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Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.Nghiên cứu đặc trưng co ngót của bê tông sử dụng cát mịn phối trộn cát nghiền từ đá trong xây dựng cầu.
MINISTRY OF EDUCATION AND TRAINING UNIVERSITY OF TRANSPORT AND COMMUNICATIONS Nguyen Đuc Dung STUDY OF SHRINKAGE CHARACTERISTICS OF CONCRETE USING FINE SAND MIXED WITH CRUSHED SAND FROM ROCKS IN BRIDGE CONSTRUCTION Industry : Transport construction engineering Code : 9580205 SUMMARY OF DOCTORAL DISSERTATION Ha Noi – 2022 The project was completed at the University of Transport and Communications Science instructor 1: Associate Professor Dr Nguyen Duy Tien Science instructor 2: Dr Thai Khac Chien Counterargument 1: Professor Doctor of Science Nguyen Nhu Khai Counterargument 2: Professor Doctor of Science Nguyen Dong Anh Counterargument 3: Associate Professor Doctor Vũ Quốc Vương The thesis will be defended before the University-level dissertation marking board according to Decision No 2596/QD-UD on 22/ 12 / 2022 Meeting at: University of Transportation and Communications ……/ …./ 2023 The thesis can be found at the library: - Library of University of Transport of Communicaions; - National Library INTRODUCTION Research problem Currently, the source of golden sand used to make concrete in the Mekong Delta is increasingly scarce While fine-grained sand has abundant reserves, the grain magnitude modulus ranges from 0.7 – 2.24 [18] [9] The Mekong Delta (Mekong Delta) is in the stage of developing transport infrastructure, and a series of key projects have been implemented To overcome the scarcity of yellow sand, contractors used fine sand mixed with crushed sand as a solution to replace small aggregates in concrete fabrication [1] Although it has been commonly used, there are no standards or technical regulations for this material In projects, only experiments are carried out on the compressive strength of concrete; Studies of the influence of material properties on mechanical characteristics, shrinkage deformation, and the effect of shrinkage on the short-term and long-term behavior of concrete structures are rarely mentioned Mixed sand that mixes fine sand (CM) with crushed sand (CN) has different physical properties than natural sand due to the grains of crushed sand having an angular, convex surface shape and texture increases pore structure, increases surface area, increases water absorption and increases shrinkage deformation of concrete [4] [93] At an early age stress – deformation due to shrinkage can lead to the formation of cracks, reducing the aesthetics, durability as well as integrity of the structure, over time dry shrinkage leads to loss of pretension, increased sagging/deterioration of the camber of the structure, changes the stress on ultra static structures [16] [17] The road bridge design standard TCVN 11823 [34] states that "Bridges constructed by the segmentation method must calculate shrinkage deformation more accurately including consideration of the effects of specific materials, structural dimensions, site conditions, construction methods" Based on the research results published at home and abroad, based on the actual situation of using fine sand materials mixed with crushed sand to make concrete and the effects of shrinkage deformation on bridge works that have been and are being built in the Mekong Delta The dissertation proposes the selected research content is: "Research on the characteristics of shrinkage of concrete using fine sand mixed with crushed sand from stone in bridge construction" Subjects of the research - C40 grade concrete uses fine sand mixed with crushed sand The influence of fine sand material properties mixed with crushed sand on concrete's shrinkage characteristics and mechanical properties Effect of shrinkage on the long-term working of reinforced concrete beams Scope of the research - Studying the mechanical properties and shrinkage characteristics of C40 grade concrete using fine sand mixed with crushed sand applied in bridge construction - The study affects the long-term deformation of reinforced concrete beams and SuperT prestressed concrete Research Methodology - Research methods are mainly theoretical research combined with experimental Scientific and practical significance of the topic - The thesis provides a set of data on the properties of crushed sand materials, fine sand, mechanical features, and shrinkage characteristics of C40 strength grade concrete using fine sand mixed with crushed sand - Develop equations that relate the properties of materials to the mechanical features of concrete; Develop a formula for forecasting shrinkage distortion over time based on current standards - Develop the equation of the relationship between shrinkage deformation and the stress and deflection of reinforced concrete beams, and develop a formula for calculating the modulus of elasticity that works over time from the results of the shrinkage deformation experiment and the deflection of the beams - The application calculates the camber/ deflection of the super T beam due to shrinkage deformation and construction process and determines the time of construction of the bridge surface to ensure the camber of the beam during mining - Regarding practical implications: The thesis provides the necessary data on concrete using fine sand mixed with crushed sand with grade C40, meeting the urgent requirements for the calculation of bridge design and construction in the Mekong Delta From there, it is allowed to limit cracks in the reinforced concrete structure and reduce the deflection of the Prestressed reinforced concrete beam span structure CHAPTER OVERVIEW OF CONCRETE AND SHRINKAGE DEFORMATION OF CONCRETE USING FINE SAND MIXED WITH CRUSHED SAND FROM ROCK 1.1 Introduction to mixed sand material (fine sand mixed with crushed sand) - Fine sand (CM): According to TCVN 7570: 2006 [30] fine sand is sand with a modulus of magnitude from 0.7 ÷2.0 Fine sand in the Mekong Delta has a modulus of magnitude ranging from 0.7 ÷ 2.24 smaller than required for concrete fabrication according to ASTM C33[50] and AASHTO M6 [102] of 2.3 ÷3.2 - Crushed sand (CN): also known as artificial sand, production sand, ground sand, ground stone, Mi stone According to TCVN 9205: 2012, crushed sand is produced by grinding natural stones to satisfactory grain sizes used to make concrete and mortar, coarse sand with a modulus of magnitude from about 2.0 to 3.3 Crushed sand in the Mekong Delta has a particle magnitude modulus ranging from 3.6 ÷ 4.2 1.2 Research on concrete using fine sand mixed with crushed sand in the world Studies on the effects of crushed sand/river sand mixing ratios Studies suggest that the mechanical features and shrinkage deformation of concrete are affected by the mixing ratio of crushed sand with river sand, the CN content accounts for 50 ÷ 70% of the best concrete quality According to Altamashuddinkhan 2020 [61], the CN content accounts for 55÷100% of mixed sand, and the compressive strength of aged concrete reaches a higher value than other mixing ratios Figure 1.1 Yajurved 2015 [112] suggests that CN accounts for 60% of the increase in concrete strength compared to other ratios Figure 1.2; Author Y Boopathi 2016 [84] also showed that the optimal replacement rate is CN accounting for 60% Meanwhile, P.M.Shanmugavadivu 201 [98] said that the optimal ratio of CN accounts for 70% of Figure 1.3, lower than 70% CN of tensile strength when bending and the elastic modulus of concrete increases, exceeding 70% CN the tensile strength changes insignificantly but the elastic modulus decreases suddenly Figure 1.1 Rn chart by [61] Figure 1.2 Rn chart by [112] Figure 1.3 Ru chart by [98] According to P.M.Shanmugavadivu, 2012 [98] Figure 1.4, in the first phase of dry shrinkage of the highest crushed sand concrete, then the mixed sand concrete, the river sand concrete has the smallest value But in the final stage, the dry shrinkage of crushed sand concrete slows down, and the dry shrinkage of river sand concrete tends to increase It is found that the dry shrinkage in river sand concrete is less than that in crushed sand concrete, according to the majority of authors [93] [94] [109] [110] Studies on the effects of stone powder Artificial sand usually contains a stone powder of fine particles with size less than 0.075mm, without clay and mud According to Tahir Celik 1996 [92] if the content of stone powder is sufficient it will serve as a filler and help fill the gaps between the cement powder and the aggregate particles, which contributes to the improvement of the quality of the concrete However, the higher dust content in the aggregate will adversely affect the quality of the concrete, the shrinkage value is higher and is more sensitive to the Amnon Katz 2006 crack [64] According to Ahmad 1989 [63], crushed sand concrete containing 10% stone powder has the highest compressive strength; According to Tahir Clik[92] also shows that having 10% fine grains in crushed sand would create maximum compression strength and bending tensile strength, Amnon Katz explains that when the amount of stone powder is large, very small particles tend to stick to the surface of larger particles and prevent proper bonding between cement powder and aggregate, resulting in the formation of a weak aggregate bond that leads to cracking and weakening of concrete According to Dukatz 1985 [72] and ZHOU Mingkai 2009 [114] both argue that when the fine particulate content is 7% or more, the compressive strength of crushed sand concrete is equal to or higher than river sand concrete According to Nam-Shik Ahn 2001 [94] for the fixed proportion of cement water, most crushed sand concrete has a higher compressive strength than the river sand, and the compressive strength increases as the stone powder in the aggregate increases Figure 1.4 Shrinkage chart by [98] Figure 1.5 Shrinkage chart by [63] Figure 1.6 Shrinkage chart by [94] Ahmed and El Kourd 1989 [63] Figure 1.5 of the 330-day-old dry shrinkage experiment showed that the shrinkage deformation of concrete increased in proportion to the rock powder’s content in crushed sand, Dukatz's study agrees According to Tahir Celik [92] the dry shrinkage of concrete increases when the content of stone powder increases from ÷10% in crushed sand but beyond this value the dry shrinkage decreases Concrete using crushed sand with a high content of stone powder up to 20% shrinkage is about 10% greater than concrete using crushed sand with a stone powder content of 0% according to Dukatz, [72] Studies on the effects of base rocks on crushed sand properties According to Hudson 1997 [83], particle shape and surface texture will affect the sand's pore volume and frictional properties, thereby affecting the properties of concrete Gaynor (1983)[93] suggested that artificial sand is mostly angular and has a higher pore volume and water requirement than round-edged sand According to the authors Wenyan Zhang, and Mohamed Zakaria, [110] the surface area of aggregates which are made from different base rocks varies relatively widely, so the pore volume is also different According to Michael L Leming 2010 [93], if the ASTM C1252 porosity measurement method is applied, river sand has the lowest pore volume of just over 45%, and artificial sand has the highest pore volume of nearly 50% However, if using the imaging method, natural sand has a pore volume of only 44.1% while crushed sand has the highest pore volume of up to 55.7% According to Nam-Shik (2001), concrete samples which are made from river sand and different types of crushed sand give different shrinkage deformation According to authors Wenyan Zhang, Michael L Leming, and Mohamed tconcrete samples which are made from different types of crushed sand give different shrinkage deformation It is found that the dry shrinkage of river sand concrete is less than that of crushed sand concrete, according to the majority of authors [93] [94] [109] [110] 1.3 Studies on concrete using mixture of fine sand and crushed sand in Vietnam In Vietnam, standards related to crushed sand have been issued: TCVN 950: 2012 [31] crushed sand for concrete and mortar; TCVN 9382:2012 [32] Technical instructions for selecting concrete components using crushed sand According to Prof Dr Nguyen Thuc Tuyen, crushed sand has been used in Vietnam since the early years of the 21st century at the construction of the Son La hydropower plant, sand is produced at Ky Son quarry, Hoa Binh province, and this crushed stone sand is made from Granite According to the research results of Dr Nguyen Quang Cung (2004) [4], crushed sand can completely or partially replace natural sand in concrete According to Prof Dr Pham Duy Huu [9], the main source of sand in the Mekong Delta is only the Tan Chau sand mine In the Southeast region, many quarries have large reserves with very good quality In general, natural materials in the Southern region are in line with the standards of developing high-quality concrete for construction and transport construction projects According to author Le Van Quang [18] fine sand from Mekong Delta has a magnitude modulus ranging from 0.7 ÷ 2.24, Tan Chau sand mine has the best quality Mk from 1.6 ÷ 2.24, then Hong Ngu Mk sand mine from 1.28 ÷ 1.56 Studies[18] [27] [11] all believe that the amount of crushed sand accounts for 50÷70% of the highest grade of concrete According to Dr Nguyen Duc Trong [23] with C20 ÷ C36 concrete grades applied in constructing cement-concretepavement, when the amount of ground sand in the sand mixture accounts for 50 ÷ 60%, it will become the suitable grain composition that meet the road design standards According to the study of author Vu Quoc Vuong [28] on self-compacted concrete using crushed sand containing large amounts of stone powder, in the early stages before 28 days, the shrinkage is almost inversely proportional to the content of stone powder but after 28 days shrinkage increases as the content of stone powder increases Authors Le Van Quang and Nguyen Duc Trong also showed that the shrinkage deformation of river sand concrete is smaller than the shrinkage deformation of concrete using mixture of fine sand and crushed sand 1.4 Studies on the effect of shrinkage on long-term deformation of prestressed reinforced concrete and reinforced concrete beams According to R Mu, and J.P Forth 2008 [99], besides load and temperature, shrinkage and magnetic variables are the main factors affecting the curvature of reinforced concrete crosssections The British standard BS, 8110-2 [68] and Eurocode2 [72] proposed the equation for predicting curvature due to shrinkage deformation of reinforced concrete beams Hobbs [88] also gave a model of the curvature of beams due to shrinkage Ghali and Favre also built models to predict the curvature of cracked parts According to Prof Dr Tran Duc Ren 2016 [16] [17], Super T beams appreared to lose the curvature after a period of time This problem has happened in many important projects, although it has not affected the load capacity, or degraded the quality of the structure However, from the perspective of project management and operation this issue raised concerns., The cause includes two nestnests of influencing factors: the properties of beam materials and the order of fabrication and construction of beams From this analysisresults, it is suggested that the shrinkage factor should be considered in the camber calculation and it is needed to to develop a standard construction process for the prestressed concrete beam span structure to ensure a camber according to the design CHAPTER THE THEORETICAL BASIS FOR STUDYING SHRINKAGE DEFORMATION OF CONCRETE USING FINE SAND MIXED WITH CRUSHED SAND FROM ROCK 2.1 Concrete shrinkage Shrinkage in concrete can be defined as the volume change observed in concrete, because of the loss of moisture at different stages due to different causes Shrinkage can be classified as follows: Flexible shrinkage; Dry shrinkage; Heat shrinkage; Autogenic shrinkage and carbonate shrinkage[7][8][9] 2.2 Factors affecting concrete shrinkage deformation using fine sand mixed with crushed sand Factors affecting shrinkage deformation were compiled in ACI 209.2R[37] and Vietnamese standard TCVN 11823[34], concentrated in the following eight nests: The effect of aggregates According to Wenyan Zhang 2013 [110], and Fanouraki 2014 [79] shrinkage properties are not only related to the mass loss of capillary water but are also affected by small aggregate physical properties Their content and characteristics account for significant value for dry shrinkage deformation of concrete According to the studies mentioned in Chapter One, the properties of mixed sand concrete are changedbecause the crushed sand grains have a concave, rough surface, so that the surface area, water absorption, rate, and pore volume are different to that of river sand grains which have undergone natural weathering and abrasion, these properties directly affect the shrinkage deformation of concrete… Adjustment factor considering the effect of fine aggregates according to ACI209.2R: sh, 0,3 0,14 if ψ ≤ 50 ; sh, 0,39 0,002 if ψ ≥ 50% (2.1) Ψ is the ratio of fine aggregates to the entire aggregate Effects of cement Cement is one of the components that cause large shrinkage deformation in concrete, the coefficient adjusted to the cement mass according to ACI209.2R: (2.2) sh,c 0,75 0,00061c c is the volume of cement / 1m3 of concrete (kg/m ) Effect of water/cement ratio According to the studies in Chapter 1, crushed sand often needs a high amount of water requirements to ensure slump, the increased water demand must be offset by the increased amount of cement to maintain the N / XM ratio, increasing the amount of capillary water and increasing dry shrinkage In addition, the increased demand for water is also due to the content of stone powder in crushed sand Coefficient adjusted through the slump of fresh concrete: (2.3) sh,s 0,89 0,00161s s is the slump of fresh concrete Influence of texture shape and size In the formula for calculating shrinkage deformation according to ACI209.2R, there is an adjustment factor according to the component size sh according to (2.4); Vietnamese standard TCVN 11823 considers the coefficient of influence of volume and surface of components on shrinkage deformation ks (2.5) v ks 1, 45 0, 0051 (2.4) (2.5) sh,vs 1, 2.e{0,00472(V / S )} s v/s – is the ratio of volume to the component surface Effect of initial maintenance time Boris Haranki sample with days of wet maintenance then transferred to a room with 50% humidity with a shrinkage greater than 10÷28% in comparision with the sample having 14-daymaintenance ACI standard 309 generally recommends moisture maintenance for at least days According to ACI209.2R, the coefficient adjusted for maintenance time sh: (2.6) sh,tc 1, 202 0, 2337 log(tc ) tc is the initial maintenance period Effects of ambient temperature CEB-FIP introduces a formula that forecasts a chronological shrinkage growth rate of approximately 6% and a critical shrinkage growth rate of 15% as the temperature rises from 23°C to 60°C with constant humidity Effects of environmental humidity In the formula for calculating shrinkage deformation according to ACI209.2R, there is a sh, 1, 1, 2h coefficient adjusted for environmental humidityshRH: (2.7) TCVN 11823 standard considers the coefficient of influence of environmental humidity on shrinkage deformation khs: khs 0,014h 0,4 ≤ h ≤ 0,8 and sh, 3,0 3,0h if 0,8 ≤ h ≤ 1,0 (2.8) 2.3 Some models forecast shrinkage deformation of concrete Road bridge design standard TCVN 11823-2017 [34] If there does not have more accurate data, the relative deformation due to shrinkage of 200x10-6 after 28 days and 500x10-6 after one year from the time the concrete dries can be used Or relative deformation due to shrinkage can be taken as follows: (2.9) sh 0, 48.103.ks khs k f khd Figures depending on structural size, humidity, and concrete strength see section 2.2 When distributed design data is not available, shrinkage and magnetism can be determined by using the following provisions: Articles 5.4.2.3.3 and 5.4.2.3.3 CEB – FIP, or ACI 209.2R ACI209.2R Standard [37] Shrinkage deformation at the time t, start to be measured at the time tc, is calculated by the following formula: sh sh,tc sh, RH sh,vs sh,s sh, sh,c sh, t tc (2.10) sh (t tc ) shu 6 f (t tc) shu 780.10 sh CEB FIP 2010 Standard [70] Shrinkage deformation is calculated as the sum of autogenic shrinkage deformation and dry shrinkage deformation cs (t , ts ) cas (t ) cds (t , ts ) cas (t ) cas ( fcm ).as (t ) cds (t , ts ) cds ( fcm ). RH ( RH ).ds (t ts ) (2.11) fcm is the average compressive strength at the age of 28 days, the coefficients depend on the concrete strength, the type of cement used, and the environmental humidity EUROCODE Standard [74] Shrinkage deformation at time t, calculated as the sum of autogenic shrinkage deformation and dry shrinkage deformation: cs (t ) ca (t ) cd (t ) ca (t ) ca () 1 exp(0.2t 0,5 ) () 2,5( f 10).106 (2.12) cd t cd ,0 t ts t ts 0.04 h03 kh cd ,0 ca ck RH 3 f cm 6 0,85 (220 110. ds1 ) exp( ds ) 10 {1,55 1 } f cm 100 The coefficients depend on concrete strength, type of cement used, and environmental humidity Russian Construction Standards [116] Shrinkage deformation at time t is calculated by the formula: cs (t , tw ) cs (, tw ) 1 e (t tw ) cs (, tw ) csN (,7)1s2s3s csN (,7) Kcs (W V )3/2 (2.13) the coefficient taken according to the pre-prepared table depends on the time of concrete maintenance, environmental humidity, and open surface modulus of the component; Kcs 0.14*10-6 for heavy concrete; W and V are the density of water and gas in the concrete mixture Japanese Standard [85] Shrinkage deformation at time t, calculated by the formula: 0.56 V /S ' ( RH /100) 0.108 t t0 ' ' cs 50 78(1 e ) 38lnW ln cs t , t0 e cs (2.14) 10 V, S is the volume and surface area of the structure, and W is the amount of water used for 1m3 of concrete British Standard BS 8110 [68] The BS 8110 standard does not provide a mathematical formula for forecasting shrinkage deformation The development of shrinkage deformation is represented as a graph Australian Standard [58] The formula for calculating shrinkage deformation is the total deformation due to ecse autogenic shrinkage deformation and dry shrinkage deformation ecsd cs cse cds (2.15) cse cse* 1.0 e0.1t * csd b 1.0 0.008 fc ' csd cse* 0,06 fc' 1,0 50.106 csd k1k4 csd b b The coefficients depend on the climatic zone 2.4 Analysis of shrinkage deformation models The majority of standards define shrinkage deformation over time through mathematical formulas of exponential or hyperbolic form Eurocode, CEB/FIP, and Australian standards are divided into parts: autogenic shrinkage and dry shrinkage, shrinkage deformation is calculated depending on concrete strength and adjustment factors taking into account the effects of humidity and the type of cement used ACI, Russian, Japanese, and Vietnamese standards calculate shrinkage according to the extreme shrinkage-dependent function multiplied by the adjustment factors taking into account the effects of aggregates, cement content, N/XM ratio, size shape, temperature maintenance method, environmental humidity, and concrete strength 2.5 Methods for determining shrinkage deformation of concrete according to standards Content of shrinkage empirical methods of synthetic standards in Table 2.1 Table 2.1 Experimental methods for determining shrinkage deformation of concrete in standards Standard ASTM C157/157M-08 [46] Europe Viet Nam TCVN11823 [34] Laboratory samples 75x75x285mm rock < 25mm 100x100x285mm rock < 50mm Temp, humidity Maintenance Soak in water for 30’, 28 days of 23±20C maintenance from 50±4% the date of sample filling No specific regulations 4, 7, 14, 28 days and 8, 16, 32, 64 weeks (448 days) Obtained according to CEB – FIP model code [70], or ACI 209.2R-08 [37] axax4a (a=70, 100, 150, 200mm) 27±20C 80±5% Soak for days after day of removing the sample Japan JIS A 1129-1-2010 [86] 100x100x400mm 20±20C 60±5% Soak in water for days United Kingdom BSISO 1920-8:2009 [69] 75x75x285mm 100x100x400mm 22±20C 55±5% Soak in water for days after 18-24h remove the formwork Russia ГОСТ 24544-81 [115] axax4a (a=70, 100, 150, 200mm) Viet Nam TCVN 3117:1993 [29] Reading figures 20±2 C 60±5% Soak for days after day of removing the sample Every 1, 3, 14, weeks Minimum 120 days Minimum shrinkage measurement 13 weeks (91 days) 7, 14, 21, 28, 56 days, and 112 days, minimum measurement for months Every 0, 3, 14, weeks Minimum 120 days The thesis aims to study the concrete applied in bridge construction, so the standards applied in laboratory work, as well as calculations, must comply with the provisions of bridge design standard TCVN11823 [34], this standard is based on the US AASHTO [102] standard, therefore shrinkage experiments must be performed by ASTM C157[46] 2.6 Develop a formula for predicting shrinkage deformation of concrete from experimental results TCVN 11823 [34] stipulates that the determination of shrinkage and magnetism can be used CEB – FIP [70] or ACI 209 [37] Therefore, the thesis proposes to develop a formula for predicting shrinkage deformation of concrete using fine sand mixed with crushed sand according to the formula format of the above two standards… The determination of coefficients adjusted according to the fluctuating parameters of the material: It can be done according to traditional methods such as the least squared method, experimental planning method, multivariate regression method, or according to numerical methods based on Particle Swarm Optimization (PSO), Karush method – Kuhn – Tucker conditions… However, if traditional methods are used in the case of crushed sand samples from three different types of rock, each type considers the influence of material fluctuation parameters, maintenance conditions, and control sample nests, resulting in a large number of sample nests, due to independent influencing factors, determining extremes from local optimization as well as global optimization is complicated, slow to converge and large errors… On the other hand, the thesis aims to develop a shrinkage deformation formula based on the formulas of ACI and CEP/FIP, not to develop new equations according to experimental data After considering that the PSO method [95] is suitable for the problem, in this case, the PSO method gives a faster optimization speed than conventional methods, and due to the self-perfecting nature of the algorithm, the calibration results not depend on the large number of test samples and can be locally optimized or globally optimized CHAPTER EXPERIMENTAL AND ANALYTICAL STUDIES ASSESSING THE INFLUENCE OF FINE SAND MATERIAL PROPERTIES MIXED WITH CRUSHED SAND FROM ROCKS ON THE MECHANICAL PROPERTIES AND SHRINKAGE DEFORMATION OF CONCRETE 3.1 Survey results of deposits of fine sand and crushed sand Fine sand deposits The thesis conducted a survey of Tan Chau, Vinh Hoa (An Giang province), and Hong Ngu (Dong Thap province), which are sand mines assessed to have good quality and large reserves in the Mekong Delta The results of experiments on mechanical and physical properties such as the content of clay, and the content of organic impurities all meet the requirements of ASTM C33 [50] and AASHTO M6 [102], but the particle magnitude modulus is only 1.4 ÷ 2.24, the particle composition curve is outside the limits according to the standard Tan Chau sand mine inTan Chau district, An Giang province is considered to have the best quality in the Mekong Delta with grain magnitude modulus from 1.6 ÷ 2.24, large bridge projects such as Binh Khanh bridge, Thu Thiem bridge, My Thuan bridge all use CM Tan Chau Crushed sand mines The thesis also surveyed the crushed sand mine 3B of Ong Cau Mountain inBa Ria Vung Tau province, the sand milled from Andesite-base- rock has a compressive strength of 131.86MPa, the magnitude modulus is 3.69 ÷ 4.2, other mechanical and physical indicators meet the requirements according to standards, mine crushed sand 3B is used for Binh Khanh cable-stayed bridge, Phuoc Khanh belongs to Ben Luc–Long Thanh expressway project Tan Dong Hiep quarry in Di An town in Binh Duong province, sand milled from granite base rock has a compressive strength of 157MPa, the size modulus of the grain ranges from 3.6 ÷ 4.4, other criteria meet the standards, sand is used for Thu Thiem bridge project Su Khe Quarry produces crushed sand from limestone with a compressive strength of 78.1MPa 12 Ru 0, 0641 BD 0,3945 BD 6, 7425 R2 = 0,984 (3.5) E 230,84 BD 1582,3 BD 36498 R2 = 0,998 (3.6) 2 3.5 Contents of concrete shrinkage experiments 3.5.1 Experiment plan In this section, the thesis carried out deep study on the shrinkage characteristics and the influencing factors of fine sand mixed with crushed sand on the shrinkage characteristics of concrete The sample nests were tested according to Laboratory Standard ASTM C157; the thesis also experimented with non-standard maintained sample nests close to actual construction conditions such as after removing the mold sealed around with Polyethylene (PE) thin film, and the sample nest after removing the mold are not soaked in maintenance water A total of 67 experimental (TM) samples were divided into nestnests as follows:: Nest 1: Considering the effect of the CN/CM mixing ratio on shrinkage deformation, including 30 sample nests TM1, TM2, TM3, TM4, TM5, TM6, TM7, TM8, and TM9 using Andesite CN stone TM TM28, TM29, TM30, TM34, TM35, TM36, TM37, TM38, TM39; TM31, TM32, TM33, TM49, TM50, TM51, TM52, TM53, TM54 have the same grading as above but use CN from Limestone and Granite Nest 2: Considering the effect of stone powder content on shrinkage deformation, including 23 nestnestssample nests TM2, TM13, TM14, TM15, TM10, TM5, TM16, TM17, TM11, TM8, TM19, TM20, TM21, TM12 using crushed sand produced from Andesite rocks The TM40, TM41, TM42, TM43, TM44, TM45, TM46, TM47, and TM48 have the same distribution as above but use crushed sand from limestone Nest 3: Considering the effect of rocks producing crushed sand on shrinkage deformation, including 64 sample nests from TM1 to TM67 changing crushed sand produced from Andesite, Granite, and Limestone, changing mixing ratio, and changing powder content (except for sample nests TM10, TM11, TM12 uses yellow sand) Nest 4: Comparing the shrinkage deformation measurement results of concrete sample nests using mixed sand with concrete control nestsusing yellow sand of Song Lo including 67 sample nests from TM1 to TM67 Nest 5: Comparing the evaluation of research results with current standards used for bridge design (64 sample nests), including TM1 to TM67 (except for TM10, TM11, and TM12 nestnestssample nests using yellow sand) Nest 6: Consideringthe effect of stress due to shrinkage deformation on concrete structures (64 sample nests) including TM1 to TM67 (except for TM10, TM11, and TM12 sample nests using yellow sand) 3.5.2 Climate chamber The climate chamber was designed and manufactured by the Institute of Climate Research and Manufacture Figure 3.19 Standard temperature and humidity are controlled by thermal relays and humid relays Switching is carried out by electromagnets connected in series to the set of thermal relays, and humid relays, ensuring regularity in temperature mode of 23 ± 2oC and humidity of 50±4% Figure 3.19 Climate chamber Figure 3.20 Sample storage and experiments 3.5.3 Fabrication, sample maintenance, and shrinkage measurement on samples Prototyping complies with ASTM C157 and ASTM C192 regulatory requirements; Each sample 13 nest consists of prototypes, two ends with copper pins for sample measurement Shrinkage measuring instruments using specialized shrinkage strain gauges of the Building Materials Laboratory Figure 3.20 The shrinkage deformation of each concrete sample at the time is calculated in mm/m according to the formula (t)=∆l(t)/l ∆l(t): the difference in length between the measuring pins of the sample at time t compared to the original in mm; l is the distance between the measuring pins, l = 0.285m 3.6 Analysis of the results and evaluation of the effect of material properties on possible deformation 3.6.1 Effect of CN/CM mixing ratio Group of sample nests maintained according to standard conditions Includes samples TM1, TM2, TM3 At the 448th day, the shrinkage deformation of the TM3 sample nest (CN/CM = 70/30) has a maximum value of 442.21x10-6, followed by the sample nest TM2 (CN/CM = 60/40) with a value of 410.96x10-6, the sample nest TM1 (CN/CM = 50/50) has the minimum value of 386.09x10-6 Figure 3.21 That shows that the shrinkage deformation of the sample nests is affected by the ratio of mixing crushed sand with fine sand according to the tendency to increase the content of crushed sand, the shrinkage deformation also increases The tendency to increase shrinkage deformation in sample nests with higher levels of crushed sand is explained by the properties of mixed sand aggregates, such as pore structure, surface area, water absorption crushed sand has a higher pore volume than natural sand, the mixing of crushed sand with river sand to reduce voids in mixed sand, thereby creating a mixture whose properties are closer to the properties of river sand Figure 3.21 chart of TM using Andesite stone Figure 3.22 chart of TM using Limestone CN Figure 3.23 chart of TM using Granite CN On the other hand, due to the physical characteristics of crushed sand with a high surface area, the absorption of water into the convex surface, and the holes inside the sand grain, this amount of water over time will gradually seep out and cement hydrochemistry (late hydrochemistry) continues to cause deformation of concrete shrinkage in the later stages Considering that the sample nests using crushed sand from the base Limestone Figure 3.22 and Granite Figure 3.23 also have the same rules as the sample nests using Andesite crushed sand Group of sample nests maintained according to non-standard conditions Sample nests sealed with PE thin film TM4, TM5, TM6 The majority of shrinkage deformation is autogenic shrinkage At the time of 448 days, the shrinkage deformation of the specimen nest ranged from 275.60x10-6 ÷ 304.99x10-6 Figure 3.24 Figure 3.24 chart of TM using Andesite stone Figure 3.25 chart of TMs using Limestone CN Figure 3.26 chart of TM using Granite CN Samples with a high content of crushed sand had higher shrinkage deformation than samples with a low content of crushed sand The effect of the CN/CM mixing ratio on shrinkage deformation of sample nests made from crushed sand Limestone Figure 3.25 and Granite Figure 3.26 is similar to that of samples made from Andesite crushed sand Group of initial non-maintenance specimens TM7, TM8, TM9 Figure 3.27 At 448 days, 14 shrinkage deformation ranges from 467.43x10 ÷ 538.20x10-6 The sample nests using crushed sand from the base stone are Limestone Figure 3.28 and Granite Figure 3.29 have the same rule -6 Figure 3.27 chart of TMs using Andesite stone Figure 3.28 chart of TMs using Limestone CN Figure 3.29 chart of TM using Granite Compared to standard maintenance, the shrinkage deformation of TM7, TM8, and TM9 was greater from 51.77 ÷ 52.93% at 28 days and 20.07 ÷ 21.78% at 448 days Compared with PE thin-film enclosures, the shrinkage deformation of TM7, TM8, and TM9 was greater from 95.20÷102.37% at 28 days and 69.61÷76.46% at 448 days This result shows that the effect of maintenance during construction on limiting shrinkage deformation of concrete is very large 3.6.2 Effects of stone powder content (group 2) Group of sample nests maintained according to standard conditions Includes models TM2, TM13, TM14 and TM15 At 448 days, the shrinkage deformation of the TM15 sample nest (7%real estate) has the highest value of 464.19x10-6, then the sample nest TM14 (5%BĐ) has a value of 451.57x10-6, TM13 (3.5%BĐ) has a value of 430.30x10-6, the sample nest TM2 (2%BD) has the smallest value of 410.96x10-6 Figure 3.30 Figure 3.30 chart of TMs using Figure 3.31 chart of TM using Figure 3.22 chart of TM using CN limestone Granite CN Andesite stone This result shows that the content of stone powder in crushed sand affects the deformation of concrete according to the trend when increasing the content of stone powder in crushed sand, shrinkage deformation also increases accordingly The reason for the increase in shrinkage deformation when the content of stone powder increases is explained as follows: When the content of stone powder in crushed sand increases, it increases fineness and increases the total surface area On the other hand, some of the activities of stone powder are directly involved in hydrations, the stone powder particles evenly distribute the particles of the cement that have not yet reacted hydrate easily continue under the right conditions causing the shrinkage deformation of the concrete to increase This result is also consistent with previous research findings presented in Chapter that suggested that shrinkage deformation is directly proportional to the amount of rock powder in crushed sand when the amount of rock powder is less than 10% The shrinkage deformation of samples using Cn Limestone Figure 3.31 and Granite Figure 3.32 has the same grading form, and the same content of stone powder tends to be similar Group of sample nests maintained according to standard conditions Group of sample nests sealed with PE thin film TM5, TM16, TM17, and TM18 At the 448th day, shrinkage deformation ranges from 288,02x10-6 ÷ 313,76x10-6 Group of initial non-maintenance models TM8, TM19, TM20, TM21 At the 448th day deformation shrinkage ranges from 500,49 x10-6 ÷ 567,22x10-6 Compared with standard maintenance sample nests, the shrinkage deformation of non-serviced specimens sample nests was greater from 52.29÷53.94% at the 28th day, and from 21.54÷23.31% at the 448th day Compared with PE thin-film enclosures, shrinkage deformation of non-serviced 15 sample nests was greater from 91.35÷98.66% at the 28th day, and from 62.34÷ 80.78% at the 448th day 3.6.3 Influenced by crushed sand-producing base rocks (group 3) Group of sample nests maintained according to standard conditions Including TM1, TM2, TM3 sample nests using Andesite crushed sand; TM28, TM29, TM30 use limestone crushed sand; TM31, TM32, TM33 use crushed sand granite Figure 3.33 With the same CM/CN mixing ratio, the shrinkage deformation of concrete produced from limestone crushed sand has the smallest shrinkage deformation, then the concrete produced from Andesite crushed sand, concrete produced from crushed sand granite has the greatest value At the same level, the difference in shrinkage deformation between samples using Andesite crushed sand was 10.71÷14.78% higher than that of samples using limestone crushed sand, and samples using Granite crushed sand was 18.07 ÷ 20.18% higher than limestone crushed sand, at 448 days Figure 3.33 chart of standard maintenance TM Figure 3.34 chart of PE-coated TM Figure 3.35 chart of standard non-maintenance TM The results of the experiment are also consistent with previous studies which said that crushed sand from different types of base rocks, the particle shape, and surface texture is also different, those properties affect the surface area, water absorption rate, and especially pore volume of crushed sand, and affects shrinkage deformation of concrete Studies also show that the harder the crushed sand from the base stone, the higher the surface roughness and porosity, the crushed sand from limestone has a smoother round surface than other types of CN, lower porosity, and smaller shrinkage deformation Sample nests maintained according to non-standard conditions Model nests sealed with PE thin film TM4, TM5, TM6, TM34, TM35, TM36; TM5, TM16, TM17, TM18; TM43, TM35, TM44, TM45 Figure 3.34 The results showed that the shrinkage deformation of crushed sand concrete produced from limestone, aldehyde, and granite has the same rules as standard maintenance samples, but the value is lower Initial non-maintenance prototypes TM7, TM8, TM9, TM37, TM38, TM39; TM8, TM19, TM20, TM21, TM46, TM38, TM47, TM48; TM52, TM53, TM54 Figure 3.35 the final value has a larger difference between the sample nests, with the same type of distribution, the shrinkage deformation of samples using granite crushed sand is greater than samples using limestone crushed sand from 23.38÷27.53%, samples using Andesite crushed sand are larger than samples using limestone crushed sand 15.54÷17.63%, at the time concrete reaches 448 days 3.6.4 Comparison with shrinkage deformation of river sand (group 4) Group of sample nests maintained according to standard conditions TM1, TM2, TM3, , TM62, TM63, and TM64 are sample nests with changes in CN/CM mixing ratio, s powder content, and crushed sand changes from types of Andesite, Limestone, and Granite, and TM10 is river sand Figure 3.36 Figure 3.36 chart of standard maintenance TM Figure 3.37 chart of PE-coated TM Figure 3.38 chart of nonmaintenance TM Before the 3rdday, shrinkage deformation of river sand is approximately equal to the shrinkage 16 deformation of mixed sand concrete, from the 3rd to the 112th days shrinkage deformation of river sand concrete has the smallest value compared to the shrinkage deformation of mixed sand concrete samples, After the 112th day, the deformation rate of river sand tends to be slightly higher than that of mixed sands At the 448th day the shrinkage deformation of river sand concrete is almost the lowest and has a value of 375,64x10-6, only higher than samples of limestone crushed sand with CN/CM mixing ratios of 50/50 and 60/40 with times the amount value of 348,75 x10-6 and 366,58 x10-6 Group of sample nests maintained according to non-standard conditions Group of sample nests sealed with PE thin film The majority of shrinkage deformation is autogenic shrinkage The shrinkage deformation of river sand is approximately the same as that of limestone crushed sand specimens, smaller than those used for Andesite and Granite crushed sand Figure 3.37 Group of initial non-maintenance specimens Figures 3.38, at the 448th day the deformation difference of crushed sand concrete samples from Andesite and Granite based rocks with river sand samples of 6.33÷32.74%, however, with concrete samples with limestone crushed sand content from 50÷60%, the shrinkage deformation is smaller than river sand concrete samples from 2.72÷8.66%, samples with 70% limestone content shrinkage deformation greater than of river sand 4.08% The experimental results are consistent with previous studies that suggest that shrinkage deformation of crushed sand increases rapidly at an early stage and slows down at a later stage compared to the deformation of river sand concrete The reason is explained by the fact that crushed sand has a large pore and high water absorption causes dry shrinkage deformation in the early stages to increase sharply, the period after dry shrinkage deformation gradually decreases, causing the shrinkage deformation rate to decrease over time… 3.7 Compare research results with current standards Using the experimental results of group 1, group 2, group 3, and group 4, compared with the standards being applied in bridge design calculations including, TCVN 11823, ACI 209, CEB / FIB 2010, and EuroCode standards The group of sample nests changes the CN/CM ratio and maintains according to standard conditions Figure 3.39 Graph of CN/CM ratio change TM Figure 3.40 chart of TM changes in real estate content Figure 3.41 chart of nonmaintenance TM Includes sample group TM1, TM2, TM3, TM28, TM29, TM30, TM31, TM32, TM33 The sample nests have a change in the CN/CM mixing ratio from 50/50 to 70/30 and the content of stone powder is available in crushed sand from Andesite, Limestone, and Granite Figure 3.39 During the first 14 days, the shrinkage deformation of most specimens is greater than the calculated values according to TCVN 11823 and ACI 209 but less than the values calculated according to CEB / FIP and EC2 From the 14th to the 28th the shrinkage deformation of the TMs was greater than the calculated value according to TCVN 11823 but approximately the value calculated in ACI 209 and less than CEB/FIP and EC2 After day 28, the shrinkage deformation of the TMs is less than the calculated value according to all criteria above Thus, shrinkage deformation of concrete using fine sand mixed with crushed sand tends to be high in the early stages and slow down in the later stages Although concrete uses crushed sand from limestone with the smallest shrinkage deformation, the Mekong Delta is rare limestone, so if used, it must be transported far from other places, so 17 the price is high While the shrinkage deformation of concrete using crushed sand from Andesite and Granite is less than the limit value according to the standards applicable to bridge construction in Vietnam Therefore, considering both technical and economic indicators, the thesis proposes to use crushed sand from Andesite stone which is available with large reserves to make concrete for traffic works, crushed sand from Granite needs to consider suitable reserves because traffic works often require the volume of materials The group of sample nests changes the content of stone powder and maintenance according to standard conditions The sample nests have a CN/CM ratio of 60/40, the content of stone powder varies from 2÷7%, and uses types of sand crushed Andesite, Limestone, and Granite Figure 3.40 At the final stage, sample nests with both a high content of crushed sand and a high content of stone powder have a shrinkage deformation greater than the standard value Specifically, at 448 days the deformation of the sample nests was smaller than the standard computational deformation; but for sample nests with high stone powder content7% for samples using Andesite crushed sand, 5÷7% for samples using Granite crushed sand, the measurement value is greater than the calculated value according to EC2 Thus, concrete using mixed sand when mixing high amounts of crushed sand needs to calculate and reduce the content of stone powder in crushed sand to ensure shrinkage deformation Group of sample nests maintained according to non-standard conditions Includes sample nests TM7, TM8, TM9, TM37, TM38, TM39, TM52, TM53, TM54, TM19, TM20, TM21, TM46, TM38, TM47, TM48 Figure 3.41 In the first 28 days, the shrinkage deformation of nearly all specimen nests was greater than the calculated value according to the standards By the end of the 448th day , the sample nests using limestone crushed sand have smaller shrinkage deformation than most standards, the sample nests using Andesite crushed sand have 3.5% higher stone powder content and 60% greater crushed sand content, granite crushed sample nests have 2.0% higher stone powder content and crushed sand content greater than 60% have shrinkage deformation higher than the standard Thus, concrete using mixed sand with high crushed sand content and high stone powder content requires appropriate initial maintenance to reduce shrinkage deformation… 3.8 The effect of tensile stress due to shrinkage on the working of concrete structures The tensile stress due to shrinkage deformation of concrete is compared with the tensile strength of concrete according to the formula of CEB/FIP 2010, ACI 209, and the average tensile strength due to experiments of concrete samples with the same shrinkage measurement level… Group of sample nests maintained according to standard conditions - Comparison according to CEB / FIP 2010 standards: Including sample nests TM1, TM2, TM3, TM10; TM13, TM14, TM15; TM22, TM23; TM28, TM29, TM30; TM31, TM32, TM33 Figure 3.42 Figure 3.42 CEP/FIP drag stress comparison chart Figure 3.43 ACI tensile stress comparison chart Figure 3.44 Comparison chart of stresses resulting in experiment results - Comparison according to ACI standards: Including sample nests TM1, TM2, TM3, TM10; TM13, TM14, TM15; TM22, TM23; TM28, TM29, TM30; TM31, TM32, TM33 Figure 3.43 - Comparison with the average tensile strength of experimental concrete: The group of sample nests maintained according to standard conditions includes samples TM1, TM2, TM3, TM10; TM13, TM14, TM15; TM22, TM23; TM28, TM29, TM30; TM31, TM32, TM33 Figure 3.44 18 For sample nests maintained under standard conditions, after ÷ 10 days of shrinkage stress reaching the tensile strength value of concrete, the risk of cracking is low… Group of sample nests maintained according to non-standard conditions The group of maintenance models according to standard conditions includes TM7, TM8, TM9, TM8, TM19, TM20, and TM21 according to CEB / FIP and ACI Figure 3.45, Figure 3.46 Figure 3.45 Tensile stress chart of CN/CM change patterns Figure 3.46 Drag stress chart of real estate changes Figure 3.47 Thermal stress comparison chart Nevertheless, for non-serviced specimen nests, the time when the tensile stress due to shrinkage reaches the limit of the tensile strength of the concrete is after ÷ days of age, coinciding with the time when the thermal stress reaches the maximum value Figure 3.47, if both effects are resonated, the probability of the concrete cracking at ÷ days old is very high 3.9 Build a formula that predicts shrinkage distortion over time Based on the formulas for calculating shrinkage deformation of concrete according to CEB/FIP and ACI 209 standards Using the PSO (Particle Swarm Optimization) algorithm to define functions that calculate the ψ adjustment factor according to the volatility parameters of mixed sand materials, to approximate the experimental shrinkage deformation value with the calculated value according to the formulas of the standard The accuracy of functions is determined by the R-squared accuracy rating factor The shrinkage deformation equation of concrete using the proposed crushed sand mixing CM takes the form: According to CEB/FIP 2010: cs (t , ts ) i [ cas (t ) cds (t , ts )] ψi is the regulatory system (3.7) According to ACI 209: (t tc ) sh (t tc ) i shu f (t tc ) (3.8) 3.9.1 Developing formula according to CEB/FIP standards The adjustment coefficients to be determined include: The adjustment factor considering the cn/cm ratio effect is ψ1; the adjustment factor considering the effect on the content of real estate stone powder is ψ2; the adjustment factor considering both factors at the same time is ψd Determination of the adjustment factor ψ1 Using the PSO algorithm tested gradually with the usual functions used in building materials to determine the appropriate ψ1 function format in this case as follows: R = 98,1% (3.9) 0,709.CN 1, 295.CM 1,6892 Determination of the adjustment factor ψ2 Similarly, determining the appropriate ψ2 function form in this case is: R = 98,2% (3.10) 0,0214.BD 0,6697 Determination of the adjustment factor ψd Similarly, determining the appropriate ψd function form in this case is: R = 96,7% (3.11) d (7, 4596.x 1,887 y 1,6859).(0,3031z 0,1016) 3.9.2 Building formulas according to ACI standards Determination of the adjustment factor ψ1 From the basic equation of ACI (3.4) Use the PSO method and try to determine the appropriate ψ1 function format in this case is: 0,931.x 0, 2959 y 0,134 R = 70% (3.12) Determination of the adjustment factor ψ2 19 Similarly, determining the appropriate ψ2 function form in this case is: R = 82% (3.13) 2,1885.BD 0,7458 Determination of the adjustment factor ψd Similarly, determining the appropriate ψd function form in this case is: R = 82% (3.14) d (0,3846.CN 0,0466.CM 0,1873)(5,0398.BD 1,7147) From the time-shrinkage deformation forecast formulas built above, the formulas prepared according to CEB-FIP 2010 standard have a very high conformity from 96.7÷98.1%, the formulas made according to ACI 209.2R have a lower conformity from 70÷85.2% Therefore, the thesis proposes that, in the calculation of bridge design, if there are no specific experimental data, it is possible to calculate the shrinkage deformation of concrete using CN mixing CM in the Mekong Delta according to the formula of CEB-FIP 2010 standard… CHAPTER STUDY OF THE EFFECT OF SHRINKAGE DEFORMATION ON THE WORKING OF REINFORCED CONCRETE BEAMS 4.1 Introduction From the analysis of the research results mentioned in Chapter 1, the thesis selects simple reinforced concrete beams to be experimented Horizontally rotated beams placed on the suspension consist of steel frames, suspended wires, and supporting rods that allow the beams to move freely in the suspended plane (horizontal), to eliminate friction between the beam and the bottom plank, and the beam is suspended horizontally to remove the influence of the weight of the beam itself to the level of sagging A latch end allows the beam to rotate freely equivalent to a fixed pillow The other end of the pin allows the beam to rotate freely and slide along the length of the beam equivalent to the expansion bearing Figure 4.1 The experimental beam has a cross-section size of b×h = 80×120 mm, and beam length L = 1500mm Concrete resembles the distribution of the TM1 sample nest Vertical reinforcement 4φ8 4ϕ8 is placed on one side of the cross-section Figure 4.2 Measurement of beam displacement by mechanical indicators at sections in the girder pillows and the cross-section between beams Results of deflection measurement of BTCT beams Figure 4.3 Figure 4.1 Erection of girder mounts Figure 4.2 Layout of steel in experimental beams Figure 4.3 Beam deflection chart 4.2 Analysis of the effect of shrinkage on the working and deformation of reinforced concrete beams Based on the mechanical equilibrium method with basic assumptions such as cross sections being considered flat, from linear variables, curvature and shrinkage are considered independent phenomena with no mutual impact The formula for determining the deflection of reinforced concrete beams shrinkage: v s cs L2 (4.1) s is the coefficient depending on the load case; Kcs is the curvature of the beam; L is the span length Using the compression force method assumed in this problem, shrinkage is a long-term load, so it is necessary to consider the influence of variable words, to consider the influence of variable words, the common method is to use long-term cutting eyes… Considering the case of concrete beams without reinforcement, shrinkage deformation causes the beams to shrink by a segment is cs, this deformation is equivalent to the beam being 20 subjected to a hypothetical center compression Ncs(t) as shown in Figure 4.4 The assumed compression force due to Ncs(t) shrinkage deformation is calculated as follows: (4.2) Ncs (t ) Ec (t).Ac cs (t) Figure 4.4: Distortion caused by shrinkage on RC beams without reinforcement Figure 4.5: Distortion caused by shrinkage on RC beams with symmetrical reinforcement Figure 4.6: Deformation caused by shrinkage on asymmetrically reinforced concrete beams Ec(t) is the effective modulus of elasticity of concrete; Ac is the cross-sectional area of concrete beams; cs(t) is the relative deformation due to shrinkage of concrete Considering the case of symmetrical reinforcement layout beams, due to the restrained reinforcement, under the effect of deformed beam shrinkage is s and the non-deformed restrained part is c, cs = s + c as shown in Figure 4.5 The assumed compression force due to Ncs(t) shrinkage is calculated as follows: Ncs (t ) s (Ac+nAs ).Ec (t) (4.3) As is the area of reinforcement; n = Es/Ec(t); Es is the modulus of elasticity of steel From the two equations (4.2) and (4.3), it is determined that the shrinkage deformation s is: (4.4) (t ) s (t ) cs p is the As/Ac ratio n p Since the concrete is restrained the deformation part c gives rise to the corresponding stress in the concrete due to shrinkage according to Hooke's law is: np (4.5) (t ) Ec(t ). (t ) Ec(t ) . (t ) c c np cs Considering the case of asymmetric reinforcement: The neutralization axis of the reinforced concrete cross-section deviates from the neutralization axis of the concrete beam is e, the assumed compression force due to Ncs(t) shrinkage is located at the center of the concrete crosssection The reinforced concrete area consists of Ncs(t) and Mcs(t) as shown in Figure 4.6: Ncs (t ) Ec (t).Ac cs (t) (4.6) (4.7) M cs (t ) e.Ncs (t ) e.Ec (t).Ac cs (t) Due to the appearance of the bending moment, Mcs(t) causes the cross-section to rotate at an angle of Kcs as shown in Figure 4.6, causing the upper grain concrete to be compressed as ctM(t) and the lower fiber to expand as cdM(t), respectively, the upper fiber compression stress is ctM(t) and the lower fiber tensile stress is cdM(t) The total stress in upper and lower fiber concrete generated by shrinkage deformation is: np e Ac h (4.8) np e Ac h (4.9) (t ) Ec(t ). (t ) e 1 np Itd cd (t ) Ec(t ). cs (t ) e 1 np Itd h (4.10) (4.11) 2 n As d h0 n Ast a Ac h Es h Es h 2 Itd Ic Ac.e Ast e a Asd e h0 e Ec(t ) Ec(t ) As d Ast n Ac ct cs Auditing, if cd(t) is less than fr(t), the concrete beam has not cracked, and the curvature of the beam is built according to the formula built according to the Material Strength as follows: M cs (t ) e.E c (t).Ac cs (t) e Ac (4.12) cs = cs (t) Ec(t ).Itd Ec(t ).Itd Itd Combining (4.12) with (4.1) determines the formula for calculating the deflection of reinforced concrete beams due to shrinkage deformation generated by the formula (4.13) Combining formulas (4.13), (4.10), and (4.11), using Mathlab mathematical software to solve the equation to determine the formula for calculating the effective modulus of elasticity of concrete Ec(t) over 21 time (4.14): (4.13) e Ac f (t ) s.L2 cs (t) Itd (4.14) 2.s.L Ac.(2h0 h) cs (t) ( A c.h Ac.h.h0 Ac.h 02 Ic) f (t ) Ec (t ) Asd Es Ac.Ic f (t ) From formula (4.9) of calculating the tensile stress at the bottom of the beam, the above result shows that the tensile stress at the bottom of reinforced concrete beams generated by shrinkage deformation is less than the tensile strength of concrete according to ACI and CEB / FIB Table 4.1, so the bottom of the concrete beam has not cracked The test beam did not show cracks at the bottom of the beams From formula 4.13 calculating the deflection of beams, the calculation results show that the measured sagging value of the experimental beams is approximately the sagging value calculated according to the formula Table 4.2 Table 4.1 Beam bottom tensile stress due to shrinkage deformation Tensile The tensile strength of stress at concrete according to the the standards (MPa) Date bottom of the beam ACI CEB/FIB (MPa) 0 0,00 0,00 0,58 2,40 2,29 1,08 3,57 4,01 1,46 4,43 5,23 14 1,64 4,95 6,05 28 1,81 5,30 6,71 56 2,11 5,50 7,22 112 2,37 5,61 7,60 224 2,79 5,66 7,89 360 2,82 5,69 8,04 Table 4.2 Deflection of reinforced concrete beams f (mm) Date As of D1 D2 D3 4.13 0,000 0,00 0,00 0,000 0,125 0,135 0,134 0,081 0,195 0,203 0,219 0,142 0,265 0,281 0,282 0,221 14 0,312 0,346 0,362 0,277 28 0,391 0,423 0,426 0,342 56 0,498 0,515 0,525 0,447 112 0,589 0,601 0,613 0,560 224 0,670 0,686 0,701 0,721 360 0,735 0,759 0,771 0,768 From the formula (4.14) it is determined that the modulus of elasticity is effective due to shrinkage deformation and deflection of beams No 1, No 2, and No Using the PSO algorithm, the formula (4.15) calculates the effective elastic modulus Ec(t) at any time of concrete using fine sand mixed with crushed sand according to the formula of ACI.: Ec (t ) Ec t 6,902t 2, 02 (4.15) 4.3 Analysis of the effect of shrinkage and construction sequence on long-term deformation of Super T beams Super T beams can be considered prestressed concrete beams of the largest length With a span length of up to L = 38.3m, the effect of the previous camber during construction is significant The thesis on the research of Super T beams produced at Chau Thoi concrete factory in a shaped form, with concrete distribution using Tan Chau fine sand and Andesite crushed sand with a mixing ratio of 50/50 Super T beam structure has a beam length of 38.33m, a height of 1.75m, a design concrete strength of 50MPa, a prestressed cable with a diameter of 15.2mm, the tension in each cable is 195kN, only cable is cut when the concrete beam reaches over 85% of the design strength Figure 4.7 Analysis of the effect of shrinkage deformation on the camber development of Super T beams 22 Results of monitoring the intensity and camber development of factory Super T beams from cable cutting to 112 days Figure 4.8 A-A 1/2 MAËT CHÍNH DẦM B B-B A 1/2 MẶT BẰNG DẦM B A Fig 4.7 SuperT beam structure Date of cable cutting 14 28 56 112 Fig 4.8 SuperT beam structure Fig 4.9 Measurement Table 4.3 Super T beam measurement results over time Beam camber (mm) Beam Beam Beam Beam Beam Beam 44,5 46 47,5 43 42 44 55,5 55,9 50 48 51 52 56,5 56 54 53 55 55 58 57 56,5 55,7 56,5 57,1 62 63,1 62,5 61,6 62,1 62,3 65,6 64,3 64,2 63,2 65,1 65,7 66,5 65,5 65,3 64,5 66,2 66,8 67,8 67,1 67 66,2 67,9 68,2 69,5 68,9 68,5 67,8 68,6 69,2 Beam 39,5 45 49 53 59 63,7 64,6 67 68,7 Beam 42 53 54 57,2 60,7 63,9 65 67,3 68,9 Application of formulated formulations and results of shrinkage deformation experiments in Chapter and Chapter Using Midas software to calculate the camber of Beam Super T over time, the results are shown in Table 4.4 Table 4.4 Calculated camber differences with experimental beams Date of cable cutting 14 28 56 112 Beam (mm) 41.8 56.5 58.2 58.9 61.2 63.1 64.3 66.2 68.1 Beam -6.1% -20.4% -19.1% -19.7% -20.0% -19.1% -15.2% -10.2% -6.9% Beam -9.1% -20.9% -18.4% -18.2% -21.4% -17.4% -13.9% -9.2% -6.1% Beam -12.0% -11.6% -15.4% -17.5% -20.6% -17.3% -13.6% -9.1% -5.5% Differential Rate (%) Beam Beam Beam -2.8% -0.5% -5.0% -7.9% -13.3% -15.0% -13.8% -16.9% -16.9% -16.3% -17.5% -18.4% -19.5% -20.1% -20.4% -16.0% -18.4% -19.2% -12.6% -14.8% -15.6% -8.0% -10.3% -10.7% -4.6% -5.7% -6.5% Beam 5.8% -1.8% -6.7% -12.1% -15.9% -16.6% -12.7% -9.1% -5.8% Beam -0.5% -16.6% -15.4% -18.5% -18.3% -16.9% -13.2% -9.5% -6.1% Comment, the results of calculating the camber of beams due to shrinkage deformation according to the formulated thesis formulas give approximately the results of sagging measurement of beams monitored at the field ranging from 5.8 ÷21.4% Analysis of the effect of shrinkage deformation and construction on the sagging/camber development of Beam Super T span structures The sequence of construction of concrete pouring on the bridge surface compared to the time of cutting the prestressed cable directly affects the camber development of Beam Super T In this section, the thesis combines the formula for calculating shrinkage deformation over time (3.1), (3.21), the formula of the relationship between the effective elastic modulus of concrete (4.15) to the long-term deformation of SuperT According to the construction process Beam camber/deflection calculation results by construction phase are shown in the figure and are summarized in Table 4.3 23 Figure 4.10 Beam camber Table 4.3 Beam deformation spreadsheet by the construction process Development of Beam from pouring concrete beam to pouring concrete on the bridge surface Elastic intensity hesitant to Pi e.L2 p prestress when tensile (loss 8.Ec (t ).I subtracted): 5.w.L4 Elastic deflection due to D1 beam self-weight: 384.Ec (t ).I Coefficient from the turn of t concrete: Deflection due to prestressed Pi 2eL2 loss calculated over time until ploss 8Ec I the bridge surface is poured: The total camber comes 1 p D1 before the spherical sheet is 1 ploss poured: Development of deflection in the period from the pouring of concrete plates Deflation due to formwork, diaphragm, and bridge plate: Deflection due loading part 2: to static Camber due to variable words: Deflection due to prestressed loss over time from the pouring of concrete plates: Total camber of concrete pouring stage on the bridge surface: D2 5.w.L4 384.Eci I D3 5.w.L4 384.Eci I 2 ploss D D3 ploss 2 Total camber of Beam: 1 Based on the results of calculating the camber of the concrete beam at the 360th day after cable cutting according to the construction process of the bridge surface, it is shown that: The construction time of the bridge surface concrete version before days from the time of cutting the cable, Beam Super T will have a hammock deformation from 4mm to 30mm after year of operation; construction of the bridge surface after 12 days of cutting the cable, Beam has camber after year of exploitation Considering the deflection of the load is about 14.6mm Then the time of pouring the concrete plate of the bridge surface must be after 36 days from the time of cutting the prestressed cable Based on the above results, it is recommended that the time to pour Beam Prestressed reinforced concrete before Super T is after cutting the prestressed cable for 36 days 24 CONCLUSIONS AND RECOMMENDATIONS Conclude The new contributions of the thesis are summarized as follows: 1.1 The thesis experimentally measured the mechanical properties of concrete using fine sand mixed with crushed sand on 42 sample nests, the f'c compressive strength value ranged from 49.96 ÷ 57.28MPa, the tensile strength when bending f'r ranged from 6.04 ÷ 6.71MPa, the modulus of elasticity from 36250 ÷ 39460MPa Thus, when mixing the CN/CM ratio changes in the range of 50/50 ÷ 70/30; stone powder content from 2÷7%, creating mixed sand suitable for making concrete with strength class C40, concrete strength is directly proportional to crushed sand content and stone powder content in mixed sand 1.2 The thesis developed formulas to determine the effect of CN/CM mixing ratio and stone powder content on the mechanical features of concrete: CN CN f c' 9,8158 35,141 CM CM 26,954 CN CN f r 1,5872 5,5912 CM CM CN CN E 4943,7 17215 CM CM 1,9674 24935 Rn 0,7622 BD 2 4,924 BD 57,572 Ru 0, 0641 BD 0,3945 BD 6, 7425 E 230,84 BD 1582,3 BD 36498 1.3 The thesis experimentally measured the shrinkage of 30 maintained sample nests according to standard conditions for values ranging from 386.09x10-6 ÷ 493.15x10-6 With a CN/CM ratio of 50/50 ÷ 70/30 and a stone powder content of 2÷7%, shrinkage deformation increases as the crushed sand content and the rock powder content in mixed sand increase 1.4 The thesis developed a formula for predicting shrinkage deformation taking into account the effects of CN/CM mixing ratio and powder content according to current standards.: 1.5 The thesis experimentally measured 17 enclosed sample nests for the smallest shrinkage values ranging from 265.18x10-6 ÷ 322.58x10-6; The 17 non-maintenance sample gave the largest shrinkage values of 404.55x10-6 ÷ 583.5x10-6 The shrinkage of non-maintenance samples was greater than that of standard maintenance samples by 52.29÷53.94% at the 28th day and from 21.54 ÷ 23.31% at the 448th day Thus, the effect of maintenance to limit shrinkage is very large… 1.6 The thesis experimentally compared with control yellow sand sample nests, the shrinkage deformation of concrete using fine sand mixed with basic crushed sand is greater than the shrinkage deformation of concrete using yellow sand 1.7 The thesis made comparisons with the current standards applied in bridge construction, shrinkage deformation of concrete using fine sand mixed with crushed sand tends to be high in the early stages and slower in the later stages compared to the calculated value according to the standards Sample nests using high levels of crushed sand and high stone powder and without maintenance under standard conditions have a greater shrinkage value than the standard 1.8 The thesis determined that the duration of tensile stress due to shrinkage deformation reaches the tensile strength limit of concrete is to 15 days old with standard maintenance sample nests, a low risk of concrete cracking However, with non-maintenance sample nests at this time being to days old, coinciding with the time of great thermal stress, the 25 probability of concrete cracks occurring 1.9 The thesis formulated the formula for calculating the stress and deflection of concrete beams according to shrinkage deformation, and formulated a formula for calculating the effective modulus of elasticity of concrete using fine sand mixed with crushed sand over time from experimental results… 1.10 Apply the experimental results into calculating the camber/ deflection of Beam Super T according to the construction process As a result, the suitable time for the construction of the bridge surface to ensure the cadence structure has camber during exploitation is after 36 days from the cutting of the prestressed cable… Recommendations for further research directions - Shrinkage deformation of concrete using limestone crushed sand has the smallest value, but the Mekong Delta is lack of limestone, traffic construction works need a large volume of materials, so considering both economic indicators, technical indicators, and the level of response to the project The thesis proposes to use Andesite crushed sand, which is popular in the Mekong Delta to make concrete in bridge construction… - Concrete using a high content of crushed sand and high stone powder with shrinkage deformation greater than the standard value if not initially maintained, the thesis proposes that concrete use 70% crushed sand and 3.5% or more of crushed sand from Andesite stone; from 60% crushed sand and 2% or more stone powder for crushed sand concrete from Granite, contractors need to strictly implement the maintenance regime in construction Shrinkage deformation of concrete using crushed sand tends to be high in the early stages compared to the calculated value according to TCVN 11823, and ACI 209 standards but lower than the calculated value according to CEB / FIP standards, the thesis proposes that design consultants can refer to the results from the thesis or use the formula in the standard CEB/FIP to calculate shrinkage deformation for this type of concrete - The thesis provided a set of data on the shrinkage deformation of concrete using fine sand mixed with crushed sand However, the new results are limited to frozen concrete, using sand materials mainly in the Mekong Delta Therefore, in order to have sufficient grounds for controlling and limiting shrinkage deformation as well as cracking in concrete structures caused by shrinkage as well as expanding the scope of application for this material in the conditions of yellow sand becoming increasingly scarce, the following contents should continue to be studied: + Study on shrinkage deformation in the early stages, when the concrete does not yet have the strength (soft shrinkage); Currently, premature cracking on concrete structures after pouring concrete occurs quite commonly and is directly related to the deformation of soft shrinkage of concrete Therefore, the determination of this deformation component of concrete will be the basis for limiting premature cracking on the structure … +Study on shrinkage deformation of crushed sand mixed with fine sand or crushed sand mixed with yellow sand for sand mines in the North and Central regions to form a complete set of data for the design and construction of bridges in Vietnam, to cope with climate change as well as the current scarcity of construction sand materials LIST OF SCIENTIFIC WORKS OF PH.D STUDENTS Nguyễn Đức Dũng, Nguyễn Duy Tiến, Thái Khắc Chiến (2019), Overview of shrinkage of concrete using crushed sand and fine sand mixed with ground stone (Mi stone) in the Mekong Delta region Journal of Transport No 11/2019, p84-86 Nguyễn Đức Dũng, Nguyễn Duy Tiến, Thái Khắc Chiến (2021) Study of mechanical characteristics of concrete using fine sand mixed with crushed sand in bridge construction Journal of Transport Science, University of Transport and Communications, no 72, 8/2021, p686-700 Nguyễn Đức Dũng, Nguyễn Duy Tiến, Thái Khắc Chiến, Trần Thế Truyền (2021) Study of the influence of crushed sand from different base rocks on the mechanical characteristics of concrete using fine sand mixed with crushed sand in bridge construction Vietnam Bridge and Road Magazine, no 8/2021, p12-18 Nguyễn Đức Dũng, Nguyễn Duy Tiến, Thái Khắc Chiến (2022) Study of the influence of stone powder on the mechanical characteristics of concrete using fine sand mixed with crushed sand in bridge construction Journal of Transport Science, University of Transport and Communications, no 73, 2/2022, p100-110 Nguyễn Đức Dũng, Nguyễn Duy Tiến, Thái Khắc Chiến (2022) Effect of mixing ratio on shrinkage of concrete using fine sand mixed with crushed sand in bridge construction Journal of Transport Science, University of Transport and Communications, no 73, 4/2022, p268-276 ... amount of crushed sand accounts for 50÷70% of the highest grade of concrete According to Dr Nguyen Duc Trong [23] with C20 ÷ C36 concrete grades applied in constructing cement-concretepavement, when... concrete are affected by the mixing ratio of crushed sand with river sand, the CN content accounts for 50 ÷ 70% of the best concrete quality According to Altamashuddinkhan 2020 [61], the CN content... mixture accounts for 50 ÷ 60%, it will become the suitable grain composition that meet the road design standards According to the study of author Vu Quoc Vuong [28] on self-compacted concrete