Lifetime-Oriented Structural Design Concepts- P6 docx

2.4 Load-Independent Environmental Impact 107 are dissolved. This leads directly to an increase in porosity and permeability and also to a loss of stability. As a rule, no direct deformation of the affected structural element is observed in case of a dissolvent process. 2.4.3.1 Sulfate Attack An external sulfate attack is caused by water and soil layers containing sulfate or SO 2 in the air. The sulfate attack can only occur if damp is present. The formation of reaction products (see Subsection 3.1.2.3.3) which cause swelling in the concrete in sufficient quantities is decisive for a swelling attack following sulfate penetration. The resulting compressive stress due to expansion causes swelling, crack formation and ultimately leads to a loss of stability and damage to the cement matrix. Due to its great technological significance on account of the prevalence of concrete structures and the sulfate compounds which oc- cur almost everywhere (e.g in ground water, seepage water and soil layers), a large number of investigations into sulphate attack have been performed in the past. Current knowledge has been integrated into rules and standards [6],[14]. No damage has been reported in Germany for concrete with a high sulfate resistance where the measures defined in the standards have been ad- hered to [147]. For a number of years there have been international reports of a new form of sulphate damage to concrete structures; this is described as the thaumasite form of sulphate attack (Subsection 3.1.2.3.3). Unlike the gener- ally known forms of sulfate attack which lead to the formation of cracks and thus to a decrease in stability of the concrete through swelling reactions (et- tringite swelling and, at high sulphate concentrations, also gypsum swelling), a damaging formation of thaumasite leads to weakening; the strength-forming CSH-phases of the cement matrix are degraded. In general, concrete founda- tions of bridges and structures which were exposed to a strong sulfate attack in the ground are affected (e.g tunnel shells), Figure 2.89. Current knowledge of the most important damage-relevant factors and the overview of thauma- site damage in Germany and abroad are summarised in the progress report DAfStb 7 [147] entitled ”Sulfate attack on concrete”. In the [147] special in- terest is taken in the damage potential of pyrite-containing soils in Germany. The oxidation of pyrite-containing minerals (Subsection 3.1.2.3.3) in the ad- jacent stone or soil has been determined in several cases as the cause of the thaumasite form of sulphate attack [291]. 2.4.3.2 Calcium Leaching If the surface of a concrete structural element is in contact with soft water over extended periods the calcium hydroxide is broken down hydrolytically and calcium in the pore liquid is released (see Subsection 3.1.2.3.2). As a re- sult, the porosity and the permeability of the structure are increased and can 7 German Committee for Reinforced Concrete. 108 2 Damage-Oriented Actions and Environmental Impact Fig. 2.89. Concrete damage caused by thaumasite (taken from [151], origin: left - BRE; right - FA Finger-Institute, Weimar) Fig. 2.90. Corrosion on mortar coatings in two drinking water reservoirs. The coating shown on the right has been almost completely destroyed after about 10 years [138] ultimately lead to a loss of stability. The progression of the dissolving and thus of the damage front takes place very slowly with calcium leaching, especially under environmental conditions which are not constantly damp (several cen- timetres per decade). For normal structures, calcium leaching can generally be classified as uncritical. This environmental attack is, however, significant for structures which are in direct contact with soft water for an extended period of time, such as the inside of cooling tower shells and cementitious layers of drinking water reservoirs (Figure 2.90). In addition, calcium leaching is a deci- sive damaging mechanism for concrete constructions of nuclear disposal sites, as the assessment periods for these are several hundred years [804]. Further structures for which calcium leaching can be a stability problem are dams, tunnels and water pipes. 2.5 Geotechnical Aspects 109 2.5 Geotechnical Aspects Authored by Theodoros Triantafyllidis, Torsten Wichtmann and Andrzej Niemunis This section deals with the effect of a high-cyclic (long-term) loading on possible ”deterioration” effects in a soil. It is worth to be noticed that a high- cyclic loading does not cause ”damage”, ”fatigue” or ”deterioration” in a soil inthecommonsense,asitisobservedfor steel or concrete materials. Effects like abrasion of the soil particles or even fragmentation of the grains are not considered here because the design of a foundation usually exclude such states. Furthermore, within the framework of a continuum approach the permanency of the soil particles is assumed. However, a high-cyclic loading may change the soil fabric and may lead to an accumulation of permanent deformations. Thus, the serviceability of a foundation is the main concern if it is subjected to a high-cyclic loading. In a constitutive relation for soils under high-cyclic loading (see Section 3.3.3) the development of these permanent deformations may be modelled similar to a ”fatigue” in steel or concrete materials. Section 2.5.1 discusses possible sources of a high-cyclic loading of soils. It deals with the different appearance of the ”accumulation” phenomenon in dependence of the boundary conditions (e.g. drained or undrained cyclic loading) and outlines the possible consequences for structures. Section 2.5.2 presents a novel definition of an amplitude capturing a mul- tidimensional cyclic excitation. The definition is applicable not only to soils but also to any other material (e.g. steel or concrete) under multiaxial loading conditions. 2.5.1 Settlement Due to Cyclic Loading Authored by Theodoros Triantafyllidis, Torsten Wichtmann and Andrzej Niemunis Structures are interacting with the soil. The stiffness of the soil depends on the loading of the foundation and in turn the behaviour of the structure is influenced by the stiffness of the subsoil. The design of foundations depends in a great extent on the conditions of the underlain soil and in this way the soil is forming a part of the building. Uniform settlements of foundations do not produce any structural damage. The admissible settlement may be restrained by serviceability requirements only. Differential settlements are much more important. They may be caused by local variations of the geotechnical conditions such as a variation of the thickness or the depth of the settlement-sensitive layers, inclusions of soft materials or non-homogeneities of the void ratio or of the fabric of the soil. Differential settlements may also occur due to different foundation schemes (pile and shallow foundations side by side) and different loadings arising from the superstructure design (despite design efforts to avoid this). 110 2 Damage-Oriented Actions and Environmental Impact traffic loading, e.g. high speed or magnetic leviation trains watergates tanks, silos surface compaction, vibro-compaction crane rails wind power plants off-shore on-shore Fig. 2.91. Sources of cyclic loading of soils Soil compaction, soil replacement or the choice of a more appropriate foun- dation design are possible measures prior to the construction to minimize differential settlements. Such procedures have been developed in the past and are not subject of the present study. While differential settlements that occur during the construction process due to unpredictable soil inhomogeneities can be counteracted to some extent (by ground improvement or a change of the method of construction), such measures are difficult and expensive during the lifetime of a structure. With reference to the subsoil, life time oriented design concepts focus on permanent deformations in the subsoil which occur due to repeated load- ing during the operating time of a structure. Examples for such cyclic load- ing caused by traffic (high-speed trains, magnetic leviation trains), industrial sources (crane rails, machine foundations), wind and waves (on-shore and off- shore wind power plants) or repeated filling and emptying processes (water- gates, tanks and silos) are given in Figure 2.91. Furthermore, construction pro- cesses (e.g. vibration of sheet piles) and mechanical compaction (e.g. vibratory compaction) introduce cyclic loads into the soil. They cause a densification at the required position which is usually desired for the future construction but may cause some detrimental effects for the existing neighbours. A stress path due to a wheel passing on the ground surface is given in Figure 2.92a. In statically indeterminate structures the differential settlements may cause changes of internal forces which may slow down or accelerate the process of deterioration in the structure. Vice versa, a change of the reaction forces leads to a different rate of settlement accumulation. In statically indeterminate structures under monotonic loading the loading of more compliant foundations decreases due to a re-distribution of internal forces. The loading of the less compliant foundations increases and this may cause plastic deformations in the subsoil, i.e. the settlements of these foundations increase. Thus, the differential 2.5 Geotechnical Aspects 111 σ v0 σ h0 = K 0 σ v0 traffic loading σ v σ h τ σ v σ v σ h σ h γ γ GW GW ground shaking rock soil τ GW ground shaking τ wave propagation γ γ τ t τ τ,σ t a) b) σ v0 σ h0 = K 0 σ v0 σ v σ h σ v σ h Fig. 2.92. Cyclic stresses in a soil element a) due to a passing wheel load and b) due to an earthquake loading t ampl av s s Fig. 2.93. Accumulation of settlement due to cyclic loading settlement is reduced. For a cyclic loading this smoothing does not always work due to the decrease of the accumulation rate with the average pressure (Section 3.2.2). A life time oriented design concept for structures should include a joint analysis of the structure and the inhomogeneous subsoil. The settlements (Figure 2.93) due to cyclic loading occur since in an element of soil closed stress loops, resulting from external loading, lead to not perfectly closed strain loops. An irreversible deformation remains in the soil, caused by particle rearrangement due to changes of the intensity and the distribution of the contact forces between the particles. This permanent deformation is accumulated with the number of cycles. Even small amplitudes can signifi- cantly contribute if the number of cycles is high. Such a loading with small amplitudes and large numbers of cycles (N c > 10 3 ) is called poly- or high- cyclic loading. As confirmed by the element tests presented in Section 3.2.2 and also by parametric studies outlined in Section 4.6.6 the amount of resid- ual settlement depends on the loading of the foundation (average load, load amplitude) and on the current state of the soil (void ratio, cyclic preloading). 112 2 Damage-Oriented Actions and Environmental Impact Unfortunately, as demonstrated in Section 4.6.6 differential settlements due to cyclic loading are much more sensitive (by a factor 3) to inhomogeneities in the subsoil than those due to monotonic loading. In the context of foundations subjected to cyclic loading, one may distin- guish between the short-term and the long-term behaviour. Studies of the short-term behaviour deal with the deformation of the structure and the sub- soil within a few cycles (e.g. examinations of the dynamic characteristics of a system). In the majority of such studies a linear response is assumed consid- ering no changes of the soil parameters during the event. In the case where a non-linear behaviour of the soil has to be considered an implicit calculation can be performed as outlined in Section 4.2.11. In long-term studies the ac- cumulation of settlements or changes of the soil-structure interaction are the main concern. This book is dedicated to the long-term behaviour. If the load cycles are applied at a low amplitude and low frequency f = ω/(2π), the inertial forces are negligible and it is spoken of a quasi- static cyclic loading. If the frequency is large, inertial forces are relevant and the loading is dynamic. A harmonic excitation with the displacement u = u ampl cos(ωt) can be considered as quasi-static, if u ampl ω 2 is small com- pared to the acceleration of gravity g. Often the amplitude-dependence is ignored and the borderline to dynamic loading is said to lay above f ≈ 5 Hz. As reported by the literature and confirmed also by tests of the authors (with f<2Hzandε ampl ≤ 10 −3 , [835]) the loading frequency f does not influence the rate of strain accumulation as long as the strain amplitude ε ampl is constant. In order to estimate settlements due to cyclic loading and in order to incor- porate them into a life time oriented design concept for engineering structures one needs special calculation strategies and a constitutive description for the soil. Such a strategy and a high-cycle model have been developed and are presented in Sections 3.3.3 and 4.2.11. In Section 3.2.2 it is demonstrated for uniaxial cycles with a constant po- larization that having packages of cycles with different amplitudes their se- quence does not play a significant role for the final value of the permanent deformation. It is further assumed that a transient or periodic signal can be decomposed into a series of cyclic signals with different frequencies (Section 2.5.2). Afterwards these signals are grouped into packages in which the ampli- tude is constant (Figure 2.94). The analysis of the permanent soil deformation can then be performed as given in Sections 3.3.3 and 4.2.11. If the cyclic stresses in the soil are not too close to the failure criterion and if the amplitudes are below ε ampl ≈ 10 −5 the accumulation rate can be expected to become very small or even vanish after a sufficiently large number of cycles (adaptation, ”shakedown”). Having reached such asymptotic state the soil behaviour is almost linear elastic during the subsequent cycles. In such cases accumulation effects need not to be considered in the design of structures. In Section 3.2.2 it is demonstrated that polarization changes lead to a temporary increased accumulation rate. Having reached an asymptotic 2.5 Geotechnical Aspects 113 h(σ) t σ t σ Fig. 2.94. Decomposition of a signal with varying amplitudes into packages of cycles with constant amplitude state a re-start of the accumulation and adaptation process may occur after a sudden change of the polarization. However, no sound experimental studies exist on the accumulation at such small amplitudes. Thus, the effect cannot be validated or quantified yet. Another asymptotic state may be observed in saturated cohesive soils sup- porting a foundation which are subjected to a cyclic loading. The accumula- tion of pore water pressure (see remarks below) is very small, if the excitation frequency f is below the ratio c v /b 2 with c v being the coefficient of consoli- dation and b the width of the foundation (almost drained conditions) and if the strain amplitude is below ε ampl ≤ 10 −2 [329]. If the cyclic stress path repeatedly reaches the failure criterion an incre- mental soil collapse may occur. An application of cyclic loading with smaller amplitudes after a strong event (e.g. a storm in the case of offshore founda- tions) can lead at least hypothetically toa”healingeffect”,i.e.toareduction of deformations imposed by the strong event. A cyclic loading may not only cause permanent deformations. Depending on the boundary conditions it may also result in a change of the average stress. In water-saturated soils under partly drained or undrained conditions the pore water pressure u av may accumulate with the number of cycles due to the contracting soil behaviour. Thus, the effective mean pressure p av ,theshear strength and the stiffness decrease or even vanish (so-called ”liquefaction” or ”cyclic mobility” in case of temporary loss of shear strength). Such effects are observed e.g. during earthquakes (Figure 2.92b). While a ”man-made” high-cyclic loading on structures is associated with small ampli- tudes and a high number of cycles the number of cycles is small in the case of a seismic loading but the amplitudes are large. The drainage conditions play a significant role. Usually undrained conditions are considered for an earthquake loading because of the great intensity and the short duration of action. In con- trast, a high-cyclic loading is calculated assuming drained conditions because of the long duration and the small intensity of action. In the undrained case a pore water pressure accumulation takes place and as a consequence effects like liquefaction, phase or layer separation and spontaneous densification (during re-consolidation) may be observed. 114 2 Damage-Oriented Actions and Environmental Impact These effects can be utilized for an intelligent foundation design in order to establish a passive screening, i.e. to reduce the seismic loading acting on the structure and thus to prevent it from damage during an earthquake. A popular example for a passive screening are the foundations of the Higashi temple in Kyoto. In the case of an earthquake layers of fine grained material are brought to liquefaction in order to avoid the passage of shear waves to overlain layers or structures (so called ”Hanchiku-effect”). The liquefaction phenomenon is also utilized for soil improvement techniques (deep vibratory compaction). However, if the described phenomena under an undrained cyclic loading are not well understood by the design engineer a non-appropriate design of the foundation may be chosen. A more detailed discussion of the effect of a cyclic loading under various boundary conditions is given in Section 3.1.3. Another source of cyclic loading of soil, which is not discussed in detail in the present book, is caused by climatic changes and seasonal effects. Such loading is connected with changes of the portions of the three phases (solid particles, pore water, air) of a soil and may lead to changes of its fabric and its mechanical properties. The cyclic change of the water table e.g. leads to an ac- cumulation of water content (degree of saturation) in the transition zone and an alteration of the effective stress and the suction. This cyclic change of the effective stress acting on the solid phase may cause permanent deformations. In the case of cohesive soils permanent deformations are generally associated with wetting and drying processes leading to swelling and shrinkage. Clusters of tension cracks may occur influencing the hydraulic and mechanical prop- erties of the soil. Such kind of cyclic loading referring to hydro-mechanical coupling and partial saturation of soils is of great importance for water reser- voirs, dam embankments, dykes, etc. Sources and effects of cyclic loading are maningfold. In a life time oriented design all relevant influences and boundary conditions a soil may be exposed to (depending in turn on the design solution) have to be kept in mind. 2.5.2 Multidimensional Amplitude for Soils under Cyclic Loading Authored by Andrzej Niemunis, Torsten Wichtmann and Theodoros Triantafyllidis A cycle is understood as a path (a trajectory parametrized by time) which is recurrently passed through by a state variable (like strain or stress). For a scalar or tensorial variable  we may define its average value  av to be the centre of the smallest (hyper)sphere that encompasses all states  upon the cycle. For a scalar variable one obtains  av = 1 2 ( max +  min )andthe amplitude is  ampl =max|− av |. For tensorial variables, apart from the size of the (hyper)sphere, we want to convey some information on the polarization and the ovality of the path, which renders the amplitude to become a tensor. Further we consider strain cycles ε(t)only,withε =lnU where U is the right stretch tensor. We distinguish between in-phase (=IP) strain cycles 2.5 Geotechnical Aspects 115 -1.0 1.0 1.0 -1.0 0.5 0.5 c) OOP - cycles: b) multiaxial IP - cyclesa) uniaxial IP - cycles 0.5 0.5 -0.5 -0.5 ε 3 ε 1 ε 3 ε 1 -1.0 1.0 1.0 -1.0 0.5-0.5 ε 3 ε 1 -1.0 1.0 -0.5 -0.5 ampl = 1, ampl = 1, = /4 13 ampl = 1, ampl = 1 13 ampl = 1, ampl = 0 13 Fig. 2.95. Distinction between uniaxial IP-, multiaxial IP- and OOP-cycles ε ij = ε av ij + ε ampl ij f(t), −1 ≤ f(t) ≤ 1 (2.76) for which the variability of all components in time can be described by a com- mon function f (t)andout-of-phase (=OOP) cycles which cannot be expressed in this way, e.g. ε = ε av +diag(ε ampl 11 sin(ωt + ϕ 11 ),ε ampl 22 sin(ωt + ϕ 22 ), 0) ϕ 11 = ϕ 22 (2.77) and which require individual time tracking f ij (t)ofvariousε ij components. The collection ε ampl ij of the amplitudes of the individual components in (2.76) should not be mixed up with the tensorial definition of the amplitude A A A ε which will be proposed further. The IP-cycles that have only one non-zero eigenvalue of ε ampl are termed uniaxial, ε = ε av +diag(ε ampl 1 , 0, 0) f(t) , (2.78) otherwise they are multiaxial ε = ε av +diag(ε ampl 1 ,ε ampl 2 ,ε ampl 3 ) f(t) . (2.79) All OOP cycles are multiaxial too. All definitions are illustrated in Figure 2.95. A harmonic OOP-cycle (Figure 2.95c) the components of which differ by the phase-shifts ϕ ij but not by the angular frequency ω ij = ω =constis termed harmonic oscillation and forms a 6-d ellipse in the strain space. This concept is useful in the Fourier analysis of the deformation treated as a 6-d signal. Arguments for expressing the amplitude and the accumulation in terms of strain rather than stress in the high-cycle model for soils (Section 3.3.3) have been discussed in [578]. Given from laboratory tests a cycle in form of a stress path σ(t) or a mixed path we must evaluate all unknown (if any) components 116 2 Damage-Oriented Actions and Environmental Impact of the strain path ε(t)solvingσ(t)=E E E : ε(t) for the unknown ε ij (t)using the secant elastic stiffness E E E of the cycle. Similarly, given the cumulative rates from experiments (measured (=  m ) or prescribed), namely pseudo-relaxation ˙ σ m (N c ) and pseudo-creep D m (N c ), the constitutive strain accumulation rate D acc is obtained by solving the material equation ˙ σ m = E E E m :(D m − D acc ). Note that all rates are meant as increments or residuals after a single cycle in the high-cyclic context. A description of polarization must involve all 6 components of the strain path ε(t) because the strain states need not be coaxial upon a cycle. In order to evaluate the tensorial strain amplitude A A A ε from a discrete path ε(t 1 ), ε(t 2 ), obtained from laboratory tests or from FE-calculations one should avoid using the first cycle (= irregular cycle discussed in Section 4.2.11). From a represen- tative (recorded or calculated) cycle ε(t) we extract the resilient strain path ε e (t). It is done by subtracting the residual (cumulative) portion (pseudo- creep) from it. This operation is called detrending. The proposed detrending procedure consists of four steps: • Calculate the hodograph D(t) ≈ ˙ ε(t), Fig. 2.96 • Find the shortest period T from the requirement  D(t) −D(t + T ) dt → min • Find the average D av and interpret it as the rate of accumulation wrt time, D av = D acc /T • Subtract the cumulative portion from the original path: ε e (t)=ε(t)−D av t with t ∈ [0,T]. 1 2 1 1 2 2 D acc D acc D 1 D D 2 D a) b) Fig. 2.96. A hodograph is a trajectory of D(t) ≈ ˙ ε(t) parametrized with time t, analogously to the strain path ε(t). The rate of accumulation can be easily identified as a drift rate (denoted with arrow) of the average strain upon a cycle. Note that the strain rate is an exactly periodic function D(t)=D(t +NT) whereas the strain ε(t) is not. The distinction between a) the cycles encompassing some area (out-of-phase cycles (= OOP) and b) the open-curve cycles is of importance [...]... and Henning Sch¨ tte u Also in metallic materials loaded cyclically at nominal stresses below the static yield strength undergo progressive, localized, and permanent structural changes, i.e also in these materials fatigue takes place The structural change thus can be described on the macroscopic level as brittle, due to the fact that under these conditions there is only microplasticity In general, this... soils (Subchapter 3.1), results and insights gained from laboratory investigations on the fatigue behaviour of concrete, metals and soils, nondestructive testing of microcrack evolution in metals and structural testing of composite structures performed within the Collaborative Research Center SFB 398 (Subchapter 3.2), numerical models developed within the SFB 398 for cementitious materials, metallic... from time variant drying and wetting processes, dissolution and chemically expansive processes such as the AlkaliSilica reaction (Subchapter 3.3) This Subsection also contains selected applications to structural durability analyses 124 3 Deterioration of Materials and Structures 3.1 Phenomena of Material Degradation on Various Scales Authored by Otto T Bruhns and G¨nther Meschke u Initiation and evolution... propagation The descending branch of the stress-strain curve (softening) in range 4 is associated with progressive localisation and accumulation of micro- and mesocracks leading finally to the fracture of the structural member by a discrete crack A lower content of coarse aggregates as well as smaller maximum aggregate sizes result in a more abrupt decrease of the stress-strain curve compared to larger contents... High Cycle Fatigue (HCF) is associated with the evolution of damage resulting from a large number of cycles at low and moderate levels, Low Cycle Fatigue (LCF) is a frequently observed mode of failure in structural components made of ductile metals subjected to repeated loading at high stresses and high stress amplitudes The damage mechanisms for LCF can be classified broadly into two major groups: transgranular... zones of very large plastic deformations, low cycle fatigue damage may be initiated by void nucleation, continuous growth and finally coalescence of micropores leading eventually to macroscopic cracks and structural failure (Figs.3.8, 3.7) This damage phenomenon highly depends on the stress triaxiality, which is the ratio between the mean and equivalent stress [524] Since nucleation and growth of micropores... Uniaxial Cyclic Compression Loads: Multi-stage Cyclic Loadings While in most of the investigations discussed up to now only constant stress levels within one cyclic test were considered, constructions and structural elements in practice normally are exposed during their lifetime to quite varying cyclic stress levels and regimes, which can be pooled by means of damage accumulation hypothesis in multi-stage... analysis will be given in future 3 Deterioration of Materials and Structures: Phenomena, Experiments and Modelling Authored by Otto T Bruhns and G¨nther Meschke u Reliable computational prognoses of the structural integrity and serviceability throughout the lifetime of structures require the realistic consideration of the damage behaviour of the construction materials for various loading scenrios including . shallow foundations side by side) and different loadings arising from the superstructure design (despite design efforts to avoid this). 110 2 Damage-Oriented Actions and Environmental Impact traffic. described phenomena under an undrained cyclic loading are not well understood by the design engineer a non-appropriate design of the foundation may be chosen. A more detailed discussion of the effect. loading are maningfold. In a life time oriented design all relevant influences and boundary conditions a soil may be exposed to (depending in turn on the design solution) have to be kept in mind. 2.5.2