# Evaluation of Creep Behavior of Soft Soils by Utilizing Multisensor Data Combined with Machine Learning

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{α}), motivated by the fact that current empirical models for C

_{α}determination are not sufficiently reliable. Within this study, the authors collected datasets of four input soil parameters determined by the simple laboratory tests and defined C

_{α}as the NN output parameter. The developed models demonstrably outperformed empirical methods, featuring as they do lower levels of prediction error. Liu et al. [31] demonstrated that the creep models can avoid artificial assumption of complex constitutive equation and can reflect nonlinear creep properties of soft soil objectively. Further, Chen et al. [32] developed an NN-based model, by utilizing the creep data of a laboratory direct shear experiment. The modeling method was validated on the creep experimental data of soft clay of Shanghai, where the study clearly demonstrated that the rheological model can effectively describe the nonlinear creep of soft clay. To assess the soil creep susceptible areas, Lee et al. [33] used several machine learning classification methods, namely the k-nearest neighbor (k-NN), naive bayes (NB), random forest (RF), and support vector machine (SVM) models, where results from almost 5000 field surveys were utilized for the development of the classification models. The benefit of the NNs is also evident in the studies for predicting the compressibility parameters of the soils, which govern the soft soil behavior before it reaches the creep phase. For example, Kurnaz et al. [34] suggested the prediction of compressibility parameters from basic soil properties, concluding that the proposed NN model is successful for the prediction of the compression index, with less accuracy in prediction of recompression index values.

## 2. Methods and Methodology of Soil Creep Prediction Based on Multisensor Data

#### 2.1. Constitutive Law Used for Numerical Modeling

_{K}and viscosity η

_{K}) and Maxwell’s unit (characterized by its shear elastic shear modulus G

_{M}, viscosity η

_{M}, and bulk modulus K

_{M}) act in series. In addition, a plastic strain–rate part, which utilizes the Mohr–Coulomb failure criteria and is characterized by the cohesion (c), friction angle (ϕ), and dilation (ψ), is connected in series with viscoelastic part of model.

_{K}and η

_{M}) is a challenging task. Therefore, these two parameters represent this study’s first two constitutive unknowns. Further, several stiffness values are required by the Burger’s model, and these include Maxwell’s bulk and shear modulus (K

_{M}and G

_{M}) and Kelvin’s shear modulus (G

_{K}). By utilizing well-known equations:

_{M,0}and K

_{M,0}are Maxwell’s small-strain shear and bulk modulus (in Pa), respectively, ρ (kg/m

^{3}) is soil density, determined in this study from continuous-by-depth CPT procedure developed by Kovačević et al. [36], v

_{s}(m/s) is a soil shear velocity obtained in this study from geophysical MASW investigations, and $\mathsf{\nu}$ (-) is Poisson’s ratio. Since creep mechanism involves large-strain moduli, which are lower than the small-strain values, these could be obtained by introducing the so-called reduction radio (r

_{d}), which in fact represents the percentage of small-strain modulus and can be defined as:

_{M}and K

_{M}are Maxwell’s large-strain shear and bulk modulus (in Pa). Therefore, a reduction ratio represents the third unknown of the creep estimation methodology, which correlates with the required large-strain Burger’s moduli with the known values of small-strain moduli. It should be noted that Kelvin’s shear modulus (G

_{K}) was assumed as zero within this methodology since it acts in series with Maxwell’s shear modulus (G

_{M}), so that the shear modulus dependence of the system could be assigned only to Maxwell’s shear modulus.

_{d}), Kelvin viscosity (η

_{K}), and Maxwell viscosity (η

_{M}), by utilizing the neural network along with the application of the particle swarm optimization (PSO) algorithm.

#### 2.2. Methodology Phases

^{3}, with ‘n’ being the selected number of values for each parameter) of predefined input creep parameters (r

_{d}, η

_{K}, and η

_{M}). The range of these parameters should be selected in such way so that upper and lower boundary of each parameter range can be considered sufficient to estimate the most probable parameter value in the subsequent phases. These sets of parameters were applied to the numerical simulations, eventually resulting in n

^{3}output sets, representing soil displacement values over a certain predefined period of time. For example, if five (5) possible values of three (3) unknowns were considered, this resulted in 125 (i.e., 5

^{3}) numerical simulations and 125 output displacements in each observed period. It should be noted that the numerical simulations in this case were time-dependent simulations, where a selection of time-step was necessary to ensure the stability of the time-dependent numerical solution.

_{d}, η

_{K}, and η

_{M}) parameters’. By utilizing the particle swarm optimization (PSO) algorithm in the fourth phase, the best fitting curve, described by one set of parameters, was identified. This ‘most probable’ set of creep parameters was implemented in a developed numerical model to evaluate how the numerical model correlated with the obtained in situ measurement data. Finally, after obtaining a reliable estimation of the constitutive model creep parameters, the fifth phase of the methodology included a prediction of the long-term creep behavior of the time-dependent numerical model for any user-defined period.

#### 2.3. Development of NetCREEP Neural Network and PSO Optimization

_{d1}, r

_{d2}, …, r

_{dn}]; [η

_{K1}, η

_{K2}, …, η

_{Kn}]; [η

_{M1}, η

_{M2}, …, η

_{Mn}], the output was determined through the n

^{3}displacements resulting from n

^{3}numerical simulation. Therefore, the displacement was defined by the form of [y

_{t1}, y

_{t2}, …, y

_{tm}]

_{1}; [y

_{t1}, y

_{t2}, …, y

_{tm}]

_{2}; …; [y

_{t1}, y

_{t2}, …, y

_{tm}]

_{n}

^{3}with ‘y’ being the displacement, ‘t’ being the observed time, and ‘m’ being the largest observed time. The developed NetCREEP consisted of four (4) hidden layers. The first and second hidden layers consisted of three (3) nodes, while the third and fourth consisted of two (2) nodes. In total, 30 distinct weightings were used, where a sigmoid activation function was utilized for hidden neurons, and a linear activation function was utilized for output, see Figure 4. The final number of hidden layers and the number of nodes in each hidden layer, was determined through a ‘trial and error’ method. Several ‘trial and error’ rule-of-thumb methods are described in the relevant literature [37]. In this study, by using the ‘trial and error’ method, 28 different NN architectures were analyzed, having a different number of hidden layers and associated number of nodes in each hidden layer. The selected architecture, from Figure 4, yielded largest values of R

^{2}, meaning that it established the highest strength of the ‘creep parameter-time-dependent displacement’ relationship.

_{d}, η

_{K}, and η

_{M}), which matched the measured InSAR and GPS displacements. As described by Jahed Armaghani et al. [43], the overall swarm size has large influence on the PSO performance, where this study utilized the size of 60 particles.

## 3. Investigation Methods and Multisensor Data

#### 3.1. Remote Sensing Data Acquisition

#### 3.1.1. Unmanned Aerial Vehicle (UAV) for Terrain Topography

#### 3.1.2. Satellite Monitoring of Ground Displacements

#### 3.2. Geophysical Near-Surface Nondestructive Methods

#### 3.2.1. MASW for Determination of a Small-Strain Soil Stiffness

#### 3.2.2. Electrical Resistivity Tomography (ERT) for Determination of Deposit Thicknesses

#### 3.2.3. Cone Penetration Testing (CPT) for Soil Classification and Determination of Its Physical-Mechanical Parameters

_{c}) and sleeve resistance (f

_{s}), as well the groundwater pore pressure (u). Despite the standardized external geometry of the cone, the measurement and transmission system used can vary considerably from one device to another [59]. By utilizing raw CPT collected data, soil layers can be identified using one of the classification procedures, such as [60], as well to provide estimates of its in situ physical and mechanical properties, such as undrained strength, compression modulus, friction angle, and unit weight. The latter correlation, developed by Kovacevic et al. [36], was particularly useful in the present study for determining soil density and for the calculation of small strain stiffness in combination with MASW results, as given in Equation (1).

## 4. Validation of the Methodology—Oostmolendijk Embankment

#### 4.1. Description of the Case Study Area

#### 4.2. Conducted Investigations and Obtained Results

^{−6}m and 1.1 × 10

^{−4}m in horizontal (X and Y directions, respectively) and 1.2 × 10

^{−4}m vertically (Z direction), providing satisfactory absolute accuracy of the reconstructed model. The development of a point cloud enabled extraction of the relevant cross-section, marked CS in Figure 9, used in the subsequent numerical analysis. Two CPTs were conducted from the Oostmolendijk crest level, while two were conducted on the downstream side. For every CPT investigation, data were continuously recorded with a vertical resolution of 2 cm. This CPT raw data, obtained from the DINOloket [63], were mostly consistent as they point to the clayey material depths up to 15–16 m from the crest level overlying the sandy layers to the investigation depths. The clayey layers showed extremely low values of q

_{c}in the clayey layers, up to 1 MPa, while for the sand deposits q

_{c}values were in a range from 10 to 20 MPa, Figure 10. By using the Robertson [60] classification and soil layering algorithm developed by Kovačević et al. [58], a soil profile was developed.

_{s}values (clay) to the depths of 10–15 m below which there is a v

_{s}increase (sands).

#### 4.3. Long-Term Monitoring Data

^{2}is 0.8911, while the RMSE has value of 0.5628.

#### 4.4. Results and Discussion

#### 4.4.1. Implementation of NetCREEP and PSO

_{d}= [0.10; 0.15; 0.20; 0.25; 0.30]; (ii) Kelvin’s viscosity, η

_{K}= [10,000; 20,000; 40,000; 60,000; 80,000]; and (iii) Maxwell’s viscosity, η

_{M}= [200,000; 250,000; 300,000; 350,000; 400,000]. These 125 sets (i.e., 5

^{3}being the possible number of combinations, where ‘5′ represents a number of predefined values for each creep parameter and ‘3′ represents the number of creep parameters) of input parameters, when used in numerical simulations, resulted in 125 displacements of the crest displacement. The displacement of a crest is marked as relevant for the implementation of methodology since it is exactly at this location where the Oostmolendijk displacements were monitored by InSAR and GPS.

_{c}, shown in Figure 10, were relatively insignificant down to the depth of sand layers. When Robertson’s 2016 [60] soil classification was used, which classifies soils based on its behavior, the entire layer was classified as ‘clay-like contractive material’. The case was similar when Robertson’s 2009 [65] soil classification was used, which relies on the textural-based descriptions and where the entire profile up to sand is classified as ‘clay’. It was only when the Dutch modification of Robertson’s 2009 classification was implemented, that some thin layers were classified as peat. This is due to fact that a soil behavior type index (I

_{c}) in the Dutch modification, with a value of 3.6, is slightly shifted toward higher Q

_{t}values in the Q

_{t}–F

_{r}chart. Therefore, it can be stated with great certainty that the mechanical behavior of the soft clay and peat is the same and that these can be evaluated as a single layer in this study. Also, the v

_{s}values from Figure 12 show an insignificant decrease in values at depths of 5 to 11 m, yielding the small influence on obtained small strain shear modulus values.

_{d}, η

_{K}, and η

_{M}) set, and output was considered as a displacement of the crest in 31 observed time (every 3 months from December 2013 to June 2021.). The total number of crest displacements calculated is 3875 (31 observation periods × 125 calculations). The overall matrix output has the form [y

^{crest}

_{1}, y

^{crest}

_{2}, …, y

^{crest}

_{31}]

_{1}; [y

^{crest}

_{1}, y

^{crest}

_{2}, …, y

^{crest}

_{31}]

_{2}; …; [y

^{crest}

_{1}, y

^{crest}

_{2}, …, y

^{crest}

_{31}]

_{125}. Figure 15 shows that R

^{2}values for the target-output evaluations for training, validation, testing, and overall datasets are equal to unity. This confirms that the developed NetCREEP established strong correlation between time-dependent crest displacements and creep parameters and that the chosen number of input combinations is representative.

_{d}, η

_{K}, and η

_{M}) set, which would yield observed measurements. The PSO was used for minimizing the sum square error between the network output and the desired output obtained by InSAR and GPS displacement measurements. In the case of Oostmolendijk, the minimum of estimation function (f

_{min}) equaled to 1.6915 × 10

^{−6}, whereas the identified values of Burger’s unknown parameters were: (i) r

_{d}= 0.2112 (meaning that the large-strain stiffness is 21% of obtained small-strain stiffness), (ii) η

_{K}= 48,050, and (iii) η

_{M}= 320,000. When these values were implemented in the numerical model, Figure 16, results show that the numerically obtained crest displacement trend correlates well with the crest monitoring results for the period up to June 2021, and this validates the overall methodology.

#### 4.4.2. Prediction of Oostmolendijk Long-Term Behavior

^{2}meaning that there is a clear trend of measured displacements in time. However, once they are extrapolated to 2030, the regression functions overestimate the numerically predicted displacement by 20% (logarithm function), 23% (linear function), or 34% (polynomial function), respectively. Apart from providing more reliable displacement prediction, having the fully defined numerical model means having the fully defined soil stress state for any desired period, something which cannot be obtained by simple extrapolation of the regression functions. Therefore, at some point a soil failure will occur due to excessive deformations and this, unlike with the fully defined numerical model, cannot be predicted by simply extrapolating the measurement data regression functions.

## 5. Conclusions

_{d}), Kelvin’s viscosity (η

_{K}), and Maxwell’s viscosity (η

_{M}) were assigned to the model. The obtained numerical input–output datasets provided the basis for the development of NetCREEP, which, after several iterations, consisted of ten nodes distributed within the total of four hidden layers. By utilizing the PSO, the most probable set of creep parameters was identified where the methodology took full advantage of the database consisting of the continuous monitoring of long-term soil displacements, obtained by InSAR and GPS. The overall methodology was verified on a case study location of an Oostmolendijk embankment in the Netherlands, well-known for its extreme settlements. The developed and PSO-optimized NetCREEP provided a set of creep parameters, which enabled the numerical simulation of a monitoring database, as well the prediction of the long-term behavior of an embankment. Within this procedure, PSO yielded sufficiently low values of minimum of estimation function. It was shown that the prediction model provides 20–35% lower values of long-term settlements when compared to traditional statistical regression functions extrapolated to the desired period. When compared to some previous studies on the embankment settlements, this study yields twice the lower values. A fully defined numerical model, with a best estimate of input creep parameters, also provides the insight into long-term soil stress state, which cannot be obtained by simple extrapolation of the regression functions used merely on monitoring data. The study also demonstrates the huge benefits of having the continuous monitoring of the embankment, not just for the current assessment of its behavior, but also for reliable prediction of future performance. For this purpose, remote sensing InSAR data can be extremely beneficial.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Different phases of creep in various stress regime, redrawn from [7].

**Figure 2.**A classic Burger’s creep viscoplastic model, redrawn from [35].

**Figure 6.**In situ investigation methods: (

**a**) MASW geophones and ERT electrodes during the investigation; (

**b**) CPT cone parts.

**Figure 12.**Values of 1D shear velocities from 4 investigation profiles: (

**a**) P1 profile on the upstream side; (

**b**) P2 on the crest; (

**c**) P3 on the crest; (

**d**) P4 on the downstream side.

**Figure 13.**Oostmolendijk displacements in time obtained from InSAR [64] and GPS.

**Figure 15.**Training (

**a**), validation (

**b**), testing (

**c**), and overall (

**d**) datasets with correlation of NetCREEP predicted time-dependent crest displacements and creep parameters.

**Figure 16.**Numerically obtained displacements of the Oostmolendijk for the identified creep parameters.

Soil Layering/Parameters | |||||||

Type | Total no. of investigation profiles or points | No. of profiles (points) on the crest | No. of profiles (points) upstream/downstream | Length of each profile (m) | Depth of investigation (m) | Source | |

MASW | 4 | 2 | 1/1 | 100 | 26 | In situ | |

ERT | 4 | 2 | 1/1 | 75 | 15 | In situ | |

CPT | 4 | 2 | 0/2 | - | 20 | [63] | |

Terrain Topography | |||||||

Type | Flight height (m) | Scanned area (m × m) | Photo overlapping | No. of photos | No. of 3D points (million) | GSD (cm) | Source |

UAV | 30 | 70 × 130 | front 70% side 70% | 87 | 63.6 | 0.83 | In situ |

Displacement Measurement | |||||||

Type | Measurement period | Satellite | Point ID from database [56] | Coordinates (EPSG:28992) of measurement point * | No. of measurements | Source | |

InSAR | from May 2015 to June 2020 | WEST-1 | L00019660P00016545 | N 102968.0 E 430885.0 | 251 | [64] | |

GPS | from June 2020 to June 2021 | - | - | N 102969.6 E 430885.8 | 3 | IM ** |

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**MDPI and ACS Style**

Kovačević, M.S.; Bačić, M.; Librić, L.; Gavin, K.
Evaluation of Creep Behavior of Soft Soils by Utilizing Multisensor Data Combined with Machine Learning. *Sensors* **2022**, *22*, 2888.
https://doi.org/10.3390/s22082888

**AMA Style**

Kovačević MS, Bačić M, Librić L, Gavin K.
Evaluation of Creep Behavior of Soft Soils by Utilizing Multisensor Data Combined with Machine Learning. *Sensors*. 2022; 22(8):2888.
https://doi.org/10.3390/s22082888

**Chicago/Turabian Style**

Kovačević, Meho Saša, Mario Bačić, Lovorka Librić, and Kenneth Gavin.
2022. "Evaluation of Creep Behavior of Soft Soils by Utilizing Multisensor Data Combined with Machine Learning" *Sensors* 22, no. 8: 2888.
https://doi.org/10.3390/s22082888