Validation of a thermal bias control technique for Coda Wave Interferometry (CWI)

Evaluation of compressive damage in concrete using ultrasonic nonlinear coda wave interferometry

This study investigates the feasibility of nonlinear coda wave interferometry (NCWI) for evaluating compressive damage in concrete, with a particular focus on the interference caused by the compressive stress-induced slow dynamics. Slow dynamics refers to a phenomenon in which the stiffness of concrete immediately decreases after moderate mechanical conditioning and then logarithmically evolves back to its initial value over time. A series of experiments were conducted to validate this concept. The experimental findings indicate that slow dynamics following the unloading of concrete specimen significantly interfere with NCWI testing. The changes in dv/v caused by the slow dynamics are opposite to those induced by the pump wave in NCWI. After the slow dynamics have been eliminated, an evaluation indicator, defined as the efficient nonlinear level αdv/v, demonstrates an excellent correlation with compressive damage. The value of the indicator decreases with increasing compressive stress. Furthermore, the coda wave interferometry (CWI) and direct wave interferometry (DWI) are performed as comparisons. In summary, the feasibility and superiority of NCWI are demonstrated in concrete compressive damage evaluation.

Impact of temperature and relative humidity variations on coda waves in concrete

The microstructure of concrete can be affected by many factors, from non-destructive environmental factors through to destructive damage induced by transient stresses. Coda wave interferometry is a technique that is sensitive enough to detect weak changes within concrete by evaluating the ultrasonic signal perturbation compared to a reference state. As concrete microstructure is sensitive to many factors, it is important to separate their contributions to the observables. In this study, we characterize the relationships between the concrete elastic and inelastic properties, and temperature and relative humidity. We confirm previous theoretical studies that found a linear relationship between temperature changes and velocity variation of the ultrasonic waves for a given concrete mix, and provide scaling factors per Kelvin for multiple settings. We also confirm an anti-correlation with relative humidity using long-term conditioning. Furthermore, we explore beyond the existing studies to establish the relationship linking humidity and temperature changes to ultrasonic wave attenuation.

Lamb Wave-Based Structural Damage Detection: A Time Series Approach Using Cointegration

Although Lamb waves have found extensive use in structural damage detection, their practical applications remain limited. This limitation primarily arises from the intricate nature of Lamb wave propagation modes and the effect of temperature variations. Therefore, rather than directly inspecting and interpreting Lamb wave responses for insights into the structural health, this study proposes a novel approach, based on a two-step cointegration-based computation procedure, for structural damage evaluation using Lamb wave data represented as time series that exhibit some common trends. The first step involves the composition of Lamb wave series sharing a common upward (or downward) trend of temperature. In the second step, the cointegration analysis is applied for each group of Lamb wave series, which represents a certain condition of damage. So, a cointegration analysis model of Lamb wave series is created for each damage condition. The geometrical and statistical features of Lamb wave series and cointegration residual series are used for detecting and distinguishing damage conditions. These features include the shape, peak-to-peak amplitude, and variance of the series. The validity of this method is confirmed through its application to the Lamb wave data collected from both undamaged and damaged aluminium plates subjected to temperature fluctuations. The proposed approach can find its application not only in Lamb wave-based damage detection, but also in other structural health monitoring (SHM) systems where the data can be arranged in the form of sharing common environmental and/or operational trends.

Towards quantifying the effect of pump wave amplitude on cracks in the Nonlinear Coda Wave Interferometry method

In Non-Destructive Testing and Evaluation (NDT&E), an ultrasonic method called Nonlinear Coda Wave Interferometry (NCWI) has recently been developed to detect cracks in heterogeneous materials such as concrete. The underlying principle of NCWI is that a pump wave is used to activate the crack breathing which interact with the source probe signal. The resulting signal is then measured at receiver probes. In this work, a static finite element model (FEM) is used to simulate the pump wave/crack interaction in order to quantifies the average effect of the pump waves on a crack. By considering both crack opening and closure phases during the dynamic pump wave excitation, this static model aims to determine the pump stress amplitude for a given relative crack length variation due to the dynamic pump wave excitation at different amplitudes. Numerical results show, after reaching certain stress amplitude, a linear relationship between the relative crack length variation and the equivalent static load when considering a partially closed crack at its tips. Then, numerical NCWI outputs, e.g., the relative velocity change θ and the decorrelation coefficient K_d, have been calculated using a spectral element model (SEM). These results agree with previously published experimental NCWI results derived for a slightly damaged 2D glass plate.

Thermo-acoustoelastic effect of Rayleigh wave: Theory and experimental verification

Previous studies showed that the thermally-induced ultrasonic bulk wave velocity change could be used to measure acoustoelastic coefficients and third-order elastic constants of elastic materials. This method is naturally immune from the ambient temperature effect and has improved sensitivity and a simpler test setup than the conventional acoustoelastic test. However, Rayleigh wave is preferred for thick components or structures with only one accessible surface. In this work, the thermo-hyperelastic constitutive equation, along with acoustoelastic theory, is used to derive the expression of the thermo-acoustoelastic coefficient (TAEC) of Rayleigh wave. The numerical relationship between the TAEC of Rayleigh wave and Murnaghan constants (l, m and n) are given for common metals. The TAEC expressions for Rayleigh wave and shear wave are similar, and both are dominated by the constant m. The TAEC of Rayleigh wave was measured on an aluminum 6061 specimen using the thermal modulation experiment in a temperature range of 22 ∼35 °C. The measured TAEC shows good agreement with the theoretical calculation. Then the third-order elastic constants were calculated based on TAECs of bulk waves and Rayleigh wave.

Monitoring saltwater corrosion of steel using ultrasonic coda wave interferometry with temperature control

Assessing corrosion is crucial in the petrochemical and marine industries. Usual ultrasonic methods based on pulse-echo and guided waves to detect corrosion lack of precision and struggle in structures with a complex shape. In this paper, a complementary and sensitive ultrasonic method based on coda wave interferometry is presented to detect and quantify thickness loss caused by saltwater corrosion of a steel sample. The method consists in exciting the sample and measuring periodically the scattered coda signal. Correlation of the coda signal with a reference taken for the sample initial state permits the monitoring of corrosion spread with a high accuracy. A laboratory experiment is conducted with two steel samples immersed in saltwater with coda and temperature measured simultaneously. One of the samples is protected from corrosion and is used as a control sample to determine the influence of temperature on the coda signals. It is shown that the coda signals on the corroded sample can be temperature-corrected using the temperature measurement only. A control sample is not needed. A good correlation is found between a parameter quantifying the stretching of the coda over time and the corrosion surface, which is monitored with a camera. Finally, a simple theoretical model of coda signal is proposed to quantify the real-time average corrosion rate during the experiment with a sub-micrometric precision. The estimated final average corrosion depth is validated by independent depth profile measurements. The uncertainties and sensitivity of the presented method are investigated.

Applications of Stretching Technique and Time Window Effects on Ultrasonic Velocity Monitoring in Concrete

Coda wave interferometry (CWI) has been used to measure the relative wave-velocity change (dV/V) caused by small changes in materials. This study uses the stretching processing technique which has been used for CWI analysis to investigate velocity changes of direct longitudinal (P) wave, direct shear (S) wave, and coda wave in concrete by choosing different time windows of ultrasonic signals. It is found that the obtained wave-velocity change depends on the time window position, because the relative contribution of P wave and S wave is different in each signal window. This paper presents three experimental scenarios of velocity change in concrete: early-age hydration, temperature change, and uniaxial loading. In early-age concrete, the S wave has a larger relative velocity change than the P wave, which is consistent with the microstructure development due to the hydration process. Temperature change causes a larger dV/V on the P wave than on the S wave, and the difference between P and S wave-velocity changes may be used to determine nonlinear elastic constants of materials. In the uniaxial loading experiment, analysis of the direct P wave can distinguish the acoustoelastic effects in the stress direction and the non-stress direction, which may potentially be used for stress evaluation in prestressed structures. However, the coda wave does not show this directional property to stress due to multiple scattering in the medium.

Ultrasonic Coda Wave Experiment and Simulation of Concrete Damage Process under Uniaxial Compression

Using the coda wave interferometry (CWI) method to obtain the ultrasonic coda wave characteristics of loaded concrete is an important method to evaluate the mechanical response of concrete. In this paper, the ultrasonic coda wave characteristics of C40–C70 concrete specimens (four strengths of concrete) under uniaxial compression were tested by laboratory experiments. Furthermore, to clarify the relationship between the internal damage process of concrete and the change rate of coda wave velocity, an ultrasonic coda wave discrete element simulation model combined with digital image processing technology was established. The results show that the coda wave is very sensitive to small changes in the compressive damage to concrete, and the change in coda wave velocity can correspond to the development process of concrete damage. This research is conducive to a better understanding of the complex material behavior of compressive concrete and proves the feasibility of ultrasonic field simulation and processing by using numerical simulation images of concrete damage.

Feasibility of Using Shear Wave Ultrasonic Probes as Pump-Wave Sources in Concrete Microcrack Detection and Monitoring by Nonlinear Ultrasonic Coda Wave Interferometry

This paper represents a first attempt to study the feasibility of using shear wave (SW) ultrasonic probes as pump-wave sources in concrete microcrack detection and monitoring by Nonlinear Ultrasonic Coda Wave Interferometry (NCWI). The premise behind our study is that the nonlinear elastic hysteretic behavior at microcracks may depend on their orientation with respect to the stationary wave-field induced by the pump-wave source. In this context, the use of a SW probe as a pump-wave source may induce the nonlinear elastic behavior of microcracks oriented in directions not typically detected by a conventional longitudinal pump-wave source. To date, this premise is hard to address by current experimental and numerical methods, however, the feasibility of using SW probes as a pump-wave source can be experimentally tested. This idea is the main focus of the present work. Under laboratory conditions, we exploit the high sensitivity of the CWI technique to capture the transient weakening behaviour induced by the SW pump-wave source in concrete samples subjected to loading and unloading cycles. Our results show that after reaching a load level of 40% of the ultimate stress, the material weakening increases as a consequence of microcrack proliferation, which is consistent with previous studies. Despite the lack of exhaustive experimental studies, we believe that our work is the first step in the formulation of strategies that involve an appropriate selection and placement of pump-wave sources to improve the NCWI technique. These improvements may be relevant to convert the NCWI technique into a more suitable non-destructive testing technique for the inspection of microcracking evolution in concrete structures and the assessment of their structural integrity.

Correlation of Load-Bearing Behavior of Reinforced Concrete Members and Velocity Changes of Coda Waves

The integral collection of information such as strains, cracks, or temperatures by ultrasound offers the best prerequisites to monitor structures during their lifetime. In this paper, a novel approach is proposed which uses the collected information in the coda of ultrasonic signals to infer the condition of a structure. This approach is derived from component tests on a reinforced concrete beam subjected to four-point bending in the lab at Ruhr University Bochum. In addition to ultrasonic measurements, strain of the reinforcement is measured with fiber optic sensors. Approached by the methods of moment-curvature relations, the steel strains serve as a reference for velocity changes of the coda waves. In particular, a correlation between the relative velocity change and the average steel strain in the reinforcement is derived that covers 90 % of the total bearing capacity. The purely empirical model yields a linear function with a high level of accuracy (R2=0.99, RMSE≈90μstrain).

An improved ultrasonic coda wave method for concrete behavior monitoring under various loading conditions

Monitoring of concrete behavior is an important task to evaluate the safety of concrete structures. This paper proposes a new stretching factor accumulation method based on the stepwise coda wave interference (CWI) to accurately calculate the relative velocity change Δv/v. The Δv/v and residual decorrelation coefficient Kd are used to study the concrete behavior in step loading experiment and short-time fixed loading experiment. The results show that: (1) In the loading stage of step loading experiments, both Δv/v and Kd can be used to monitor the load and the microcrack development; (2) In the relaxation stage of step loading experiments, the slow dynamics effect of concrete specimens can be characterized by Δv/v and Kd; (3) In the short-time fixed loading experiments, both Δv/v and Kd increase with the time of fixed loading, and the increasing rate of Δv/v decreases with the increase of concrete strength. This work can be used to promote the development of ultrasonic testing techniques that aid in concrete behavior monitoring.

Sensitivity of Ultrasonic Coda Wave Interferometry to Material Damage-Observations from a Virtual Concrete Lab

Ultrasonic measurements are used in civil engineering for structural health monitoring of concrete infrastructures. The late portion of the ultrasonic wavefield, the coda, is sensitive to small changes in the elastic moduli of the material. Coda Wave Interferometry (CWI) correlates these small changes in the coda with the wavefield recorded in intact, or unperturbed, concrete specimen to reveal the amount of velocity change that occurred. CWI has the potential to detect localized damages and global velocity reductions alike. In this study, the sensitivity of CWI to different types of concrete mesostructures and their damage levels is investigated numerically. Realistic numerical concrete models of concrete specimen are generated, and damage evolution is simulated using the discrete element method. In the virtual concrete lab, the simulated ultrasonic wavefield is propagated from one transducer using a realistic source signal and recorded at a second transducer. Different damage scenarios reveal a different slope in the decorrelation of waveforms with the observed reduction in velocities in the material. Finally, the impact and possible generalizations of the findings are discussed, and recommendations are given for a potential application of CWI in concrete at structural scale.

Pump-probe localization technique of varying solid contacts

A baseline-free defect localization method in thin plates is proposed and tested. In this proof-of-concept work, a steel ball pressed against an aluminum plate is used to mimic a surface contact defect. The technique takes benefit of a repetitive nonlinear pump-probe interaction with a backpropagation imaging algorithm. High-frequency probe waves are periodically emitted by a piezoelectric patch transducer glued to the plate. Propagated flexural waves are recorded using a distributed array of transducers. At the same time, a continuous low-frequency pump vibration provided by a shaker fixed to the plate modulates the contact state. By combining multiple probe signals, the contact can be successfully localized. Contrast of the localization images is finally improved by a factor of 3 to 5 by implementing a modified version based on synchronous detection of the imaging algorithm.

Local damage detection by nonlinear coda wave interferometry combined with time reversal

Coda wave interferometry (CWI) is a sensitive ultrasound method for the detection of weak and local changes in complex inhomogeneous media. In a nonlinear modification of the method discussed here, a high-frequency probe coda is compared to its replica obtained in the presence of low-frequency pumping. If, after the filtering-out of low frequencies, the coda signals are different, this is attributed to nonlinear pump-probe interaction induced by contact acoustical nonlinearity in the damaged zone. Actually, the CWI methods are used for global inspection of complex media, such as for example, concrete structures. In this work, a step forward is made; it consists in combining the CWI with the time-reversal (TR) technique in order to allow one to focus the pump wave on a selected area in the structure and to detect and localize a flaw. Time-reverse pump is possible only in pulsed mode due to the spatio-temporal wave compression. By this reason, the particularities of coda wave mixing in conventionally used continuous and pulsed pump mode are considered. It has been experimentally observed that an aftereffect of a pulsed pump provides a nonlinear interaction between pump and probe waves of a sufficient overall level for defect detection with TR. Finally, it was shown that a TR focusing even with the minimal available quality i.e., with only one transducer produces a sufficient contrast allowing to distinguish intact and damaged zones with nonlinear CWI.

Detection of Multiple Cracks in Four-Point Bending Tests Using the Coda Wave Interferometry Method

The enlargement of the cracks outside the permitted dimension is one of the main causes for the reduction of service life of Reinforced Concrete (RC) structures. Cracks can develop due to many causes such as dynamic or static load. When tensile stress exceeds the tensile strength of RC, cracks appear. Traditional techniques have limitations in early stage damage detection and localisation, especially on large-scale structures. The ultrasonic Coda Wave Interferometry (CWI) method using diffuse waves is one of the most promising methods to detect subtle changes in heterogeneous materials, such as concrete. In this paper, the assessment of the CWI method applied for multiple cracks opening detection on two specimens based on four-point bending test is presented. Both beams were monitored using a limited number of embedded Ultrasonic (US) transducers as well as other transducers and techniques (e.g., Digital Image Correlation (DIC), LVDT sensors, strain gauges, and Fiber Optics Sensor (FOS)). Results show that strain change and crack formation are successfully and efficiently detected by CWI method even earlier than by the other techniques. The CWI technique using embedded US transducers is undoubtedly a feasible, efficient, and promising method for long-term monitoring on real infrastructure.

Experimental Study of Defect Localization in a Cross-Ply Fiber Reinforced Composite with Diffuse Ultrasonic Waves

Diffuse wave inspection benefits from multiple scattering and is suitable for the nondestructive testing of complex structures with high sensitivity. This paper aims to localize the defect in a cross-ply carbon fiber reinforced polymer composite with the diffuse wave field experimentally based on the Locadiff technique. Firstly, the wave diffusivity and dissipation parameters are determined from the diffuse waveforms. Great dissipation is found for this composite plate due to its strong viscoelasticity, which makes the amplitude attenuate fast in a short propagation distance. The signal-to-noise ratios degrade significantly at off-axis directions so that only measurements along the X and Y axes are chosen. Secondly, the decorrelation coefficients are determined using the stretching technique. The decorrelation coefficients decrease initially due to the interaction between the wave fields and the defect and subsequently increase due to the low signal-to-noise ratio at the later time. Based on these data, a sensitivity time domain is chosen to center at t = 50 μs. Together with the defect sensitivity kernel calculated under constant diffusion property assumption, the defect is localized at [270 mm, 265 mm] compared to [300 mm, 280 mm] in the final reference state. This method is promising for early damage detection in fiber reinforced composite structures.

Evaluation of crack status in a meter-size concrete structure using the ultrasonic nonlinear coda wave interferometry

The field of civil engineering is in need of new methods of non-destructive testing, especially in order to prevent and monitor the serious deterioration of concrete structures. In this work, experimental results are reported on fault detection and characterization in a meter-scale concrete structure using an ultrasonic nonlinear coda wave interferometry (NCWI) method. This method entails the nonlinear mixing of strong pump waves with multiple scattered probe (coda) waves, along with analysis of the net effect using coda wave interferometry. A controlled damage protocol is implemented on a post-tensioned, meter-scale concrete structure in order to generate cracking within a specific area being monitored by NCWI. The nonlinear acoustic response due to the high amplitude of acoustic modulation yields information on the elastic nonlinearities of concrete, as evaluated by two specific nonlinear observables. The increase in nonlinearity level corresponds to the creation of a crack with a network of microcracks localized at its base. In addition, once the crack closes as a result of post-tensioning, the residual nonlinearities confirm the presence of the closed crack. Last, the benefits and applicability of this NCWI method to the characterization and monitoring of large structures are discussed.

Frequency selection for coda wave interferometry in concrete structures

This study contributes to the establishment of frequency recommendations for use in coda wave interferometry structural health monitoring (SHM) systems for concrete structures. To this end, codas with widely different central frequencies were used to detect boreholes with different diameters in a large concrete floor slab, and to track increasing damage in a small concrete beam subjected to bending loads. SHM results were obtained for damage that can be simulated by drilled holes on the scale of a few mm or microcracks due to bending. These results suggest that signals in the range of 50-150kHz are suitable in large concrete structures where it is necessary to account for the high attenuation of high-frequency signals.

Ultrasonic Monitoring of the Interaction between Cement Matrix and Alkaline Silicate Solution in Self-Healing Systems

Alkaline solutions, such as sodium, potassium or lithium silicates, appear to be very promising as healing agents for the development of encapsulated self-healing concretes. However, the evolution of their mechanical and acoustic properties in time has not yet been completely clarified, especially regarding their behavior and related kinetics when they are used in the form of a thin layer in contact with a hardened cement matrix. This study aims to monitor, using linear and nonlinear ultrasonic methods, the evolution of a sodium silicate solution interacting with a cement matrix in the presence of localized cracks. The ultrasonic inspection via linear methods revealed that an almost complete recovery of the elastic and acoustic properties occurred within a few days of healing. The nonlinear ultrasonic measurements contributed to provide further insight into the kinetics of the recovery due to the presence of the healing agent. A good regain of mechanical performance was ascertained through flexural tests at the end of the healing process, confirming the suitability of sodium silicate as a healing agent for self-healing cementitious systems.

Nonlinear coda wave interferometry for the global evaluation of damage levels in complex solids

A nonlinear acoustic method to assess the damage level of a complex medium is discussed herein. Thanks to the highly nonlinear elastic signatures of cracks or, more generally, internal solid contacts, this method is able to distinguish between contributions from linear wave scattering by a heterogeneity and contributions from nonlinear scattering by a crack or unbounded interface. The coda wave interferometry (CWI) technique is applied to reverberated and scattered waves in glass plate samples featuring various levels of damage. The ultrasonic coda signals are recorded in both the absence and presence of an independent and lower-frequency elastic "pump" wave, before being analyzed by CWI. The monitored CWI parameters quantifying changes in these coda signals, which therefore quantify the nonlinear wave-mixing effects between the coda and pump waves, are found to be dependent on the damage level in the sample. A parametric study is also performed to analyze the influence of sensor positions and average temperature on the method's output. The reported results could be applied to the non-destructive testing and evaluation of complex-shape materials and multiple scattering samples, for which conventional ultrasonic methods show strong limitations.

Diffuse ultrasound monitoring of stress and damage development on a 15-ton concrete beam

This paper describes the use of an ultrasonic imaging technique (Locadiff) for the Non-Destructive Testing & Evaluation of a concrete structure. By combining coda wave interferometry and a sensitivity kernel for diffuse waves, Locadiff can monitor the elastic and structural properties of a heterogeneous material with a high sensitivity, and can map changes of these properties over time when a perturbation occurs in the bulk of the material. The applicability of the technique to life-size concrete structures is demonstrated through the monitoring of a 15-ton reinforced concrete beam subject to a four-point bending test causing cracking. The experimental results show that Locadiff achieved to (1) detect and locate the cracking zones in the core of the concrete beam at an early stage by mapping the changes in the concrete's micro-structure; (2) monitor the internal stress level in both temporal and spatial domains by mapping the variation in velocity caused by the acousto-elastic effect. The mechanical behavior of the concrete structure is also studied using conventional techniques such as acoustic emission, vibrating wire extensometers, and digital image correlation. The performances of the Locadiff technique in the detection of early stage cracking are assessed and discussed.

Locating and characterizing a crack in concrete with diffuse ultrasound: A four-point bending test

This paper describes an original imaging technique, named Locadiff, that benefits from the diffuse effect of ultrasound waves in concrete to detect and locate mechanical changes associated with the opening of pre-existing cracks, and/or to the development of diffuse damage at the tip of the crack. After giving a brief overview of the theoretical model to describe the decorrelation of diffuse waveforms induced by a local change, the article introduces the inversion procedure that produces the three dimensional maps of density of changes. These maps are interpreted in terms of mechanical changes, fracture opening, and damage development. In addition, each fracture is characterized by its effective scattering cross section.

Embedded ultrasonic transducers for active and passive concrete monitoring

Recently developed new transducers for ultrasonic transmission, which can be embedded right into concrete, are now used for non-destructive permanent monitoring of concrete. They can be installed during construction or thereafter. Large volumes of concrete can be monitored for changes of material properties by a limited number of transducers. The transducer design, the main properties as well as installation procedures are presented. It is shown that compressional waves with a central frequency of 62 kHz are mainly generated around the transducer’s axis. The transducer can be used as a transmitter or receiver. Application examples demonstrate that the transducers can be used to monitor concrete conditions parameters (stress, temperature, …) as well as damages in an early state or the detection of acoustic events (e.g., crack opening). Besides application in civil engineering our setups can also be used for model studies in geosciences.

Applying diffuse ultrasound under dynamic loading to improve closed crack characterization in concrete

Recent studies show the ability of diffuse ultrasound to characterize surface breaking cracks in concrete. However, derived parameters are sensitive to the presence of partially opened zones along the crack whose pattern may differ from one sample to another. The aim of this letter is to study the variation of diffuse ultrasound parameters while the sample is driven by a low frequency bending load which alternatively opens and closes the crack, allowing to access supplementary information about its morphology. The results show the sensitivity of the method for various crack depths and highlight its potential for concrete nondestructive evaluation.

Study of stress-induced velocity variation in concrete under direct tensile force and monitoring of the damage level by using thermally-compensated Coda Wave Interferometry

In this paper, we describe an experimental study of concrete behavior under a uniaxial tensile load by use of the thermally-compensated Coda Wave Interferometry (CWI) analysis. Under laboratory conditions, uniaxial tensile load cycles are imposed on a cylindrical concrete specimen, with continuous ultrasonic measurements being recorded within the scope of bias control protocols. A thermally-compensated CWI analysis of multiple scattering waves is performed in order to evaluate the stress-induced velocity variation. Concrete behavior under a tensile load can then be studied, along with CWI results from both its elastic performance (acoustoelasticity) and plastic performance (microcracking corresponding to the Kaiser effect). This work program includes a creep test with a sustained, high tensile load; the acoustoelastic coefficients are estimated before and after conducting the creep test and then used to demonstrate the effect of creep load.