648 4 Methodological Implementation Void ratio e 26.0 m 13.0 m 1.0 5.0 1.0 1.0 σ σ σ ampl = 50 kPa σ av = 100 kPa 0 5 10 15 20 0 10 20 30 40 50 Correlation length 0.5 m 2.0 m 20.0 m (Δs/s) stat [%] (Δs/s) cyc [%] a = 3.1 a = 2.9 a = 2.6 a) b) s l s l s r s r s Δs s σ s stat s cyc σ av (Δs/s) cyc (Δs/s) stat a = N c = 10 5 cycles Fig. 4.182. FE calculations with stochastically fluctuating fields of the initial void ratio: a) dimensions and an example of a field e(x), b) differential settlement due to cyclic loading as a function of the differential settlement due to static loading different fields e(x) (see an example in Figure 4.182a) were tested. Let s l and s r be the settlements of the left and the right foundation, respectively (Figure 4.182a). The differential settlement Δs = |s l − s r | was divided by the mean value ¯s =(s l + s r )/2. The ratio (Δs/¯s) stat due to static loading up to σ av was compared to the ratio (Δs/¯s) cyc describing the additional differential set- tlement accumulated during the subsequent 10 5 cycles. Independently of the correlation length the differential settlement (Δs/¯s) cyc resulting from cyclic loading was observed to be approximately three times larger than (Δs/¯s) stat caused by static loading (Figure 4.182b). This finding can be attributed to the fact that the settlement due to monotonic loading is proportional to the load, while the accumulation rate under cyclic loading is proportional to the square of the strain amplitude, i.e. approximately proportional to the square of the load. Therefore, a cyclic loading has a smaller range of influence than a monotonic loading and inhomogeneities of the field e(x) near the foundations have a larger effect (i.e. the differential settlements are larger due to averaging over a smaller region). Keßler [428] used the high-cycle model to simulate a vibratory compaction in a certain depth (Figure 4.183a, the pulling-out of the vibrator was not modelled yet). The initial densitiy and the frequency were varied. In that case, the implicit steps of the calculation were performed dynamically. Canbolat [168] determined the settlements of the abutment of a bridge (”H¨unxer Br¨ucke”) under 53 years of traffic loading. The geometry of the problem and the FE mesh are given in Figure 4.183b. The profile of void ratio with depth was chosen in accordance with in-situ CPT measurements using correlations. A special calculation strategy was used in order to apply the initial stress within the embankment [168]. The traffic loading was esti- mated based on the general development of traffic in the period 1951 - 2004, with traffic measurements for similar streets and with an information about 4.6 Application of Lifetime-Oriented Analysis and Design 649 void ratio e 0 = 0.715 I D0 = 0.4 N c = 4,000 infinite elements vibrator 0246810 4 6 8 10 s [cm] Number of cycles N c [10 6 ] s Pack. large small Pack. small large Settlement s [m] a) b) 15 m σ σ t Fig. 4.183. a) FE calculation of a vibratory compaction see Keßler [428], b) FE calculation of the settlements of a bridge cp. Canbolat [168] the percentage of the different classes of vehicles. The varying amplitudes due to different classes of vehicles were collected in packages of a constant amplitude. The accumulation model was also used by Niemunis et al. [580] for the calculation of excess pore water pressures and settlements in a water-saturated sand layer under earthquake loading. This problem was studied using the Finite Difference Method. A special numerical strategy was tested (Figure 4.184a). The fast processes (propagation of shear wave) were decoupled from the slow processes (accumulation of the mean values, e.g. excess pore water pressure) for one period T of the harmonic excitation of the rock bed. The dynamic calculation of the shear wave propagation in the sand layer during the first period T of excitation was performed with fixed values of σ av (average effective stress), u av (average excess pore water pressure) and e av (average void ratio). At the end of the period, the change of σ av , u av and e av during T was calculated by means of the accumulation model. For this purpose the strain amplitude ε ampl was obtained from the dynamic calculation. The pore water dissipation was also calculated in a separate step, i.e. decoupled from the ”dynamic” and the ”cumulative” mode. The values u av and σ av were modified over a period T (consolidation). The dynamic calculation of the wave propagation during the second period of excitation followed using the modified values of σ av , u av and e av , and so on. The introduction of special boundary conditions lead to a reflection of the shear wave at liquefied layers. Figure 4.184b presents an example of a calculation, i.e. the distributions of shear strain γ, shear strain amplitude γ ampl and excess pore water pressure u av with depth z for 15 calculated periods T (N = 15). It has to be critically remarked, that the shear strain amplitudes mostly exceed γ ampl =10 −3 (Figure 4.184b) and thus lay in a range, which was scarcely covered by laboratory tests up to now. 650 4 Methodological Implementation 0 T 2T 3T 0123 Time t Number of cycles N dynamic analysis (elastoplastic wave) explicit calculation of accumulation σ av , u av , e av = constant time increments Δt << T v s u calculation of consolidation u 0 T 2T 3T Time t 1 2 3 4 Depth z [m] 100 80 60 40 20 0 -6 -4 -2 0 2 4 6 γ [10 -3 ] 0 200 400 600 800 1000 u [kPa] 0213456 γ ampl [10 -3 ] liquefied layer N c = 15 a) b) sand rock u ampl earthquake −σ v0 −σ v0 −σ v0 z Fig. 4.184. Calculation of the pore water pressure accumulation in a water- saturated sand layer under earthquake loading (displacement amplitude u ampl = 1 cm at the rock bed in a depth z = 100 m) after Niemunis et al. [580]: a) numerical strategy, b) profiles of shear strain γ, shear strain amplitude γ ampl and excess pore water pressure u with depth Geogrid-reinforced soil structures under cyclic loading were studied by Ar- wanitaki & Triantafyllidis [65] (Fig. 4.185a). In particular, a geogrid-reinforced embankment on piles in soft ground was investigated. In such systems the ver- tical loads are conducted into the piles via stress arches developing in the base layer. The cyclic loading was applied on the soil surface simulating traffic load- ing caused by trains. Arwanitaki & Triantafyllidis demonstrated that cyclic loading leads to a weakening of the stress arches causing large settlements. A reduction of accumulated settlements with increasing number of geogrid layers was observed (Fig. 4.185b). The high-cycle model has been also applied to predict the long-term defor- mations of wind power plant foundations. The construction of many offshore wind parks is planned in the North Sea and the Baltic Sea during the next years. The foundations of OWPPs are subjected to a high-cyclic loading due to wind and waves. During its life time apart from many (millions or billions of) cycles with small to intermediate amplitudes an OWPP is also subjected to a few load cycles with large amplitudes (due to strong storms) Both the large and the small cycles may cause permanent deformations. However, the small cycles may theoretically lead to a ”self-healing” of the structure, i.e. large deformations occuring during strong storms may be reduced due to 4.6 Application of Lifetime-Oriented Analysis and Design 651 a) b) σ [kPa] σ (traffic loading) soft ground sand 1.6 m 0.5 m 2.3 m piles geogrids base layer 4.0 m t 10 20 30 40 50 60 Settlement s [mm] N c [-] 10 2 10 3 10 5 10 1 10 4 10 6 4 mm 19 mm s with 3 geogrid layers without geogrids 10 70 control cycles Fig. 4.185. FE calculation of a geogrid-reinforced embankment under traffic loading see Arwanitaki & Triantafyllidis [65]: a) geometry and loading, b) comparison of the curves of settlement s(N c ) for an embankment with three geogrid layers and a non- reinforced embankment Detail 60 m 20 m 20 m 5 m t 33 m z 6.3 m 5 m -0.01 0 0.01 0.02 0.03 0.04 -35 -30 -25 -20 -15 -10 -5 0 5 N c = 0 N c = 10 N c = 110 N c = 1,200 N c = 11,000 N c = 110,000 N c = 1,100,000 Depth z below seabed [m] Horizontal displacement [m] a) b) c) d) 0 10 20 30 40 50 60 Moment M [MNm] Packege No. 12345 678 910 12 14 16 18 210,000,000 100,000,000 49,000,000 340,000,000 14,000,000 9,600,000 11,000,000 24,000,000 2,400,000 960,000 2,100,000 1,300,000 1,700,000 1,100,000 730,000 440,000 4700 5,200,000 870,000,000 N c = Q, M/(2d) M/(2d) M/(2d) Q/4 Q/4 seabed many small cycles strong storm medium dense to dense fine sand wind waves Fig. 4.186. FE calculation of a monopile foundation of an offshore wind power plant in the North sea compare Wichtmann et al. [843]: a) geometry of the foundation, b) FE model, c) idealized cyclic loading, d) increase of the horizontal displacement of the monopile with increasing N c , calculation of load package No. 16 subsequent millions of cycles with small amplitudes. The long-term deforma- tion behaviour of the foundations of OWPPs is not well-understood yet. Little operating experience exists and no established methods for a prediction of the 652 4 Methodological Implementation serviceability (e.g. tilting after 20 years of operation) are available in the lit- erature. Experiences from existing offshore or onshore wind power plants or conventional offshore foundations cannot be easily adapted due to the large dimensions and large loads of the new OWPPs. Figure 4.186a presents an example of a monopile foundation, i.e. the wind power plant is founded on a single steel pile with a large diameter (usually > 5 m). The FE mesh is given in Figure 4.186b. Since an uni-directional cyclic loading was studied the symmetry of the system could be utilized. The ideal- ized loading resulting from wind and waves was grouped into packages with similar average value and amplitude (Figure 4.186c). Figure 4.186d exhibits that the high-cycle model predicts an increase of the horizontal deformations, i.e. an increase of the tilting of the OWPP with the number of cycles N c . The aim of future research will be to exploit the limits of foundation design for extreme load events. 5 Future Life Time Oriented Design Concepts Authored by Friedhelm Stangenberg, Dietrich Hartmann, Tobias Pfister and Andr´es Wellmann Jelic 5.1 Exemplary Realization of Lifetime Control Using Concepts as Presented Here Authored by Friedhelm Stangenberg, Dietrich Hartmann, Tobias Pfister and Andr´es Wellmann Jelic In the following two possible applications of the lifetime control concepts proposed within this book are examplarily presented. 5.1.1 Reinforced Concrete Column under Fatigue Load Authored by Friedhelm Stangenberg and Tobias Pfister In this first example, a reinforced concrete column under static and fatigue load is investigated. It is subjected to a static load case, which is assumed to appear once a year and a fatigue load case with one million cycles per year. The reliability of the structure as the major design matter is investigated in the initial state and during the scheduled lifetime of 80 years. The column is shown in Figure 5.1. A basic quantity for the estimation of the reliability is the scatter of ma- terial and model properties and of the load: the compressive strength, the tensile strength, the stiffness, and fracture energy are assumed normally dis- tributed and fully correlated. The scatter of the lifetime N f according the S-N-approach, as the basic quantity for the fatigue model, is correlated to the scatter of the compressive strength like described in Section 3.3.1.2.2.1, see e.g. eq. (3.125). The static load is assumed normally distributed. 654 5 Future Life Time Oriented Design Concepts static static cyclic h =4.00 m e P P f T 40 cm 40 cm 2×3d16 6elments, each 10 concrete la yers Fig. 5.1. Reinforced concrete column under fatigue loading load P [ MN ] displacement f [ cm ] P f 0.0 0.5 1.0 1.5 2 . 0 0 2 4 6 8 10 12 compressive stregth f c [ MPa ] load P [ MN ] 20 30 40 50 60 70 0.0 0.5 1.0 1.5 2 . 0 Fig. 5.2. Degradation of the load-carrying-capacity and response surfaces at T =0a and T = 80 a together with Monte Carlo simulation points The reliability in the initial state is estimated with the response surface method according to Section 4.4.2.3. The original design with 3 bars of di- ameter 16 mm on each side results in P f =0.532×10 −6 and could thus be accepted. The time-dependent reliability is estimated with the time-discretization approach according to Section 4.4.3.2. The failure rate is evaluated with the response surface method for each time instant and integrated over the number of load events. Figure 5.2 (left diagram) shows the simulated degradation of the load-carrying capacity of the column due to increasing deformation and damage. The right diagram shows the resulting response surfaces in the 5.1 Exemplary Realization of Lifetime Control 655 log h P ( t ) ,logP f ( t ) time T [ a ] 020 40 60 80 -10 -9 -8 -7 -6 -5 -4 -3 P f (t) h P (t) lo g h P ( t ), lo g P f ( t ) time T [ a ] 0 20 40 60 80 -10 -9 -8 -7 -6 -5 -4 -3 Fig. 5.3. Time-dependent hazard function and time-dependent reliability: original design (left) and improved design (right) initial state and after 80 years lifetime, together with a cloud of Monte Carlo simulation points. The developing of the values of the hazard function as well as of the time-dependent reliability are shown in the left diagram in Figure 5.3. After 50 years, EC1 demands a safety index of β =3.8. Under assumption of a normal distributed limit state function, this corresponds to a failure probability of P f =7.24×10 −5 . Like indicated in the diagram, this failure probability is missed, so the design has to be changed. As one possible alternative, the number of reinforcing bars has been changed from 3 to 4 on each side. The resulting values of the hazard function and of the reliability are shown in the right diagram in Figure 5.3. This design could be accepted. 5.1.2 Connection Plates of an Arched Steel Bridge Authored by Dietrich Hartmann and Andr´es Wellmann Jelic The lifetime-oriented design of an arched steel bridge has been discussed al- ready in Section 4.6.4, at full length. Here, therefore only the general approach for the lifetime analysis is recapitulated with respect to an implementation into the practice. The bridge contemplated in Section 4.6.4 is an arched steel bridge erected in M¨unster, Germany, in 2001. Structural details of this struc- ture, which are sensitive to fatigue, are the plates connecting the vertical tie rods with the main girders. During the design phase of this bridge, the checking methods for fatigue ac- cording to the German standard EC3 have been applied indicating that the stresses in the connecting plates are not exceeding the corresponding limit val- ues. However, several connecting plates of the real structure showed macro cracks, already two years after the construction. Hence, more sophisticated 656 5 Future Life Time Oriented Design Concepts P a r a l l e l / d i s t r i b u t e d s o f t w a r e s y s t e m L e v e l o f o p t i m i z a t i o n e l a c s e m i t o r c i M e l a c s e m i t o r c a M Loading / Load capacity Damage model Strucural detail Damage evolution F t L e v e l o f r e l i a b i l i t y Total structure Load model EA EI Fig. 5.4. Multi-level system approach followed during the lifetime analysis of the arched steel bridge [826] lifetime-oriented design concept methods have been developed to estimate re- liable lifetime values and, furthermore, investigate possible structural improve- ments. The design concept, suggested in Subsection 4.6.4, comprises two main approaches (Figure 5.4 and 5.5) which are to be explained more detailed. As depicted in Figure 5.4, a multi-level system approach is chosen having the following sublevels: • Level of load model where external loads are described analytically • Level of total structure where those structural members are identified that are most sensitive with respect to fatigue • Level of structural member for which a structural analysis and a compu- tation of stress-time histories is carried out • Level of fatigue in the critical structural components of the bridge identi- fied according to used verification concepts for fatigue • Reliability level for the time-variant limit state of fatigue • Optimization level of the total structure as well as the identified weak structural components All sublevels are embedded in a parallel and distributed software system as illustrated by the external shell in the diagram (see Figure 5.4). Another key idea of the design concept is the multi-scale resolution of load actions with respect to time allowing the separation of the two computing 5.1 Exemplary Realization of Lifetime Control 657 F(t) t X 2 X 1 Load Structure Response Load process Fatigue process Micro time [t] = s Macro time [t] =h X(t) ! t X 3 ! = 1  ! = 2  ! = 3 d(t) ! t ! = 1  ! = 2  ! = 3 Fig. 5.5. Multi-scale modeling and analysis of fatigue-related structural problems tasks structural analysis and reliability analysis. For that, different time scales in the micro and macro scale are introduced and analyzed in an interlocked fashion, as demonstrated in Figure 5.5. Within the micro time scale single load events, i.e. 10-min wind processes or vehicle crossing, are analyzed with regard to their structural impact. The numerical results of the structural analyses, carried out by means of a Finite Element Analysis for different parameter sets of the corresponding load event, are stored in a file-based lookup table. Subsequently, the random sequence of these single load events is modelled in the macro time scale represented by stochastic pulse processes. Here, partial damage values induced by each load event are estimated using stochastically defined S-N-curves. Finally, the partial damages are accumulated analogously to the pulse process until a predefined damage limit state is reached. The numerical methods, used in the above-named sublevels, have already been explained in section 4, together with exemplary results in Subsection 4.6.4. In the given context, only the achieved lifetime increase of the ex- emplarily researched structural problem is highlighted. For that, Figure 5.6 shows the time-dependent evolution of computed failure probabilities of the connection plate. The comparison of the two plotted curves substantiates the drastically increased lifetime of the optimized plate shape. E.g. at a reliability level of P f =2.3%, the lifetime of the original shape (T L =0.025 a) has been improved to T L =5.6 a for the optimized plate shape. Finally, the main benefits of the proposed multi-scale and multi-level ap- proach can be summarized as follows: According to the multi-level system approach, a well-organized and simplified model of the initially complex struc- tural design problem is provided. By that, suitable analytical solution methods [...]... introduced into structural design processes and into the management of existing structures A reasonable and sufficiently simplified handling of the resulting tools of these lifetime related structural control concepts will be the next step in a continuing development 5.3 Incorporation into Structural Engineering Standards Authored by Friedhelm Stangenberg The realization of lifetime control in structural engineering... links are implemented for providing later detailing of regulations concerning lifetime control 5.3 Incorporation into Structural Engineering Standards 659 E.g EC1 mentions five “building classes” distinguishing different design working life”: • • • • • temporary buildings, renewable structural components (e.g bearing elements), agricultural or similar structures, residential and business buildings,... • • • • effecting a change in structural engineering mentality; pointing out the significance of a reliable service-life control to owners, users, licensing authorities, insurance companies, designing and controlling engineers; integrating service-life control aspects in quality assurance systems; transfer into codes, model codes and international regulatory principles of structural engineering References... 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Theory, Computation and Applications, pp 67–155 Springer, Heidelberg (2000) 205 Committee on Fatigue and Fracture Reliability of the Committee on Structural Safety and Reliability of the Structural Division Fatigue reliability: A stateof-the-art review Journal of the Structural Division 108, 1–88 (1982) 206 Cooke, R.D., Malkus, D.S., Plesha, M.E., Witt, R.J.: Concepts and Applications of Finite Element Analysis... tie rods In: Proceedings of the 2nd International Conference Lifetime Oriented Design Concepts, Bochum, pp 421–429 (2004) 297 Galffy, M., Wellmann Jelic, A., Hartmann, D.: Lifetime-oriented modelling of wind-induced vibrations on bridge tie rods In: Soize, C., Bonnet, G., BricoutBonnet, M.-A (eds.) 6th European Conference on Structural Dynamics (EURODYN 2005), Paris, France, pp 1–6 Millpress, Rotterdam... adhesives 21, 17–34 (2001) 47 Ang, A., Tang, W.H.: Probability concepts in engineering planning and design, Part II John Wiley & Sons, New York (1984) 48 ANSYS Theory Reference, Release 7.1 SAS IP Inc., Southpointe - Canonsburg (2002) 49 Antoulas, A.C.: Approximation of large-scale dynamical systems Advances in design and control SIAM, Philadelphia (2005) 50 Antoulas, A.C.: An overview of approximation methods... Frost-Tausalzwiderstandes von Beton, pp 121–131 Cuvillier Verlag (2006) 120 Bevanda, I., Setzer, M.J.: Frost damage in laboratory and practice In: Stangenberg, F., Bruhns, O.T., Hartmann, D., Meschke, G (eds.) Lifetime-oriented Design Concepts, pp 287–296 Aedificatio Publishers (2007) 121 Bialecki, R.A., Kassab, A.J., Fic, A.: Proper orthogonal decomposition and modal analysis for acceleration of transient FEM thermal... physical attacks” For steel reinforcement, EC2 mentions, in context with reinforced concrete structural longtime resistance: “Where required, the products shall have adequate fatigue strength” EC3, for steel structures, gives regulations for taking into account degradation effects due to “fatigue” Further references to structural lifetime control can be found in other modern building codes However, these . bridge [826] lifetime-oriented design concept methods have been developed to estimate re- liable lifetime values and, furthermore, investigate possible structural improve- ments. The design concept,. in Figure 5.3. This design could be accepted. 5.1.2 Connection Plates of an Arched Steel Bridge Authored by Dietrich Hartmann and Andr´es Wellmann Jelic The lifetime-oriented design of an arched. Level of total structure where those structural members are identified that are most sensitive with respect to fatigue • Level of structural member for which a structural analysis and a compu- tation