混凝土相關(guān)外文翻譯

1、<p>　　Application of thermodynamics-based rate-dependent constitutive models of concrete in the seismic analysis of concrete dams</p><p>　　Abstract: This paper discusses the seismic analysis of concrete

2、 dams with consideration of material nonlinearity. Based on a consistent rate-dependent model and two thermodynamics-based models, two thermodynamics-based rate-dependent constitutive models were developed with considera

3、tion of the influence of the strain rate. They can describe the dynamic behavior of concrete and be applied to nonlinear seismic analysis of concrete dams taking into account the rate sensitivity of concrete. With the<

4、;/p><p>　　Key words: concrete; constitutive model; rate dependency; concrete dam; nonlinearity; seismic analysis</p><p>　　1 Introduction</p><p>　　China has abundant water resources. As

5、 part of the national energy and water conservancy plan, a batch of 300 m-level high concrete arch dams are or will soon be under construction. Most of the dams are situated in regions of strong seismic activity. Their d

6、esigned seismic accelerations reach 0.2g-0.32g ( g = 9.81 m/s2 ), with a probability of exceedance of 2% over a 100-year period. The designed maximum acceleration of the Dagangshan Arch Dam even reaches 0.5575g. The infl

7、uence of earthquakes s</p><p>　　Great progress has been made in the field of technology for dynamic analysis of concrete dams during earthquakes. However, some issues need to be better understood, including

8、the nonlinear constitutive model and dynamic behavior of concrete, which are still based on elastic analysis (Lin and Chen 2001; IWHR 1997).</p><p>　　A rational constitutive model of concrete is the foundati

9、on of further research on thenonlinear behavior of concrete. An appropriate constitutive model can reflect the mechanical characteristics of the material in all the stages of deformation, including strain hardening and s

10、oftening, strength reduction, and stiffness degradation, which determine the progressive damage of concrete. After several decades of development, the plastic theory describes these characteristics of concrete with a rat

11、her</p><p>　　In the meantime, concrete is a typical rate-sensitive material, whose strength, stiffness and ductility (or brittleness) are subject to a loading speed. Obviously, considerable deviation would b

12、e caused by the static mechanical parameters for seismic analysis. Identifying material characteristics of concrete under different strain rates and establishing proper dynamic constitutive models of concrete have become

13、 prerequisites for nonlinear dynamic analysis of arch dams. The descriptions of dynami</p><p>　　Based on a consistent viscoplastic model, two thermodynamics-based consistent rate-dependent models were derive

14、d from two thermodynamics-based static models with consideration of the influence of the strain rate. They satisfy thermodynamic laws automatically and can authentically describe the dynamic behavior of concrete. With th

15、e two models, the seismic responses of the Koyna Gravity Dam and the Dagangshan Arch Dam were analyzed. The nonlinear dynamic behavior of concrete dams and the influence</p><p>　　2 Introduction to thermodyna

16、mics-based rate-dependent</p><p>　　constitutive models of concrete</p><p>　　On the basis of the classical plastic theory, a consistent rate-dependent model takes into consideration the influence

17、 of the strain rate and maintains that stress remains on the yield surface in viscoplastic flow (Wang 1997). Therefore, the consistency condition is satisfied. The yield criteria with the strain rate effect can be expres

18、sed generally as </p><p><b>　　（1）</b></p><p>　　where is the stress tensor, is an internal variable, is the rate of the internal variable, and is the viscoplastic multiplier.<

19、/p><p>　　Due to the rarity of multiaxial dynamic experiments of concrete at present, the multiaxialdynamic constitutive relationship cannot be established directly. It is assumed for simplicity’s sake that the

20、dynamic increase factor (DIF) of multiaxial strength is the same as that of uniaxial strength.</p><p>　　Concrete shows completely different behavior under tension and under compression.</p><p>　

21、　Therefore, the internal variable is split into two parts, and , and behaviors under tension and under compression are described separately by means of these two internal variables. Under uniaxial compressive or tensile

22、 loading, we have</p><p>　　, （2） </p><p>　　and in a complex stress state, we have</p><p>　　， （3） &

23、lt;/p><p>　　where and are the weighting functions of compressive and tensile internal variables, respectively. The principles for determining and are as follows: for the loading process with dominant tensile

24、 stress states, =1 and =0 ; similarly, for the loading process with dominant compressive stress states, =0 and =1; for other loading conditions, 0<<1, 0 <<1 , and + =1.</p><p>　　Finally, the y

25、ield criterion can be expressed as</p><p>　??； (4)</p><p>　　According to the theory of the consistent rate-dependent model, a consistency condition should be satisfied:<

26、;/p><p>　?。?(5)</p><p>　　Two thermodynamics-based plastic constitutive models of concrete that have simple forms and can satisfy the energy laws naturally have been developed by Leng et

27、 al. (2008). Results from both models, obtained under static loading, agree with experimental results. The two models have been established, respectively, in Haigh-Westergaard stress space and principle stress space, the

28、 difference being that the Lode angle is neglected in the Haigh-Westergaard stress space model and considered in the pri</p><p><b>　　(6)</b></p><p><b>　　and</b></p>

29、<p><b>　　(7)</b></p><p>　　where p is the volumetric stress; q is the shear stress; and are the shift stresses on the hydrostatic axis and principle stress axis, respectively; , , and

30、are the stress dimensions, where i=(1,2,3,); and are the intersection points of the yield surface and hydrostatic axis; and , , ，and are dimensionless parameters to be determined</p><p>　　The plastic f

31、low rules of the two models are, respectively,</p><p><b>　　(8)</b></p><p><b>　　and</b></p><p><b>　　(9)</b></p><p>　　where ；, the re

32、lative level of shift stress; and are the volumetric plastic strain increment and deviatoric plastic strain increment, respectively; ; ; and , and are three principle plastic strain increments.</p><p>

33、　　According to the results of experiments (Suaris and Shah 1985; Reinhardt 1984), the relationships between the compressive and tensile strengths of concrete and the internal variable and rate of the internal variable ar

34、e</p><p><b>　?。?0）</b></p><p><b>　　and</b></p><p><b>　?。?1）</b></p><p>　　where and are dynamic strengths of concrete under uniaxial

35、 compression and tension, respectively, and , , and are assumed functions that can be obtained from experimental data.</p><p>　　The internal variable is considered the equivalent plastic strain:</p>

36、<p><b>　　(12)</b></p><p>　　where is the viscoplastic strain increment, and m is the unit tensor of plastic flow, which is determined by Eq. (8) or Eq. (9).</p><p>　　Substitut

37、ing these equations into the consistency condition leaves us with</p><p><b>　　(13)</b></p><p><b>　　where</b></p><p>　　The consistent viscoplastic model can b

38、e solved with an implicit backward Euleralgorithm, which has been studied and modified by Winnicki et al. (2001), Carosio et al. (2000) and Montans (2000).</p><p>　　The thermodynamic approach not only achiev

39、es greater generality, but also offers significant theoretical insights. In thermodynamics-based models, fewer hypotheses are made about the form of the dissipation function, and no assumptions are made about the plastic

40、 potential functions and flow rule. Benefitting from appropriate hardening and softening functions and relationships between the strength, modulus and strain rate, thermodynamics-based rate-dependent models reasonably de

41、scribe the behavio</p><p>　　以熱力學(xué)為基礎(chǔ)的頻率依賴性混凝土本構(gòu)模型在混凝土壩于地震作用中分析的應(yīng)用</p><p>　　摘要：本文論述了大壩在地震中考慮材料性能的非線性分析。根據(jù)連續(xù)性模，兩個基于熱力學(xué)的頻率依賴性混凝土本構(gòu)模型在考慮了應(yīng)變率影響完善后的應(yīng)用。這兩個模型可以描述混凝土的動態(tài)性能。并且適用于混凝土壩在考慮了其材料的敏感性后在地震作用中的非線性分

42、析。運(yùn)用這兩個模型可以對重力壩和大崗山拱壩在地震中進(jìn)行非線性分析。本文對于混凝土壩動態(tài)性能中的混凝土壩非線性動力響應(yīng)和應(yīng)變率對其的影響這兩個因素是通過比較線彈性模型和非頻率依賴性這兩個模型進(jìn)行討論的。從分析中可以得出：在混凝土抗震安全評估中，抗拉應(yīng)力是控制應(yīng)力?；炷翂蔚乃苄詰?yīng)變和應(yīng)變率分布曲線在不同的模型中有著相似的分布情況。當(dāng)考慮了應(yīng)變率的影響，最大塑性應(yīng)變和應(yīng)變率將會有所降低。</p><p>　　關(guān)鍵詞：

43、混凝土；本構(gòu)模型；頻率依賴性；混凝土壩；非線性；抗震分析</p><p><b>　　1前言</b></p><p>　　中國有豐富的水資源。作為國家水利規(guī)劃的一部分，一批300M級高強(qiáng)度的混凝土的拱壩很快會被建設(shè)起來。大多數(shù)大壩位于強(qiáng)震地區(qū)。他們的設(shè)計(jì)地震加速度是以100年內(nèi)達(dá)到0.2g～0.3g（g=9.81m/）超過2%為概率設(shè)計(jì)的。大崗山拱壩的設(shè)計(jì)最大地震加速

44、度甚至達(dá)到0.5575g。設(shè)計(jì)應(yīng)該考慮地震的影響，精準(zhǔn)的調(diào)查應(yīng)該以大壩在地震中的安全狀態(tài)為論據(jù)，以確保大壩的安全和減少大壩受地震的影響。</p><p>　　目前，在混凝土壩在地震中的動態(tài)分析技術(shù)領(lǐng)域已取得重大的突破。然而，基于混凝土彈性分析的非線性模型動態(tài)分析的具體問題仍需進(jìn)一步探索（Lin and Chen 2001;IWHR1997）。</p><p>　　合理的混凝土本構(gòu)模型是建立

45、在進(jìn)一步研究混凝土的非線性基礎(chǔ)上。一個適當(dāng)?shù)慕Y(jié)構(gòu)模型可以反映機(jī)械的特殊性材料在所有階段的變形，包括收縮和徐變、強(qiáng)度、剛度的降低，從而進(jìn)一步確定混凝土的破壞狀況。經(jīng)過了幾十年的發(fā)展，闡述混凝土特性的塑性理論已具有相當(dāng)好的理論基礎(chǔ)。然而，目前的塑性和彈塑性混凝土也有許多假設(shè)沒有明確的物理意義或不符合熱力學(xué)定律的，其中包括德魯克假設(shè)、相關(guān)或非相關(guān)流動法則和塑性勢函數(shù)(Leng et al.2008)?；炷翂蔚姆蔷€性分析，可以用很少的假設(shè)建立

46、結(jié)構(gòu)模型，況且符合能量守恒和反應(yīng)混凝土的非線性。</p><p>　　同時，混凝土是一種典型的應(yīng)變率敏感材料，其強(qiáng)度、剛度和塑性（或脆性）受加載速度影響明顯。顯然，用靜態(tài)力學(xué)參數(shù)進(jìn)行地震作用分析會引起很大的誤差。標(biāo)識混凝土在不同應(yīng)變率下特點(diǎn)，建立合理的動態(tài)混凝土本構(gòu)模型已經(jīng)成為拱壩非線性動態(tài)分析的先決條件?？拐鹨?guī)范中的混凝土動態(tài)性能分析描述運(yùn)用到水利結(jié)構(gòu)設(shè)計(jì)（IWHR 1997）是不夠的，需要進(jìn)一步的補(bǔ)充與改進(jìn)。

47、</p><p>　　根據(jù)連續(xù)粘塑性模型，兩個基于熱力學(xué)的連續(xù)頻率依賴性模型是由考慮了應(yīng)變率的影響的兩個基于熱力學(xué)靜態(tài)模型派生而來的。他們滿足熱力學(xué)定律且能真實(shí)的反應(yīng)混凝土的動態(tài)性能。用這兩種模型就能對重力壩和大崗山拱壩的地震作用進(jìn)行分析。對于混凝土壩動態(tài)性能中的混凝土壩非線性動力響應(yīng)和應(yīng)變率對其的影響這兩個因素是通過比較線彈性模型和非頻率依賴性這兩個模型進(jìn)行討論的。</p><p>　　

48、2混凝土結(jié)構(gòu)模型熱力學(xué)原理的相關(guān)說明</p><p>　　以經(jīng)典塑性理論為基礎(chǔ)，連續(xù)頻率依賴性模型需要考慮應(yīng)變率和粘塑性流動表面屈服應(yīng)力的影響（Wang 1997）。因此，連續(xù)性條件是滿足的。受應(yīng)變率影響的屈服準(zhǔn)則可以表示為：</p><p>　　, (1)</p><p>

49、　　其中σ是拉壓應(yīng)力。是內(nèi)部變量，是內(nèi)部應(yīng)變率，是粘滯性系數(shù)</p><p>　　由于目前混凝土的多軸動態(tài)試驗(yàn)不多，因此無法直接建立多軸動態(tài)結(jié)構(gòu)之間的關(guān)系。它是由于取多軸強(qiáng)度的動態(tài)增加量和單軸強(qiáng)度一樣作為簡單假設(shè)的緣故。</p><p>　　由于在受拉和受壓兩種狀態(tài)下完全不同的性能，因此，內(nèi)部變量可以分為兩類。和,分別描述了兩個內(nèi)部變量在拉伸和壓縮狀態(tài)下的性能。因此在拉壓狀態(tài)公式為：

50、 </p><p><b>　　(2)</b></p><p>　　在復(fù)雜的應(yīng)力狀態(tài)下：</p><p>　　， (3)</p><p>　　其中，分別是自變量在受

51、壓和受拉狀態(tài)下加權(quán)函數(shù)。，的確定原則如下;當(dāng)加載過程中受到主拉應(yīng)力作用時，=1 ;=0 </p><p>　　加載過程中受到主拉應(yīng)力作用時，=0 ；=1</p><p>　　其他加載情況下， 0< <1 ; 0< <1 ; 并且+=1 </p><p>　　綜上所述：屈服準(zhǔn)則可以表示為：；</p><p>　　根據(jù)

52、連續(xù)相關(guān)模型理論，應(yīng)該滿足一個連續(xù)性條件：</p><p>　　： ; (5)</p><p>　　Leng at al .(2008)進(jìn)一步探究兩個混凝土本構(gòu)模型，他們以熱力學(xué)為基礎(chǔ)，有簡單的結(jié)構(gòu)形式并且滿足能量守恒定律。在靜態(tài)荷載作用下得到兩個模型的結(jié)果和實(shí)驗(yàn)結(jié)果一致。兩個本構(gòu)模型已分別在Haigh-Westergaard應(yīng)力空間和主應(yīng)力空間建立。但是兩

53、個模型在兩個不同空間里也有不同的地方。區(qū)別在于羅德角在Haigh-Westergaard應(yīng)力空間模型中被忽視了，然而在主應(yīng)力空間模型中被考慮到了。這兩個屈服準(zhǔn)則可以分別表示為：</p><p><b>　　(6)</b></p><p><b>　　(7)</b></p><p>　　其中p：體積應(yīng)力 q：剪應(yīng)力，

54、和分別是：靜水壓力軸和主應(yīng)力軸的遷移應(yīng)力。,,是應(yīng)力尺寸， i=(1,2,3,)，和是靜水壓力軸和屈服面的交叉點(diǎn)，，，，， ：由無量綱參數(shù)確定。</p><p>　　兩個模型的塑性流動法則分別是：</p><p><b>　　(8)</b></p><p><b>　　(9)</b></p><p&

55、gt;　　其中 ；:遷移應(yīng)力的相對水平量。和分別是體積應(yīng)變和偏應(yīng)變增量。 ; ; ,, 是三個塑性原理的應(yīng)變增量。</p><p>　　根據(jù)(Suaris and Shah 1985; Reinhardt 1984)研究結(jié)果中的混凝土的抗拉、抗壓強(qiáng)度和內(nèi)部變量的變化速率之間的關(guān)系：</p><p>　　(10) </p><

56、;p><b>　　(11)</b></p><p>　　分別是混凝土在單軸壓縮和張拉狀態(tài)下的動態(tài)強(qiáng)度。，，，這些是從實(shí)驗(yàn)數(shù)據(jù)中得出的假定條件。</p><p>　　這些變量以塑性應(yīng)變等效為條件得出：</p><p><b>　　(12)</b></p><p>　　是粘塑性應(yīng)變增量，m是由（8

57、）式和（9）式?jīng)Q定的塑性流動的單位張量</p><p>　　用著這些條件的一致性條件可以得出：</p><p><b>　　(13)</b></p><p>　　一致粘塑性模型可以用歐拉公式解決。熱力學(xué)不僅取得了廣泛的應(yīng)用，而且為混凝土性能的研究提供了更重要的依據(jù)。在以熱力學(xué)為基礎(chǔ)的模型中，關(guān)于耗散函數(shù)的形式的假設(shè)幾乎沒有，關(guān)于塑料的潛在功能和