Back Analysis Method Research Articles

Estimation of Mechanical Characteristics of the Ground Ahead of a Tunnel Face

In order to identify the mechanical parameters of the ground ahead of a tunnel face, a three-dimensional back-analysis method is newly proposed. The method consists of a three-dimensional finite element analysis and the secant method, and is based on an iteration procedure. The Poisson's ratio, the modulus of elasticity and the six components of the initial stress levels of the ground around a tunnel face are back analyzed from displacements obtained by field measurement, which are produced by one-step excavation of the tunnel face. Influence of measurement errors of field displacements on accuracy of the results identified is made clear through numerical calculation.

A displacement-based back-analysis method for rock mass modulus and horizontal in situ stress in tunneling – Illustrated with a case study

This paper presents a displacement based back-analysis method for the determination of rock mass modulus ( E) and the horizontal in situ stress ( P) perpendicular to the axis line of the tunnel excavation in hard and intact rock masses. The rock mass is assumed to respond in an isotropic and linear elastic manner. Essentially, the method is a best-fit solution of back-analysis by comparing the measured displacements near a tunnel face during excavation with those calculated using a three-dimensional finite element method. The method can be applied efficiently and effectively by iterative algorithms such as direct search technique and damping least square technique. In particular, a three-dimensional finite element pattern technique (3-D FEPT) is used to compute the theoretical displacements for saving computation time. The method is further illustrated with a case study. The case study deals with a test adit at Zhanghewan Pumped Storage Power Station in Hebei Province, North China. It is shown that the back-analyzed results of E and P are reliable and representative for the actual rock masses.

Geotechnical parameter estimation in tunnelling using relative convergence measurement

Accurate estimation of geotechnical parameters is an important and difficult task in tunnel design and construction. Optimum evaluation of the geotechnical parameters have been carried out by the back-analysis method based on estimated absolute convergence data. In this study, a back-analysis technique using measured relative convergence in tunnelling is proposed. The extended Bayesian method (EBM), which combines the prior information with the field measurement data, is adopted and combined with the 3-dimensional finite element analysis to predict ground motion. By directly using the relative convergence as observation data in the EBM, we can exclude errors that arise in the estimation of absolute displacement from measured convergence, and can evaluate the geotechnical parameters with sufficient reliability. The proposed back-analysis technique is applied and validated by using the measured data from two tunnel sites in Korea. Copyright © 2005 John Wiley & Sons, Ltd.

Back-analysis of laterally loaded bored piles

Field lateral load tests were conducted on two single 1·5 m diameter large bored piles in Hong Kong. The test piles are embedded in superficial deposits and weathered rocks with various degrees of decomposition. In this paper, the pile load test results are interpreted and reported. A simple and rational method of back-analysis for long piles, using inclinometer data and assuming a fourth-order polynomial to represent the shape of soil reaction profile, is introduced. The method, requiring only simple spreadsheet-type operations, makes it possible to incorporate non-linear concrete behaviour in the back-analysis, and to deduce the p–y curves for future design of piles in similar ground conditions. In order to verify the rational method, an analysis is carried out using the back-analysed p–y curves, and the predictions are found to agree well with the measured pile head deflections. This proposed method demonstrates how p–y curves are back-analysed rationally for long piles embedded in complex ground conditions, in contrast to traditional back-analyses using recommended p–y curves for a uniform soil stratum.

Back-analysis of laterally loaded bored piles

Field lateral load tests were conducted on two single 1·5 m diameter large bored piles in Hong Kong. The test piles are embedded in superficial deposits and weathered rocks with various degrees of decomposition. In this paper, the pile load test results are interpreted and reported. A simple and rational method of back-analysis for long piles, using inclinometer data and assuming a fourth-order polynomial to represent the shape of soil reaction profile, is introduced. The method, requiring only simple spreadsheet-type operations, makes it possible to incorporate non-linear concrete behaviour in the back-analysis, and to deduce the p–y curves for future design of piles in similar ground conditions. In order to verify the rational method, an analysis is carried out using the back-analysed p–y curves, and the predictions are found to agree well with the measured pile head deflections. This proposed method demonstrates how p–y curves are back-analysed rationally for long piles embedded in complex ground conditions, in contrast to traditional back-analyses using recommended p–y curves for a uniform soil stratum.

A rock bolt and rock mass interaction model

Abstract An analytical model for rock bolts has been developed based on an improved Shear–Lag Model. The development of the model is based on the description of the interaction behavior of the rock bolt, the grout medium and the rock mass. On the basis of the model, the coupling and decoupling behavior of the rock bolt in pullout tests, uniform deformation the rock mass and intersecting joints are analyzed. The pullout test characteristic is described by the proposed model, and a back analysis method is proposed to calculate the shear strength of the interface media. For the rock bolts in a deformed rock mass, the influence of the installation time of the rock bolt has been taken into account, and the theoretical prediction is verified by the measured data. According to the proposed model, the position of the neutral point is not only related to the length of the rock bolt and the radius of a tunnel, but also is strongly influenced by the mechanical properties of the rock mass. Analysis of the joints intersecting the rock bolt shows that there may be more than one neutral point on the rock bolt, and the prediction of the simplified model is consistent with the pullout model. By using this model, a method is proposed to analyze the interaction behavior of the rock bolt and the surrounding rock mass, with a way of evaluating the supporting performance quantitatively.

Reinforcing effect of FRP multi-step grouting method for NATM tunnel by back analysis method

A fiber glass reinforced plastic (FRP) pipe has been newly developed for grouted-reinforcing members and widely used in the tunnel excavation in Korea. The multi-step grouting method using FRP pipe, has the advantage in reinforcing effect and handling of reinforcing members, compared to typical reinforcing methods such as fore-poling and steel pipe reinforced grouting methods. Generally, when excavating tunnel in soft ground, it is grouted through the steel or FRP pipe to reduce the displacement of tunnel. However, in practice it is difficult to evaluate correct design parameter in grouted zone. In this paper, based on the measured data of tunnel 3-dimensional back analyses were employed to evaluate design parameter of grouted zone. From the back analysis results, it could confirm reinforcing effect by increment of elastic modulus in grouted zone and decide the space and length of FRP reinforcing member at the other adjoined tunnel also. This paper presents the reinforcing effect of FRP multi-steps grouting for tunnel by evaluating the change of stress measured on FRP pipe and in the ground, and the displacement of the ground, according to the excavation steps. Measured results are shown that FRP pipes play an important role as reinforcing members in the excavation of NATM tunnel, and keep in the convergence limit of the displacement in tunnel effectively. With consideration of the geology of the construction area and the application of FRP reinforcement grouting based on countermeasure and measurements, the Song-Am tunnel could be constructed safely while suppressing the displacement of tunnel and surrounding ground. (A). Reprinted with permission from Elsevier. For the covering abstract see ITRD E124500.

Displacement Back Analysis Research on Bolt-Grouting Supporting Parameter of Rock Mass in Jointed Rock Roadway

The method of bolt-grouting supporting, grouting into surrounding rock mass by bolts in jointed rock mass roadway, is obtained wide application. However, it is difficult to determine rock mass parameter of bolt-grouting supporting. This paper begins with the displacement, which is measured easily in practice. The method of back analysis is adopted to calculate the equivalent mechanics parameters of bolt-grouting rock mass. In process of back analysis three mechanics models is supposed which are homogeneous elastic model, inhomogeneous elastic model and elastic-plastic model and corresponding algorithm is established. What's more, this paper discusses the stability of inverse algorithm and copes the problem of back analysis parameter probably instable with QR decomposed algorithm and singular value decomposed algorithm, which will be a theoretical base to determine the mechanics parameter of bolt-grouting supporting rock mass and to estimate the surrounding rock stability. In a word, the method is established to estimate mechanics parameters of bolt-grouting jointed surrounding rock mass, and some significant results are obtained, which are of reference for actual project.

Stability analysis of mine pit slopes in interior Alaska

An analytical model for rock bolts has been developed based on an improved Shear–Lag Model. The development of the model is based on the description of the interaction behavior of the rock bolt, the grout medium and the rock mass. On the basis of the model, the coupling and decoupling behavior of the rock bolt in pullout tests, uniform deformation the rock mass and intersecting joints are analyzed. The pullout test characteristic is described by the proposed model, and a back analysis method is proposed to calculate the shear strength of the interface media. For the rock bolts in a deformed rock mass, the influence of the installation time of the rock bolt has been taken into account, and the theoretical prediction is verified by the measured data. According to the proposed model, the position of the neutral point is not only related to the length of the rock bolt and the radius of a tunnel, but also is strongly influenced by the mechanical properties of the rock mass. Analysis of the joints intersecting the rock bolt shows that there may be more than one neutral point on the rock bolt, and the prediction of the simplified model is consistent with the pullout model. By using this model, a method is proposed to analyze the interaction behavior of the rock bolt and the surrounding rock mass, with a way of evaluating the supporting performance quantitatively.

Stiffness Estimates Using Portable Deflectometers

The use of falling weight deflectometers and portable falling weight deflectometers (PFWDs) is now common for field characterization of pavement system layers. In particular, the application of portable deflectometers in quality assurance of newly constructed granular base has become more widespread. Typically, these devices are used for an in situ assessment of the Young's modulus of the base layer. The traditional backcalculation uses an elastostatic half-space framework to relate Young's modulus of the pavement foundation to the stiffness estimates obtained from force and velocity measurements. The data interpretation method that is customarily used for stiffness estimation uses peak values of the force and displacement records in lieu of their static counterparts. The performance of a particular device, PRIMA 100, was examined with the newly developed beam verification tester (BVT) of known static stiffness. It was shown that the conventional, peak-based method of backanalysis produces incorrect estimates of the static stiffness of the BVT. An alternative, spectral-based data interpretation method was proposed. This method, based on ( a) concept and measurement of the frequency response function and ( b) a single-degree-of-freedom mechanical model, was employed to extract the true static stiffness from PRIMA 100 measurements. The results show a good agreement between the true static stiffness of the BVT and its PFWD estimates stemming from the modified approach. The BVT apparatus can therefore be used to assess the performance of the sensors and data interpretation of PRIMA 100-type deflectometers.

Different rescattering trajectories related to different total electron momenta in nonsequential double ionization

We extend earlier work on two-electron photo-ionization to analyze electron momentum. We provide theoretical evidence distinguishing two categories of e-e trajectory associated with the correlation that develops when an "outer" electron returns to the nucleus in the presence of a high-intensity optical-wavelength laser field. We use the method of back-analysis to connect these two categories of trajectory with NSDI events having either nearly zero (Z) or substantially non-zero (NZ) total electron momentum.

Identification of rock mass properties in elasto-plasticity

A simple and effective back analysis method has been proposed on the basis of a new criterion of identification, the minimization of error on the virtual work principle. This method works for both linear elastic and nonlinear elasto-plastic problems. The elasto-plastic rock mass properties for different criteria of plasticity can be well identified based on field measurements.

Intelligent back analysis of displacements using precedent type analysis for tunneling

Abstract Based on comprehensive monitored data obtained from typical tunnel projects, and by using engineering experiences of experts together with numerical modeling results, the precedent type analysis (PTA) technique developed was for back-analyzing in situ stress and elastic modulus of rock masses surrounding tunnels. Then, the PTA is used as a supporting technique in the method of intelligent back analysis (IBA). The IBA method can integrate the mechanism analysis with experimental identification. Such integration is based on ‘certainty factors’, and is implemented with the computer program BMP90 with a global inference engine. The program BMP90 can solve a series of back analysis problems—such as identifying potential problems to be encountered during back analysis, assessing the strategy to be adopted, selecting criteria for back analysis, and ensuring convergence of back analysis results. Based on the engineering applications to approximately 100 tunnel projects in China, it is found that the IBA method supported by the PTA technique can be successfully applied to tunnel projects, i.e. back-analyzing the lateral in situ stress factor (λ), and the elastic modulus ( E ) of rock masses. The method of IBA supported by PTA and its application to a tunnel project are presented in this paper.

Back-analysis of viscoelastic displacements in a soft rock road tunnel

The rheological behavior of the rock proximate to excavations is of importance and practical interest for engineers in the design of soft rock tunnels. In situ rheology tests may be conducted to determine the appropriate parameters of the rock masses and the ground stress component; however, this can cost a great deal in both expense and time. Hence, it is useful to study back-analysis of viscoelastic displacements induced by the excavation of tunnels. Taking four rheological models, namely, Kelvin body, Maxwell body , Poynting–Thomson body and Kelvin–Voigt body as examples, this paper presents the basic finite element equations for such back-analysis, and the associated calculation methods for practical applications. A trial calculation method for the different models is adopted so as to obtain the most suitable rheological model and corresponding parameters. Furthermore, the authors have successfully applied the back-analysis method in a test section of a road tunnel excavated in soft rock. Compared with the direct in situ rheology tests, the back-analysis method presented by this paper is more concise and involves less money and time.

Displacement back analysis for a steep slope at the Three Gorges Project site

Abstract This paper contributes to two aspects of displacement back analysis of rock slopes. First, a novel method for displacement back analysis is presented, based on error back-propagation neural network and genetic algorithm (GA). The BP network replaces the time-consuming finite element method, thus enhancing the efficiency of the analysis. The GA is used as an optimization method, whose global search strategy can effectively improve the reliability of the analysis, thereby, making the back-analyzed results independent of the initial values. Application of this methodology is illustrated with a numerical example. Secondly, the deformation mechanism of rock mass is duly taken into account in the displacement back analysis of Profile 17–17 of the permanent shiplock slope at the Three Gorges Project site, by treating the disturbed zones as weakened media, yielding reasonable results.

Estimating mechanical rock mass parameters relating to the Three Gorges Project permanent shiplock using an intelligent displacement back analysis method

Establishing the mechanical rock mass parameters is one of the important tasks for the highwall stability analysis of the permanent shiplock at the Three Gorges Project in China. Existing back analysis methods are not sufficient to provide the necessary accuracy and to recognize non-linear relations. The new displacement back analysis method proposed in this paper is a combination of a neural network, an evolutionary calculation, and numerical analysis techniques. The non-linear relation involving displacement and mechanical parameters is adequately recognized by the neural network techniques. The neural networks learn using an evolutionary technique, with samples created by orthogonal design and tested with new cases given by event design. With the neural network model established, the mechanical parameters are recognized using a genetic algorithm over a large search space in the global range. The predicted displacement occurring for each excavation step from January 1998 to the end of excavation and their cumulative values for 5 later excavation steps are closely characterized by the new analysis technique.

DEFLECTION AND ELASTIC MODULUS IN REPEATED PLATE-LOADING TESTS ON MODEL ASPHALT PAVEMENTS

To evaluate the behavior of asphalt pavement in high temperature based on deflection just like FWD a repeated plateloading test was carried out on relatively-large scaled model asphalt pavements with 4 different sections under three different temperatures conditions, as immediately after construction, normal temperature and 60°C. As a result, a large deflection near the loading plate took place for the temperature condition of immediately after construction. But as temperature goes down, the deflection decreases near the loading plate and a bit increases away from the loading plate due to rejuvenation of the stiffness, as load transmissibility of asphalt mix layer accompanied with temperature decrease. From the back-analysis of measured deflection, a tendency was observed that the elastic modulus asphalt mix layer decreased with its average temperature and that the estimated values of elastic modulus werea bit larger than those of past studies at a relatively high temperature. It was also indicated that there was a room for research and investigation on the back-analysis method and interpretation of the test results on ground that the modified asphalt mix layer was a bit more sensitive to temperature thanthe straight one exhibiting a bit lower elastic modulus at a relatively high temperature, which seem to contradict the reality.

Use of FWD Data for Prediction of Bonding Between Pavement Layers

A new back-analysis method is suggested to assess the bonding condition between bituminous layers in addition to the pavement layer stiffnesses, from Falling Weight Deflectometer (FWD) test results. The shear bond stiffness at the interface is considered as a variable affecting the FWD deflections and therefore back-calculated in a similar manner to a layer stiffness. A sensitivity analysis carried out on theoretical pavements showed that, assuming full bonding between bituminous layers instead of the actual values will change the FWD back-analysed bituminous and sub-base stiffnesses by up to 50% and will not affect the sub-grade stiffness. Case studies are presented describing the evaluation of several flexible pavements using the new back-analysis process. Poor bonding was suspected between the bituminous layers due to the following reasons; i) the conventional back-analysis method predicted low effective stiffness for the bituminous layers, ii) separation of the layers during coring was noticed, iii) acceptable laboratory measured bituminous stiffnesses were found. Re-testing the above pavements after six months indicated an improvement of bonding condition between bituminous layers after trafficking and at higher testing temperatures.

New back analysis method of slope stability by using field measurements

The authors have proposed the idea that landslide movement is caused by both the reduction of shear rigidity at sliding surface and the body force of the sliding block. Based on this idea, the authors have developed a new back analysis method to represent slope movement with/without external force. This method is applicable to not only natural landslide but also landslide caused by tunnel excavation or cut slope. In this method sliding surface has been assumed to be anisotoropic continuous material which has the smallest shear rigidity parallel to the boundary of slide surface. The mechanical constants on the sliding surface can be calculated from fitting between the measured and calculated displacement. This method can be easily applicable to practical engineering.

New back analysis method of slope stability by using field measurements

New back analysis method of slope stability by using field measurements