515 7.576
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
3
Fig. 1. Rheogram of KC-1 at initial time.
Fig. 2. Rheogram of KC-2 at initial time.
of the fresh cement-based grouts was measured using a slump cone with an upper diameter of 36 mm, a lower diameter of 64 mm and height of 60 mm. The mold was lifted vertically to spread out of the fresh grouts on a horizontal base plate. And the average spread diameter at the end of the flow was measured, shown in Figs. 1 and 2. The spread diameter is 13.87 cm for KC-1 and 14.92 cm for KC-2. Larger spread diameter means higher fluidity and spreading ability. In other words, KC-2 provides better workability and injectability than KC-1. A series of experiments were carried out at the 2nd, 5th, 10th, 20th and 30th minutes before KC-1 and KC-2 reaching their steady states. The experimental data scatters, the fitting curves and the fitting equations of KC-1 and KC-2 are shown in Figs. 3 and 4. Under the premise that the yield stress and the flow behavior index are constant (KC-1: s0 = 360 Pa and n = 0.9118; KC-2: s0 = 50 Pa and n = 0.8751), the consistency coefficient increases with hydration time growing in half an hour. It can be seen that as the hydration time increases, the magnitude of the consistency coefficient of KC-1 changes more rapidly, demonstrating its lower workability once again. The evolution of the consistency coefficient against time due to hydration is depicted in Fig. 5 and obtained by exponential equations for KC-1 and KC-2 as follows:
KKC - 1 ¼ 0:4172e0:0012t
ð2Þ
KKC - 2 ¼ 0:4077e0:0009t
ð3Þ
3. Numerical investigation of grout behavior 3.1. Modification of viscosity model in OpenFOAM CFD work conducted in this study was achieved with opensource software OpenFOAM in Ubuntu 16.04. OpenFOAM is primarily a CFD package written in C++ for the customization and extension of numerical solvers for continuum mechanics problems. It is used to create executables by utilizing classes and templates to manipulate and operate scalar, vectorial and tensorial fields [22]. OpenFOAM provides pre- and post-processing environments. The interface to the pre- and post-processing are built-in OpenFOAM utilities, thereby ensuring consistent data processing across all environments. Programming languages that are object-oriented, such as C++, provide the mechanism, i.e. classes, to declare types and associated operations that are part of the verbal and mathematical languages used in science and engineering. In OpenFOAM, the viscosityModel
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Fig. 3. Rheogram of KC-1 at different times.
Fig. 4. Rheogram of KC-2 at different times.
Fig. 5. Effect of hydration time on consistency coefficient.
is an abstract base class. Among the viscosityModel are inherited subclasses, i.e. incompressible viscosity models, which are available to be re-used, designed and bug-fixed for specific tasks. In
order to achieve the simulation results, a new class including time-varying parameters for non-Newtonian fluid’s viscosity is essential. In this paper, a new time dependent and shear-rate
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
related viscosity model named timeSlurry was coded and compiled as the exponential equations shown in Fig. 5. The dependency of yield stress obeys the following equations:
sKC - 1 ¼ 360 þ 0:4172e0:0012t c_ 0:9118
ð4Þ
sKC - 2 ¼ 50 þ 0:4077e0:0009t c_ 0:8751
ð5Þ
CFD is widely employed to simulate the details of fluid flows. In this study, the Euler-Euler approach, in which the fluid volume is discretized into several small control volumes, was used for the water-grout flow [23–26]. A flow field is characterized by balance in mass, momentum, and total energy governed by the continuity equation, the Navier-Stokes equations, and the total energy equation. The continuity equation is given by:
ð6Þ
ð7Þ
! where p is pressure, s is viscous stress tensor and F refers to interfacial forces. The viscous stress tensor s is defined according to the Newtonian formulation.
s ¼ 2lS S ¼
1 ! !T rt þ rt 2
ð8Þ ð9Þ
where S is the rate of strain tensor and l is the coefficient of dynamics viscosity. In our study, s is expressed by Eqs. (4) and (5) mentioned above. The total energy equation is given by:
@ 1 1 q e þ t2 þ r q! t e þ t2 @t 2 2 ! ! ! ! ¼ r ðkrT Þ þ r p t þ s t þ t F þ Q
ð10Þ
where T is temperature and e is the internal energy per unit mass. The two phases (water and grout) interact through the drag and lift forces acting between them, as well as through heat and mass transfer. Owing to the presence of more than one phase, the simulation in a two-phase system is more complex compared with that in single phase flow. In the Euler-Euler approach, the complicated mixture, where the interactions between each other need to be interpolated, is solved on the basis of the Volume of Fluid (VOF) method, assuming that the fluid acts as a continuum throughout the domain. In VOF method, the interface between the phases is tracked by the volume fraction of phase k, ak. The volume fraction equation is the continuity equation of phase k divided by the density of that phase, and its discretization is crucial for obtaining a sharp interface.
1 @ðqk ak Þ ! þ r qk ak t k ¼ 0 @t qk
np X
ak ¼ 1
ð12Þ
where np is the total number of phases. The fluid properties, such as density and viscosity, are calculated by their volume weighted average.
Ueff ¼
np X
ak Uk
ð11Þ
The benefit of using volume fractions is that only a scalar convective equation needs to be solved to propagate the volume fractions, and hence interface or topological changes are tracked with time in the computational domain. The volume fraction equation indicates whether a chosen phase is present inside the control
ð13Þ
k¼1
In this study, VOF is implemented between the phases to capture the free interface of the grout. To do this, the transport equations are solved for mixture properties, assuming that all field variables are shared between the phases.
@C ! þ t rC ¼ 0 @t
! where q is density and t is velocity. The momentum equation is given in the form:
! ! @ðq t Þ !! þ r ðq t t Þ ¼ rp þ r s þ F @t
volume. If ak = 1, the control volume is completely filled with the chosen phase; if ak = 0, the control volume is filled with a different phase. A value between 0 and 1 indicates that the interface between phases is present inside the control volume. The sum of the volume fractions for each phase must be one, which is described as follows:
k¼1
3.2. Numerical model
@q ! þ r ðq t Þ ¼ 0 @t
5
ð14Þ
Then an advection equation for the fraction function is solved. This is given by Eq. (15) where Cf denotes the volume fraction flux. The advection can be made much more accurate by reconstructing the function in each cell before finding the fluxes. n Cnþ1 i;j;k ¼ Ci;j;k ðC fe C fw þ C fn C fs þ C ft C fb Þ
ð15Þ
The flow chart of the simulation is covered in Fig. 6. In this study, a transient simulation was conducted with the consideration of the gravity effect and the assumption that no mass transfers between phases. CFD method is usually performed in four steps [27]. Firstly, numerical model describing the flow domain is established by means of abstraction and simplification. Secondly, a numerical discretization method is selected for governing equations, such as finite difference method, finite element method and finite volume method. The third step is to create the numerical network and define the initial and boundary conditions. Finally, post-processing is performed to visualize the results. Details of computational geometry, grid and boundary conditions will be discussed below in section 3.4. 3.3. Numerical validation In order to verify the reliability of CFD, the fluidity test of the new cement-based grouts was simulated, and the results were compared between the experimental tests and the numerical simulations. Firstly, a circular truncated cone filling with grout was modeled. The yield stress, the consistency coefficient and the flow behavior index of fresh grout at the initial moment were used as input parameters in OpenFOAM. Fig. 7 shows the shapes of KC-1 and KC-2 at the end of the flow. The diffusion radius given by numerical simulation is 6.91 cm for KC-1 and 7.42 cm for KC-2, respectively. The errors with the true values are both around 0.5%. Therefore, it is validated that the calculation result for the fluidity is in good accordance with the experimental result. 3.4. Geometry and boundary conditions As shown in Fig. 8, the 3-D pipe for washout resistance test is devided into four functional sections: the water-inlet section, the grout-inlet section, the test section and the outflow section. Detailed dimensions of the geometry are referred to in the figure, which were discretized into finite elements with the size of 0.01 m.
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Fig. 6. Flow chart of simulation.
There are two inlet boundaries, namely velocity boundaries, for inflow water and grout respectively, and one outlet boundary for both of them. For the initial condition (t = 0 s), the whole domain
is filled up with still water. From then on grout is injected by specifying the inflow speed of 0.1 m/s from the top portion along the –z direction for the first 30 s. Grouting stops at the 30th second, and
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
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Fig. 7. Spread radius at the end of the flow.
Fig. 8. Geometry and mesh.
the grout-inlet boundary changes into a symmetrical boundary in the next 570 s (t = 30–600 s). The magnitude of inlet water velocity stays zero until the grouting stops. Then it changes into a gradient, i.e. 0.1 m/s, 0.5 m/s, 1.0 m/s, 1.5 m/s and 2.0 m/s, along the x direction in each set of the numerical simulations. After the injection is completed (t = 30 s), the washout resistance within the last 570 s is under observation. 4. Results and discussions The main purpose of the current study was to explore the washout resistance of KC-1 and KC-2 under different water velocities. Detailed comprehension of the washout resistance can help with the prediction of its behavior in engineering. Therefore, in this section, the grout injection velocity of 0.1 m/s was designated as a representative case. First presented is the shape evolution combined with moving distance. Then the variation of volume amount combined with final residual rate is discussed. Both are investigated to characterize the washout resistance. 4.1. Shape evolution and moving distance Figs. 9 and 10 show the typical shape evolution of KC-1 and KC2 in x-y plane at different time intervals, which evaluates the washout resistance intuitively. Grout with more scattered shape indicates the process of a worse washout resistance. In addition,
moving distance of grout was measured (Fig. 11), i.e. the displacement of the centroid from t = 30 s to t = 600 s. It is presented in Fig. 11 the comparison between KC-1 and KC-2 at different water velocities. With moving distance of 0.02 m and 0.03 m for KC-1 and KC-2, it can be observed that the influence of low water velocity (t = 0. 1 m/s) on grout shape can almost be ignored. The initial grout shape basically kept well until the 600th second with slight changes in the shape of the upstream grout due to the direct damage by water flows. In this occasion, washout resistance was adequately possessed by the two new grouts. With the water velocity up to 0.5 m/s, the grout continued to move downstream. However, the stability of both KC-1 and KC-2 was still well maintained. As the velocity reached 1.0 m/s, the centroids of KC-1 and KC-2 moved downwards by 0.14 m and 0.18 m. When the velocity increased on this basis, the grout gradually scattered apart and the shape was severely affected accompanied by a large deviation from the original position. The grout failing to solidify in the upper part of the accumulation layer was more washed away by velocity over 1.5 m/s. Compared with the previous cases of water velocity below 1.0 m/s, the grout no longer deposited effectively and the shape at the 600th second changed significantly. As the velocity increased to 2.0 m/s, it is reasonable to predict that almost all of the grout will be washed out of the pipe if the observation continues. In general, KC-1 performs better washout resistance than KC-2, and the difference is more significant when the water velocity is
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W. Cui et al. / Construction and Building Materials 242 (2020) 117959
Fig. 9. Shape evolution of KC-1.
Fig. 10. Shape evolution of KC-2.
higher than 1.0 m/s, which can be concluded easily from the enlarged vertical distance between the two curves as shown in Fig. 11. 4.2. Volume amount and final residual rate A key indicator for evaluating washout resistance is the volume amount (V) of grout remaining in the pipe with the accumulation of time steps (Figs. 12 and 13). The curve, that indicates the injection amount, reaches peak at 30 s (Vmax) and keeps unchanged after grouting completed. Residual rate (g) is another quantitative characteristic, which is defined as:
g ¼ Vfinal =Vmax
ð16Þ
where Vfinal refers to the volume amount of grout remaining at the 600th second of each simulation. Through the residual rate, the volume amount of the remaining grout can be expressed clearly. When the velocity reached 0.1 m/s, the integrity of the grout was well preserved with the residual rates both more than 90%. In consequence, the velocity of water through the pipe was slowed down significantly, indicating good plugging performance. Both the final residual rates were above 85% when the velocity reached 0.5 m/s, accompanied by relatively gentle slopes in the descent of residual rate. When the velocity reached 1.0 m/s, part of the grout
W. Cui et al. / Construction and Building Materials 242 (2020) 117959
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Fig. 11. Moving distance of KC-1 and KC-2.
Fig. 12. Volume amount of KC-1.
was washed out of the pipe by the water flow with the edge diluting slightly. But the residual rates of 75% and 71% respectively were at least in line with the requirements, with a little washout volume loss. As the velocity increased to 2.0 m/s, the remaining volume amount of the grout was the least. In this occasion, only 54% of KC-1 and 45% of KC-2 stayed in the pipe. By horizontal comparison, KC-1 always kept more amount in the pipe, showing a higher residual rate than KC-2 on the whole. Similarly, the difference is more significant with the increase of the water velocity, especially after 1.0 m/s. 4.3. Washout resistance evaluation Fig. 11, showing the moving distance versus water velocity, reveals that the moving distance increases slowly when the water
velocity is lower than 1.0 m/s. The distance between the final position and the original position is short as demonstrated. When the water velocity exceeds 1.0 m/s, the increasing trend begins to accelerate. Another observation is that, by examining the trend of final shape variation at 600 s as shown in Fig. 9, the diffusion size of KC-1 increases firstly (with velocity no more than 0.5 m/s) and then shows a noticeable decrease in width (with velocity over 0.5 m/s). The same phenomenon applies to KC-2, which is attributed to the fact that the grout has not fully diffused while part of them is taken away. Analysis of volume amount in Figs. 12 and 13 indicates that washout resistance of grout is getting worse as the velocity increases. The grout withstands washout effectively when the velocity is no more than 1.0 m/s, with the residual rates of 70% guaranteed. KC-1 and KC-2 totally lose efficacy as the velocity reaches 2.0 m/s.
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Fig. 13. Volume amount of KC-2.
Another point to note is that, considering the better maintained integrity and the more satisfying residual rate, KC-1 is a more leading grout to be used in high hydrodynamic pressure conditions. However, its high viscosity (as depicted in Fig. 5) gives rise to low fluidity and low workability, which means a high-pressure grout pumping system is essential when grouting. The washout resistance of KC-2 is sufficient in seepage control for foundation under general water inlet conditions. With the cooperation of solid materials, KC-2 can block the rest of the small leakage channels, which is superior to conventional cement grouts. 5. Conclusions Firstly, the rheological properties of the fast-setting cementbased grouts were analyzed as the focus in this paper. Then, a CFD approach was chosen to study the washout resistance. The shape evolution combined with moving distance and the variation of volume amount combined with final residual rate were obtained under different water velocities. The following conclusions were summarized based on the investigations. (1) The rheological properties of KC-1 and KC-2 are determined based on the Herschel-Bulkley model. The variation of the consistency coefficient with hydration time in the equation is considered, which is described by exponential equations. KC-1 has a larger consistency coefficient and a faster growth rate, as is reflected in the fact that its flow behavior index n is larger than that of KC-2. (2) When injected at 0.1 m/s, the grout maintains integrity and effectively resists the washout against the water flow at no more than 1.0 m/s, obtaining a residual rate above 70%. The grout is washed away by the water flow over 1.0 m/s, with no longer capability to deposit at the bottom of the pipe. Some supplementary measures are needed to ensure the success of grouting in this occasion. For example, filling the pores with an appropriate amount of gravel graded aggregate can be conducted. (3) KC-1 performs better washout resistance especially in high hydrodynamic pressure conditions attributing to its shorter setting time and better long-term durability, but overall it
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