Algorithm for selecting a concrete pump in the construction of high-rise buildings

The use of concrete pumps in construction allows you to reduce manual labor and use additive technologies significantly. But this imposes several requirements on the rheological properties of cement materials. 3D printing using cement materials is an emerging technology and represents an active area of research. Rheological studies are important for successful 3D printing of concrete. The main task for successful 3D printing is the good characteristics of concrete. It must be sufficiently fluid to be pumped through the hose and gain sufficient strength and rigidity to build up after layer-by-layer deposition [1]. Despite this, only limited studies of the pumping behavior of fluids with high yield strength, such as printed concrete. The paper [2] presents the results of a study of the rheological behavior of cement materials for 3D printing with a different ratio of aggregate to a binder. An increase in this ratio leads to a significant increase in the plastic viscosity and a nominal increase in the yield strength.

To facilitate the study of the rheological properties of cement materials, researchers [3] modified a commercial bench-mounted three-dimensional printer for the production of fused filaments (3-D) for dosing cement paste mixtures. The changes included the design and assembly of the pumping system and the modification of the 3-D printer firmware software necessary to accommodate the new equipment.

In the study [4], a slag-based mixture was developed as a cementless material for stable spray 3D printing. To obtain the optimal mixture, the effect of the addition of MgO and fly ash to the cenosphere on the setting, hydration, and rheological properties of fresh mixtures were studied. The material with adapted rheology results in better feed and deposition performance of the mixture and improved spray printing quality.

In [5], the influence of a viscosity-modifying additive based on hydroxypropylmethylcellulose on 3D printing and mechanical characteristics of a cement material based on limestone and calcined clay was studied.

In the study [6], the rheological behavior of cement pastes with nanotubes and various types of polymer plasticizing impurities was analyzed using a rotating rheometer with coaxial cylinders.

The rheological properties of the lubricating layer between the bulk concrete and the pump pipe wall are a key factor determining the pumpability of concrete [7, 8]. In the study [9], the rheological behavior of the lubricating layer was modeled in the form of a suspension of different volume content of fine sand (<1.25 mm) in viscoelastoplastic cement pastes, namely, fine solutions.

The results obtained showed that an increase in the content of fine sand increases the relative viscoelastic properties of the studied mixtures. Several studies on the quantitative prediction of concrete pumping using the rheological properties of concrete and the lubricating layer have been conducted [10]. It was found that the pressure loss in the bends of the pipes is about twice large as in the straight pipeline.

It is shown [11] that knowledge of the actual thickness of the lubricant layer, its rheological properties, and the type of flow is sufficient to predict the behavior of pumping fresh material.

Particle migration is essential for both fluid, and very fluid concretes with a high volume fraction of solid particles. Changes in the rheological properties are serious enough to affect the determination of the flow structure and the injection rate of the pumped concrete [12].

The most important task is to find acceptable rheological properties for applications such as cementing oil and gas wells, where it is necessary to pump cement mortar [13].

The paper [14] presents an experimental study of the influence of the binder type, content, chemical properties of water, and temperature on the rheological properties of the cemented paste material obtained using additives from a copper mine in South Australia.

In order to reduce friction or improve pumpability, in [15] various ultrafine powders are introduced into a high-flow concrete mixture with a low water-binder ratio as a substitute for cement.

The use of a large amount of fly ash in cement-sand solutions significantly increases the fluidity of cement-sand solutions [16].

A set of rheological tests was carried out to assess the torque required for the rotation of steel fibers immersed in various fresh cement pastes and mortar mixtures with the behavior of the Bingham liquid [17]. Fibers with different aspect ratios (length/width) and different geometries, straight and hooked, were rated as the most commonly used. On the other hand, various parameters (the type of mixture, the size of aggregates, the volume fraction of aggregates) that affect the cement mixtures are analyzed, and their influence on the orientation of the fibers is discussed.

Adding superplasticizers to cemented paste can improve its rheological properties and facilitate pumping operations [18].

The properties of shotcrete with different fiber lengths were tested. The proportionality coefficients of the wet shotcrete mixture were analyzed to obtain the optimal proportions of the wet shotcrete mixture [19].

The concrete pumps methods of the distribution of concrete mixtures increase the quality and efficiency of concrete work in the construction of a wide variety of monolithic and prefabricated monolithic structures in industrial, civil, hydraulic, rural, and other types of construction [20,21].

Laying of a concrete mix by concrete pumps includes the acceptance of a concrete transport unit from the concrete mixing equipment into the loading hopper, pumping the mixture through the concrete guide to the place of laying, its distribution in the concreting zone (using flexible hoses or distribution arrows), and related maintenance work for this process [20,21].

Among modern concrete pumps, the most popular are concrete piston pumps with a hydraulic drive that provides smooth operation with reliable performance control, the ability to reverse and feed the mixture through lightweight concrete guides mounted on articulated boom arms with remote control.

Stationary piston concrete pumps are widely used in the construction of high-rise buildings [22,23]. The value of the piston pressure on the concrete is its main characteristic. The piston pressure of the reciprocating concrete pump on the concrete mixture should choose considering the pressure losses in the pipeline during the transportation of the mixture and changes in the performance characteristics of the concrete pump under load. Determining the hydraulic losses in the concrete guide remains relevant at present. Hydraulic losses in the pipeline depending on the specific resistances to the movement of the concrete mixture, the total length of the concrete pipeline, the size of its vertical section, and the local pressure losses in the transition cone bends [20-23]. The work aims to develop an algorithm for selecting a concrete pump that considers the rheological characteristics of the concrete mixture, the hydraulic resistance of the network in the construction of high-rise buildings.

2    Materials and Methods

The main stages of selecting a stationary piston concrete pump using performance diagrams were described in [24, 26]. However, the difference between the actual pump supply and the theoretical one was not taken into account. Previously, it was shown that it is necessary to use the performance characteristics of pumps to select their parameters that correspond to the construction conditions.

The first stage is a preliminary calculation of the pressure drop in the concrete guide at a given feed of the mixture Q . The hydraulic characteristic of the concrete pipeline is the dependence of the pressure drop on the supply of the mixture [20]:

p = f_Q = ap + удНдЛР = ap_l + ap_m ,

where ΔP L , ΔP M are pressure losses along the length and in local resistances when transporting the mixture through the concrete guide, respectively, Pa; γ is the volume mass of the concrete mixture, kg/m³ ; g is the acceleration of free fall, m/s²; H is the height of the concrete mixture feed, m.

In order to be able to use the calculation method more widely, including for modified concrete mixes, it is necessary to use a rheological model. Several known rheological models are used to calculate the pressure loss along the length of the pipeline when pumping concrete mixtures.

The Buckingham-Reiner formula (see, for example, [23, 27]):

nd ⁴ AP_L [   4 / 4Lt₀ \  1 / 4Lt₀ VI

$ = 128^ L ^[1 - 3(dAP_L ) ⁺ 3(dAP_L ) ^],

where d, L are the diameter and length of the concrete conduit, respectively, m; τ0 is the ultimate shear stress, Pa; µ is the plastic (structural) viscosity, Pa·s.

It was previously established (see [27]) that the calculation of hydraulic losses in the concrete guide by formula (1) gives results more than 3 times higher than the experimental data. It should note that the similar to (2) formula does not have the diameter d in the denominator of fractions in some publications. Also, there is no π multiplier in [23].The results of calculations based on the Kaplan model are in much better agreement with the experimental data:

AP= 4 ^L(_T£ + ^p) , d V ^c nd² k /

AP =

(4Q dTtdig X т , лД2к ВЦ 60^\

Tt +    1+nd

8Ц/

where k is the fill factor, in the first approximation it can be taken to be equal to one.

Formula (3) is intended for the case when the shear stress on the pipe wall is less than the yield strength; otherwise, formula (4) should be used.

For the application of formulas (3), (4), in addition to the previously specified values, it is required to determine with a tribometer the additional parameters τ t (Pa) and η (Pa•s/m) on the surface between the inner cylinder and the concrete mixture. In case of their absence, it is necessary to carry out their estimated calculation. Replace in (3) τ t by τ 0 , the parameter η is found by the approximate formula η ≈µ/δ, where δ is the thickness of the wall layer:

H

^П “ ⁰ , ^5d-W 7T)

.

From dependencies (3), (5), it follows nd2 di   2TgL\ ZAPd     \

^e=irl2-7rJ hr^-T0) .

From (6) follows the quadratic equation in dimensionless form

Ap² - 2(0 + 1)Ap + 1 = 0, Ap = —, 0 = 4^^- .

^{1        v        v 1                  1}     4Lt₇'        nd³T _g

The solution of the quadratic equation (7) allows us to calculate the dimensionless pressure Δp from the relative flow rate Θ:

Др = / 1 (0) = 1 + 0 + ^(1 +0) 2 -1 .                                 (8)

Let us consider some features of the determination of hydraulic pressure losses in local resistances Δ P M .

In [20], a table is given with experimental data on hydraulic losses depending on the speed of the mixture and the radius of the elbow (rotation by 90°) R . For example, if the speed in a concrete guide with a diameter of d =100 mm is 0.5 m/s, then at R =0,5 m Δ P k = 39,33 kPa, and at R = 2 m Δ P k = 52,47 kPa. It turns out a paradoxical picture; with an increase in the radius of the knee, hydraulic losses increase. In [28], it was shown that the losses per meter of the arc AB (see 1) decrease with increasing arc radius. But this does not solve the problem, as it does not explain why the absolute losses increase. To explain the resulting paradox, consider the diagram in Fig. 1.

In the experiments in [20], the pressure drop in the pipeline between sections A and B was measured. But the larger the radius of rounding of the elbow, the smaller the pipeline's total length. Reducing the length of the pipeline

ДL = |ЛС| + |СВ| - |ЛВ| = 2R- 0,5hR = 0,43R .

The pipeline losses on the length Δ L from the Δ P k are subtracted to find the hydraulic losses of Δ P ko at the elbow:

^Д Р к0

0,43RДP!

= ДР_к--

In the example of the calculation from [20], the specific hydraulic losses along the length of the concrete pipeline ΔP L /L = 24,9 kPa/m. Then, from the formula (9), for R =0,5 m, the Δ P Ко = 34,0 kPa is obtained; for R = 2 m, the Δ P Ко = 31,0 kPa. In the latter case, the hydraulic losses are 9,7% less, which corresponds to the physical meaning. But such a decrease can hardly be considered significant, given the low accuracy of the DRC definition. Moreover, this approach does not take into account the rheological properties of the concrete mixture.

Fig. 1. Diagram of the concrete pipeline elbow

Another approach [20] suggests increasing the actual length of the concrete duct L by 9 m for each knee and increasing the estimated length of the transition cone L C by 3-4 times. The use of the reduced length of the concrete guide L П in the calculations allows us to take into account the rheological properties of the mixture:

L_n=L + 9k + 3,5L_C .

where k is the number of elbows, L C is the length of the transition (distribution) cone.

Next, this approach was used to calculate the local hydraulic losses in the concrete guide.

The second stage is to determine the parameters of the piston concrete pump that correspond to the construction conditions. The technical documentation provides diagrams with the pump QT's theoretical performance (flow) (see Figure 2). It is related to the actual flow at a pressure drop P according to the formula:

Q = Q_Tf 2 (P),f 2 (P) = 1- ⁽¹ _p ^K)P .K = ^Q^ , ^PH        ^QT

where K , Q H , P H are the volumetric efficiency, flow, and pressure drop in the nominal mode, respectively.

3    Results and Discussion

Example of the calculation. Let it be required to ensure the supply of concrete mix at least Q = 45 m³/h = 0,0125 m³/s. The stationary piston concrete pump will be used in the range of height differences and lengths of the concrete pipeline H min = 30 m, H max = 60 m, L min = 90 m, L max = 105 m. The inner diameter of the concrete pipe d = 0,125 m. The number of concrete guide bends kmin= 6, kmax = 11. The length of the transition cone L C = 3 m. Properties of the concrete mixture: τ 0 = 28 Pa, µ = 50 Pa * s, γ = 2200 kg / m³.

According to the formulas (7), (8) Θ = 14,55; Δp = 31,07. Then the specific pressure loss Δ P/L = 4τ 0 Δ p/d = 27,84 кПа.

Hydraulic losses at the highest height and length of the concrete pipeline

^ ^Pmax   ^ ^(Lmax +H max + 9 ^kmax ⁺ 3,^5L C ) ⁺ Yd^ max   9>935MPtl.

Let the pressure drop value Δ P max , calculated at the first stage correspond to the nominal pressure (that is, P / P H = 1). The volumetric efficiency (another name is the fill factor) allows you to calculate the theoretical supply of Q T for a given Q . However, in the manufacturers' technical documentation of reciprocating concrete pumps, there is no information about the efficiency. In [21], the values for the efficiency were obtained experimentally for one of the types of a piston concrete pump with a cone draft of 5-10 cm: K = 0,75. Then in the example by the formula (11) Q T = Q / K = 16.67 dm³/s.

In the working section of the pump performance diagram, the net power Nu, calculated from the theoretical supply, remains unchanged:

N_u = PQ_T = -^^-. u      М/     ^ _(p)

The formula (12) gives Δ P max · Q T = 148,9 kW. Therefore, it is necessary to choose a piston concrete pump in which the N u parameter has a value of at least the calculated one. Some manufacturers give the value of this parameter directly on the charts. For example, the performance diagram of the Putzmeister BSA 1409-D reciprocating concrete pump [29] shows a value of 140 kW, and the diagram of the JUNJIN JSP.90HP-D reciprocating concrete pump [30] shows a value of 147 kW. In the latter case, after recalculation according to the diagram (Fig. 3), a more accurate value was obtained for the specified pump N u = 150,0 kW, which fully satisfies the conditions of the example.

Fig. 2. Performance diagram of a reciprocating concrete pump

BSA 1409-D [29]: 1 – piston side, 2 – rod side

Fig. 3. Performance diagram of the stationary piston concrete pump JSP.90HP-D [30] on the rod side: 1-point corresponds to Δ P max , 2- Δ P min

In the high-flow mode (road side), according to the performance diagram, P H = 9.39 MPa. Higher pressure is not possible, as the safety valve is triggered.

The final stage is the recalculation of the parameters, taking into account the selected piston concrete pump. Characteristics of the concrete pipeline in MPa:

^iCOxi = 10 ⁶(AC——)"3— (L_max+H_max + 9k_max + 3,5L_C) + YgH_max).              (13)

• 1    X )              1      3              ШЛ     ZltUA          LLIA,           C             HL^A

The solution of equation (13) gives a refined value Q min = 12,64 дм³/с:

1S0,0f2(F1(Qx))

^Fi⁽ ° x) =     ^ooqa   .                                            ⁽¹⁴⁾

Similarly, (13), the function F 2 ( Q x ) is formed at the lowest pressure drop and the supply Q max = 16.49 dm³/s is calculated. Recalculating the differential pressure:

Δ P max , = F 1 ( Q min ) = 9,017 МПа; Δ P min = F 2 ( Q max ) = 7,321 МПа.

Next, the calculation can be performed for the next range of heights.

4 Conclusions

To increase the reliability of the calculation of the actual performance of the piston concrete pump, it is necessary that their manufacturers give the value of the filling factor, at least in the nominal mode.

Currently, it is almost impossible to choose a piston concrete pump according to the energy efficiency criterion, since the technical documentation does not show the dependence of the total pump efficiency (or the power consumed) on the pressure drop.