# Assessment of uncertain soil properties for complex infrastructures from monitoring

Franck Schoefs, Katheirne Le, Francesca Lanata

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Franck Schoefs, Katheirne Le, Francesca Lanata. Assessment of uncertain soil properties for complex infrastructures from monitoring. International Conference Durable Structures: from construction to rehabilitation, ICDS12, May 2012, Lisboa, Portugal. hal-01007916

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Distributed under a Creative Commons Attribution 4.0 International License
ASSESSMENT OF UNCERTAIN SOIL PROPERTIES FOR
COMPLEX INFRASTRUCTURES FROM MONITORING

Schoefs F. <sup>a</sup>, Le K.T. <sup>a</sup>, Lanata F. <sup>b</sup>

<sup>a</sup> LUNAM Université, Université de Nantes, Institute for Research in Civil and
Mechanical Engineering, CNRS UMR 6183/FR 3473, Nantes, France; <sup>b</sup> Ecole
Supérieure du bois, France

ABSTRACT

Since several decades, quite a lot of structures have been monitored to
analyze their displacement during the works or during the service-life. This
paper presents a methodology for identifying soil characteristics from data
structural health monitoring, applying for to a wharf with instrumented tie-
rods. Loading and soil parameters are modelled as random variables. The
modelling is performed though a meta-model fitted on a numerical database
obtained from direct simulations on a complex finite element model under
PLAXIS software: a quadratic Response Surface Model (QRS) is
considered.

KEYWORDS: NDT, stochastic field, random properties, capacitive method, chloride ingress.

# 1 INTRODUCTION

In the context of maintenance and reassessment of existing civil
engineering structures, improvement of the in-service behaviour requires
disposing of a wide range of technical and methodological tools. Among
these tools we can mention on the one hand, the data collection,
concerning a feedback, and on the other hand, modelling of progressive
phenomena such as fatigue and corrosion. Systematic predictive
maintenance programs are not easy to implement in a whole system of
infrastructures due to heterogeneity of building ages and building
techniques. This is the case of structures in coastal area. The survey of
structures (displacement) gives additional information but the updating of
the modelling is a great challenge when a lot of influencing factors are
involved. Thus, intrusive structural monitoring of complex structures is
actually the only way on the one hand, for reaching as close as possible
their real in-service behaviour, influenced by building conditions and
settlements that are expected to separate the present behaviour from the
theoretical one and on the other hand to understand complex interaction
mechanisms, as soil-structure interaction for example.

Due to the randomness of building (concrete, embankment) and natural
properties of material (soil), probabilistic methods are more and more
considered. They offer the theoretical framework to deal with uncertainties
involved in structural assessment of Civil Engineering structures in view to
perform sensitivity analysis or reliability assessment.

In this paper we focus on the characterization of powdery embankment
physical and mechanical properties for soil pressure quantification from the
monitoring of tie-rods in a wharf.

## 2 DESCRIPTION AND INSTRUMENTATION OF THE STRUCTURE, THE AVAILABLE DATA

### 2.1 DESCRIPTION OF THE STRUCTURE

The studied structure is the extension of the timber terminal of Cheviré, the station 4, named Cheviré-4 wharf. The Cheviré-4 wharf is located downstream of the Cheviré bridge near Nantes city (west of France), in a river environment. A sketch of a typical cross section and main components is presented on Fig. 1.

<figure><img src="image_2.png" /><figcaption>Fig. 1 Cross section of the wharf.</figcaption></figure>

Instrumentation strategy aims following the global behaviour of the wharf
during at least 5 years after building with a view to improve prediction
models. These validated models will allow basing the maintenance policy
on a better understanding of the in-service behaviour.
The objective being the understanding of the wharf behaviour under
horizontal loading – actions of the embankment, ship berthing and wind
action on the cranes, we chose to monitor the tie-rods, which are sensitive
elements of the wharf that are not accessible after the building period. The
wharf has been instrumented on twelve tie-rods (regularly distributed along
the length of the wharf, (see [1] for detail) in order to follow the normal load
in the rods cross-section.

## 2.2 AVAILABLE DATA

Measured loads in the tie-rods come from a two years monitoring period (from January 2004 to October 2005) and have been analyzed in [1]. Two types of variations characterize the loads in the tie-rods:

- temporal: medium-term variations (monthly) and short-term variations (daily: tide with a period of about 12 h);

- spatial: variations of the load in each spatially distributed tie-rod.

The analysis of the spatial load variations shows an important scatter from
a tie-rod to another. These variations have been analyzed in [1]. Yáñez-
Godoy et al. have shown that when considering the variation of this loading
during a tide, it is much more stable from a tie-rod to another one and in
time. This paper focuses on this behaviour.

## 2.3 MAIN ASSUMPTIONS FOR PROBABILISTIC MODELLING FROM SPATIAL PROFILE AND TIME-SERIES

Since a decade, investigations of structural behaviour through Non
Destructive Testing or Monitoring have underlined the need for methods of
data processing and structural computation. We classify the obtained time-
series in three categories:

- time-series describing the evolution of an ageing phenomena like chloride ingress in concrete, crack propagation,

- time-series measuring the strain affected by non-periodic loading like wind and truck loading,

- time-series measuring the strain due to cyclic loading like temperature, tide or waves.

This paper focuses on data obtained from the two last categories during the training period that means before any ageing mechanism occurs. Moreover, when similar components placed at a given location $x_i$ are monitored (beams [2] or tie-rods [1]), and subjected to the same loading, a statistical study of their loading $L_T(x_i, t, \theta_j)$ can be performed, where t denotes the time and $\theta_j$ the event that represents mainly the hazard during building
works and composition of the material around; $\theta_j$ is a realization of the hazard $\theta$, $\theta \in \Omega$, the probabilistic space that gather all the hazard that generates events, thus realization of random variables (material properties, tide level, ...). Is has been proved [3] that assuming some properties with an abuse of notation, that $L_T(x_i, t, \theta_j)$ can be replaced by $L_T(\theta_k)$.

It has been shown that there is a strong relationship between the loading and the difference of water levels, especially for high CMAR coefficients (see [3] for the definition). In this paper, we aim to provide a probabilistic model of soil properties for reliability analysis of wharf during storms [4]. These extreme events occur mainly in winter when CMAR are higher: we analyze only the horizontal wharf behaviour for these conditions.

# 3 NUMERICAL MODELLING AND META-MODEL ASSESSMENT

## 3.1 NUMERICAL STRATEGY

Numerical models must be integrated in the future in an optimization procedure in view to identify the soil characteristics. Computation time should be reduced as low as possible due to the necessary huge number of calls to the model for optimization procedures. Thus we suggest to develop a complete two-dimensional Finite Element Model (FEM) under the Plaxis environment and to find the best meta-model $M(X(\theta_j))$-with $X(\theta_j)$ input random variables- to represent this numerical behavior. Several meta-models have been developed for deterministic or probabilistic analysis of wharves during these two last decades: neuronal and Bayesian networks, spectral stochastic finite element models based on regression or projection methods [4], polynomial or other response surfaces. We decide here to select quadratic polynomial response surfaces due to their asymptotic properties.

## 3.2 FINITE ELEMENT MODEL

The problem is modeled through a PLAXIS finite element model by considering all the work phases. We use a 2-D model to represent a standard cross section, not affected by the ends and consistent with the assumptions in 2.4. Geometry modelled under PLAXIS environment by the FE model see [3] and the main characteristics of the mechanical model can see [3], for details.
## 3.3 META MODEL: QUADRATIC RESPONSE SURFACES

We focus here on the second one and more especially on the polynomial models of order less than 3 with or without interaction terms, called Quadratic Response Surfaces (QRS) and developed in several fields [5]. This form has specific properties especially an asymptotic behaviour for the transfer of distribution tails that fits the physical meaning. It is essential when only few experiments are available to ensure a realistic transfer of distribution tails [5].

The general form of the full QRS is the following (1):

$$L_{T,SR} = b_0 + \sum b_i X_i + \sum_{i \neq j} b_{ij} X_i X_j + \sum_i b_{ii} X_i^2 \quad (1)$$

where $L_{T,SR}$ is the load in the tie-rod, $X_i$ is the i-th random variable and the $b_k$ values are determined by regression method from a numerical experimental plan based both on the probabilistic distribution of the variables (distribution of numerical values) and their potential influence on the response (number of numerical values –i.e. size of the sample- for each variable).

# 4 RANDOM VARIABLES AND PROBABILISTIC MODELING

## 4.1 NUMERICAL EXPERIMENTAL DESIGN

For identifying values of coefficients $b_k$ in (1), we fit a QRS on a numerical database with a probabilistic sense: that means that samples are generated from a probability density function for each variable. Basic random variables selected herein are: $\gamma_{sat}$ and $\gamma_{unsat}$ respectively saturated and unsaturated own-weight of the embankment, E and v its respective Young and Poisson modulus and $\phi$ its internal frictional angle. Cohesion c is neglected. Note that the structure is analysed in the first two years when no exploitation by ships occurred. The range of variation for each variable is selected from literature or preliminary knowledge. Available published data for sand and embankment see in [6], for detail. The selected basic variables are:

Own weight (kN/m3) $\gamma_{sat}$ and $\gamma_{unsat}$, Young modulus E (Mpa), Frictional internal angle $\phi$ (°), Poisson modulus v (-), High tide level Hmax, Low tide level Hmin. Cohesion c (kPa) is considered as deterministic. Their distribution, parameters (range if bounded) of the distributions and selected values for experimental design are available in [6]. A deterministic functional relationship is used between unsaturated $\gamma_{unsat}$ and saturated $\gamma_{sat}$ own weight of the embankment to reduce the number of independent variables:
$\gamma_{sat} = \gamma_{unsat} + 2$. Concerning the tide-river level and the corresponding level of water in the embankment, we consider a tide with a high and frequent CMAR of 70. In the two years database, a CMAR of 69 has been observed: the 2nd of March 2005 with a high level $H_{max} = 6.21m$ and a low level $H_{min} = 2.19m$ from the 0 level of the sea along the French coasts. We choose to discretize the tide-river lever in six phases between these values to get a good representation of potential situations during this type of tide.

## 4.2 SELECTION OF RANDOM VARIABLES AND QRS CALIBRATION

With the 6 random variables presented upon, 28 coefficients should be calibrated to fit a full QRS. That leads to a huger database. We use the first numerical database described above to highlight the most influent Basic Random Variables (BRV) and to reduce their number. All the results are available in [6]. We recognize that $1/E$ and $\gamma_{unsat}$ act in very similar way in the response; $\nu$ has no influence in the response. From the 6 random variables, four random variables are finally selected that leads to the calibration of 15 coefficients for a full QRS. Table 1 gathers the results and the selected BRV.

<table><caption>Table 1 Selection of input random for the calibration for QRS.</caption><thead><tr><th>Initial random variables</th><th>Studies</th><th>Relationship</th><th>Name of selected BRV</th></tr></thead><tbody><tr><td>γ<sub>unsat</sub>: Unsaturated own weight</td><td>Variable change</td><td>X<sub>1</sub> = γ<sub>unsat</sub>/E</td><td>[X<sub>1</sub>]: RV</td></tr><tr><td>E: Young modulus</td><td>Variable change</td><td></td><td></td></tr><tr><td>φ: Internal frictional angle</td><td>-</td><td>X<sub>2</sub> = φ</td><td>[X<sub>2</sub>]: BRV</td></tr><tr><td>γ<sub>sat</sub>: Saturated own weight</td><td>Functional relationship with γ<sub>unsat</sub></td><td>γ<sub>sat</sub> = f(γ<sub>unsat</sub>)<br>or γ<sub>sat</sub> = γ<sub>unsat</sub> + ε</td><td></td></tr><tr><td>ν: Poisson modulus</td><td>Sensitivity analysis</td><td>ν = 0.27</td><td>ν: deterministic parameter</td></tr><tr><td>Tide level of Loire</td><td>Mesured data of CMAR69</td><td>-</td><td>[X<sub>3</sub>]: BRV</td></tr><tr><td>Underground level in the embankment</td><td>Mesured data of CMAR69</td><td>-</td><td>[X<sub>4</sub>]: BRV</td></tr></tbody></table>

The QRS calibration described in (1) is carried out based on the numeral database obtained from the calculations of Plaxis. Loading simulations in the tie-rod, from Plaxis model and the QRS, show that the full quadratic response surface gives the best fitting [1].
## 5 RESULT FOR FRICTIONNAL ANGLE IDENTIFICATION

We use a zero-order method (simplex) based on the least square method for the identification of these quantities for each tie-rod.

The objective function $F_{err}(\theta)$ of identification method is written as the following (2):

$$F_{err}(\theta) = \sum_{i} F_{err_i}^2(\theta) = \sum_{i} (F_{mes_i} - (f_i(F_{sr_i}, \theta)))^2 = \sum_{i} r_i^2(\theta) \quad (2)$$

where $F_{err_i}$ denotes the deviation between measured loadings $i^{th}(F_{mes_i})$ and the corresponding loading calculated by the numerical model of QRS ($F_{sr_i}$); $r_i(\theta)$, denotes the deviation between measured loadings $i^{th}(F_{mes_i})$ and the corresponding prediction $f(F_{sr_i}, \theta)$ by model of QRS; $\theta$ is unknown variables that are identified.

The first interesting result is that we highlight the existence of two groups of tie-rods [1, 6]. The correlation coefficient between $X_1$ and $X_2$ for two families is respectively 0.1252 and -0.423 for the family 1 and the family 2. They are low, this result allows us to assume independent random variables. We present the results of $X_2$ only here.

<figure><img src="image_3.png" /><figcaption>Fig. 2 Distribution of frictional angle (left); evolution of the measured loading and the computation during a tide (right)</figcaption></figure>

After fitting probability density function from Maximum Likelihood Estimate, we obtain the following parameters (mean and standard deviation) for a normal distribution: ($\mu$ = 39°; $\sigma$ = 1,4°) for family 1 and ($\mu$ = 41,7°; $\sigma$ = 1,2°)
for family 2. The support of the distributions contains acceptable values in
comparison to litterature.

The empirical distribution and the fitting with existing probability density
functions are plotted on Fig. 2 (left). A direct computation of the loading in a
tie-rod considering this random variable and others is plotted on Fid. 2
(right) (mean and 5%-95% fractiles): a quadratic response surface fitted on
a numerical database is used.

6 CONCLUSION

The paper shows how to identify random properties from monitoring and
illustrates that a quadratic response surface can be suitable for predicting
the loading in a tie-rod in a wharf.

REFERENCES

[1] SCHOEFS F., YÁÑEZ-GODOY H., LANATA F., 2011, "Polynomial Chaos Representation for Identification of Mechanical Characteristics of Instrumented Structures: Application to a Pile Supported Wharf", *Computer Aided Civil And Infrastructure Engineering*, 26-3, pp. 173-189.

[2] LANATA F., SCHOEFS F., 2012, “Multi-algorithm approach for identification of structural behaviour of complex structures under cyclic environmental loading”. *Journal Structural Health Monitoring*, Published online before print February 22th 2011, Vol. 11, No 1, pp. 51-67.

[3] LE K.T., SCHOEFS F., LANATA F., 2012, “Meta-Models For The Assessment Of Soil Stochastic Properties From Monitoring: Application To Harbour Structures”, In “Proc. 5th European Conference on Structural Control (EACS 2012), , 18-20 June 2012, Genoa, Italy.

[4] BOÉRO J., SCHOEFS F. YÁÑEZ-GODOY H., CAPRA, B. 2012, “Time-function reliability of harbour infrastructures from stochastic modelling of corrosion”, *Europ. Journ. of Environmental and Civil Engin.*, in press.

[5] BAROTH J., BREYSSE D., SCHOEFS F. (coord). 2011, Construction reliability, ISTE Ltd - Wiley, 368p.

[6] LE K.T (2012). Identification des caractéristiques aléatoires de remblais à partir du suivi de santé des structures : application aux structures portuaires. *PhD Thesis*.