混凝土的潛變與收縮

混凝土的潛變與收縮是混凝土的兩種物理性質，是應用混凝土時需要考量的變因。混凝土如果長時間受應力，便會緩慢變形，移除持續施予的力之後，變形只有部分會恢復，可以恢復的變形稱為彈性變形，不能恢復、永久的變形稱為潛變[1]。而在沒有受力的情況下，混凝土水含量變多或變少也會使混凝土的體積變化，稱為膨脹與收縮。

機制

潛變

混凝土的潛變為其中水泥的矽酸鈣水合物（C-S-H）在持續受應力下緩慢流動引起。

水泥漿漿體由固體的水泥凝膠（cement gel）組成，水泥凝膠又由矽酸鈣水合物形成的薄片以及薄片之間大量的空隙（大約佔凝膠40%至55%的體積）組成。[2] 這些空隙中含有會蒸發的層間水，水會對孔壁施加分離壓力（disjoining pressure），並削弱薄片與薄片之間的結合力。[3] 混凝土受力造成薄片之間滑動可能就是潛變的原因。

同樣的應力下，潛變（永久變形）通常是彈力變形（去除載荷後可恢復的變形）的三倍。[1]

收縮

混凝土中的水泥硬化過程會產生收縮。水泥中的矽酸鈣水合物薄片間的水分減少之後，薄片與薄片之間的間隔因為缺乏水分的流體靜拉力（hydrostatic tension）支撐而縮小，導致混凝土體積變小。 混凝土的收縮依水分減少的方式或發生收縮的部位不同可以分為：

  • 乾燥收縮（Drying Shrinkage）：水分蒸發到混凝土外部導致總體的體積收縮。[4]只要將乾燥收縮的混凝土泡水一段時間就可以回復部分體積[5]。乾燥收縮的機制與潛變關係密切[6]
  • 塑性收縮（Plastic Shrinkage）：混凝土表面與內部蒸發速率不一致[7]，導致收縮的速率也不一致，造成開裂的現象，稱為塑性收縮。
  • 自體收縮（Autogenous Shrinkage）：水分被混凝土中的水泥吸收，導致孔隙中的水分減少而收縮。水灰比過低的混凝土特別容易因自收縮而開裂。[8]

並非因為水分變化造成體積變小的收縮：

變因

如果在混凝土中混入足夠多的骨料的話，可以抑制水泥凝膠的潛變和收縮，因為骨料的蠕變較不明顯。[10] 孔隙水含量小或孔隙濕度低時的潛變較小[11]，而完全乾燥的混凝土不會潛變。

混凝土加載（受應力）時，材料年齡越大，潛變越小[12]，這是因為混凝土會隨著時間越來越乾燥的關係。大部分的應變都發生在受力前期，大約有四分之一到三分之一的潛變發生在第一個月，並且大約一半到四分之三的總潛變會發生在持續載荷的前半年。[1]

理論上溫度越高，潛變的程度也要越大，但實務上升溫增加的潛變會與混凝土失去水份減少的潛變互相抵消。升溫會加速層間水與其他物質發生水化，使混凝土孔隙中的水分減少。沒有水分施加的分離壓力，矽酸鈣薄片與薄片之間就難以滑動，使增加的潛變抵消。[13]

另外，乾燥過程的水分變化越劇烈，從濕潤到完全乾燥中間的潛變總量也會越多。較大試體乾燥較緩慢，因水分含量變化引起的潛變較小，所以潛變總量會較少，收縮總量也較少。[14]

本構方程

混凝土的本構方程中可以出現的變量有溫度、材料年齡、水化程度、孔隙濕度（與環境濕度有關）和孔隙水含量。這些變量被稱為狀態變量（state variables），是可以用來描述材料中任何一點的點屬性的變量。[15] 試體尺寸雖然也會影響潛變，但不列在本構方程中。環境濕度是影響孔隙濕度的條件之一，因為本構方程中已經包含孔隙濕度了，所以環境濕度就不會出現在本構方程中。[16]

應用

參考資料

  1. ^ 1.0 1.1 1.2 Gambali.Ajay Kumar; Shanagam.Naveen Kumar. Creep of Concrete (PDF). International Journal of Engineering Development and Research. 2014, 2 (4): P.3800 [2021-08-07]. （原始内容存档 (PDF)于2015-04-13）. 
  2. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.164~165 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. The paste consists of solid cement gel and contains numerous capillary pores. The cement gel contains about 40 to 55% of pores in volume, has an enormous pore surface area (roughly 500 m2/cm3), and is made up of sheets of colloidal dimensions (of average thickness about 30 A, with average gaps about 15 A between the sheets). The sheets are formed mostly of calcium silicate hydrates and are strongly hydrophylic. 
  3. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.164~165 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. Because the pores of cement gel are micropores of subcapillary dimensions they cannot contain liquid water or vapour; but they do contain evaporable water (water that is not chemically bound in the hydrates), which is strongly held by solid surfaces and may be regarded as (hindered) absorbed water or interlayer water. This water can exert on the pore walls a significant pressure called the disjoining pressure the value of which depends on temperature and the degree of water saturation of capillary pores. 
  4. ^ Neenu S.K. Types of Shrinkages in Concrete and its Preventio. THE CONSTRUCTOR. [2021-08-10]. （原始内容存档于2021-08-10）. Drying shrinkage is caused by the loss of surface -absorbed water from the calcium silicate hydrate ( C-S-H) gel and also due to the loss of hydrostatic tension in the small pores. 
  5. ^ Neenu S.K. Types of Shrinkages in Concrete and its Preventio. THE CONSTRUCTOR. [2021-08-10]. （原始内容存档于2021-08-10）. A part of this shrinkage caused can be recovered by immersing the concrete in water for a specified time. This is termed as the moisture movement. 
  6. ^ Neenu S.K. Types of Shrinkages in Concrete and its Preventio. THE CONSTRUCTOR. [2021-08-10]. （原始内容存档于2021-08-10）. This shrinkage is mainly due to the deformation of the paste, though the aggregate stiffness also influences it. 
  7. ^ Ravindra K.DhirOBE, Jorgede Brito, Rui V.Silva, Chao Qun Lye. Sustainable Construction Materials. 愛思唯爾. 2019: 9.4.2 Plastic Shrinkage [2021-08-10]. ISBN 978-0-08-100985-7. （原始内容存档于2021-08-10） （英语）. Plastic shrinkage occurs in a freshly mixed concrete, with loss of water by evaporation from its surface, after placing and before hardening of the concrete. This can lead to plastic shrinkage cracking if the rate of evaporation is higher than that of the bleeding water rising to the surface of the concrete. 
  8. ^ Shen Jianxi. Comprehensive Renewable Energy. 愛思唯爾. 2012: 6.14.2.3.2 Autogenous shrinkage [2021-08-14]. ISBN 978-0-08-087873-7. （原始内容存档于2021-10-29） （英语）. Autogenous shrinkage is the uniform reduction of internal moisture due to cement hydration, which is typical of high-strength concrete. Autogenous shrinkage contributes significantly to concrete cracking when the water–cement (w/c) ratio is less than 0.4 . The use of concrete with a somewhat higher w/c ratio can mitigate this problem. However, the strength and impermeability of concrete will be decreased if the w/c ratio is increased. 
  9. ^ Yves F. Houst. Carbonation Shrinkage of Hydrated Cement Paste. CANMET/ACI International Conference on Durability of Concrete. 1997,. supplementary papers (Fourth): pp.481–491. [2021-08-15]. （原始内容存档于2021-08-15）. 
  10. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.164~165 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. The main intrinsic factors are the design strength, the elastic modulus of aggregate, the fraction of aggregate in the concrete mix, and the maximum aggregate size. Increase of any of these factors causes a decrease of creep as well as shrinkage. This is because the aggregate does not creep appreciably and has a restraining effect on creep and shrinkage. 
  11. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.169 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. Creep at constant pore water content is less for a smaller pore water content or a lower humidity in the pores. 
  12. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.168 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. Creep decreases as the age of concrete at the instant of loading increases (this is actually the effect of the increase in the degree of hydration). 
  13. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.169 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. Creep also increases with increacing temperature, but this effect is offset by the fact that a temperature increase also accelerates hydration which in turn reduces creep. 
  14. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.169 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. Another important non-local extensive factor which is not a state variable is the size of specimen or structural member. The drying process in a larger specimen is slower, and consequently the creep increase due to drying is less, i.e. creep is less for a larger specimen. Similarly, shrinkage is less for a larger specimen and it is also less for a higher environmental humidity. 
  15. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.168 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. Among the extensive factors we must distinguish the local from the external ones. The former, also called the state variables, are those which can be treated as a point property of a continuum. They are the only ones which can legitimately appear in a constitutive equation. Temperature, age,degree of hydration, relative vapour pressure (humidity) in the pores, and pore water content represent state variables affecting creep. 
  16. ^ Z. P. BaZant、F. H. Wittmann (编). Creep and Shrinkage in Concrete Structures (PDF). 約翰威立. 1982: P.168 [2021-08-04]. ISBN 0 471 10409 4. （原始内容存档 (PDF)于2021-08-04） （英语）. On the other hand, the size of specimen and the environmental humidity are not admissible as state variables in a constitutive equation even though they have a great effect on creep of a concrete specimen. Properly, the environmental humidity must be considered as the boundary condition for the partial differential equation governing pore humidity. It is the pore humidity, not the environmental one, which directly affects creep and can appear in the constitutive equation.