esa-sceva/satcom-chunk-collection huggingface dataset:
# A TDMA-Based Access Protocol for Dense Networks with Moving Nodes for IoT Applications
###### Abstract  
Low-power wide-area (LPWA) technologies have gained popularity in accordance with the explosive growth of the Internet of Things (IoT). Among others, LoRa is considered as the leading standard that can meet the needs of modern wireless networking, mainly offering energy efficiency and broad coverage as well as a massive amount of device support. In addition to the ALOHA protocol, which is the default channel access mechanism used by the standard, a number of alternatives have been proposed in the literature in an effort to ameliorate the overall network performance. Furthermore, with moving nodes gaining ground more and more in the IoT realm and the research being at a relatively premature stage, it is imperative to create innovative algorithms that support highly dense networks with fast moving nodes. Motivated by these reasons, this work proposes a novel medium access protocol that takes advantage of the increased capabilities of modern wake up radio (WuR) technology in order to achieve low latency and mitigate the risk of lost packets in IoT networks with moving nodes based on the LoRa technology. A number of simulation scenarios have been devised and the findings suggest that the proposed protocol achieves the set goals and improves existing solutions.  
LPWAN; LoRa; IoT; MAC protocol; moving nodes; WuR; dense networks Article  
A TDMA-Based Access Protocol for Dense Networks with Moving Nodes for IoT  
[PERSON]; [PERSON]; [PERSON]; [PERSON] ATDMA-Based Access Protocol for Dense Networks with Moving Nodes for IoT  
Applications, Electronics **2023**, 12, 1628. [[https://doi.org/10.3390/electronics12071628](https://doi.org/10.3390/electronics12071628)]([https://doi.org/10.3390/electronics12071628](https://doi.org/10.3390/electronics12071628))  
Academic Editor [PERSON] Received: 20 February 2023  
24 March 2023  
28 March 2023  
28 March 20230 March 20230 March 20230
# Enhancing the Integration of Protein-Rich Oat Waste Material into Meat Formulations
## 3 Results
### Assessing the Possibility of Lsing OPH as a Meat Additive
#### 3.2.1 Product and Batter Moisture, Protein and Fat Content, pH, and Cooking Yields  
The dry matter and fat content in both the raw batters and the cooked samples, as well as cooking yields, were analysed to determine the differences caused by OPH addition. The results are presented in Table 3. A total of 2 and 3% of OPH inclusion in meat batter improved cooking yields. Fat content decreased beginning with the application of 1% OPH. The pH of the meat batters increased with OPH addition, although the differences were not statistically significant.  
\begin{table}
\begin{tabular}{c c c} \hline  & **Amino Acid Profile [\%]** & **Free Amino Acids [mg/100 g]** \\ \hline Aspartic acid & 8.42 \(\pm\) 0.02 & 7.43 \(\pm\) 0.45 \\ Serine & 4.99 \(\pm\) 0.01 & 19.83 \(\pm\) 1.21 \\ Glutamic acid & 23.77 \(\pm\) 0.03 & 32.74 \(\pm\) 1.99 \\ Glycine & 5.21 \(\pm\) 0.02 & 10.87 \(\pm\) 0.66 \\ Histidine & 2.43 \(\pm\) 0.00 & 23.55 \(\pm\) 1.43 \\ Arginine & 7.05 \(\pm\) 0.05 & 9.76 \(\pm\) 0.59 \\ Threonine & 3.54 \(\pm\) 0.01 & 12.23 \(\pm\) 0.74 \\ Alanine & 5.35 \(\pm\) 0.18 & 16.62 \(\pm\) 1.01 \\ Proline & 5.83 \(\pm\) 0.02 & 22.78 \(\pm\) 1.39 \\ Cysteine & 0.09 \(\pm\) 0.00 & 0.00 \(\pm\) 0.00 \\ Tyrosine & 3.60 \(\pm\) 0.00 & 11.03 \(\pm\) 0.67 \\ Valine & 6.21 \(\pm\) 0.00 & 32.35 \(\pm\) 1.97 \\ Methionine & 1.58 \(\pm\) 0.02 & 2.13 \(\pm\) 0.13 \\ Lysine & 4.25 \(\pm\) 0.00 & 44.02 \(\pm\) 2.68 \\ Isoleucine & 4.43 \(\pm\) 0.00 & 58.36 \(\pm\) 3.55 \\ Leucine & 8.46 \(\pm\) 0.00 & 49.43 \(\pm\) 3.01 \\ Phenylalanine & 4.78 \(\pm\) 0.09 & 4.09 \(\pm\) 0.25 \\ \hline \multicolumn{2}{c}{Sum of amino acids (mg/100 g of hydrolysates)} & 357.23 \(\pm\) 21.76 \\ \end{tabular}
\end{table}
Table 2: Amino acid profile and free amino acid content in protein hydrolysates from oats by-products.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multicolumn{2}{c}{**Variant**} & \multicolumn{2}{c}{**pH**} & \multicolumn{2}{c}{**Dry Matter [\%]**} & \multicolumn{2}{c}{**Fat [\%]**} & \multicolumn{2}{c}{**Cooking Yield [\%]**} \\ \hline C & Raw & 6.28 & \(\pm\)0.21 & 26.82  & \(\pm\)0.24 & 10.33  & \(\pm\)0.16 & & \\  & Cooked & & & 33.76  & \(\pm\)0.09 & 13.69  & \(\pm\)0.05 & 90.63  & \(\pm\)0.20 \\ \hline \multirow{2}{*}{\(1\)H} & Raw & 6.37 & \(\pm\)0.27 & 26.87  & \(\pm\)0.15 & 9.49  & \(\pm\)0.22 & & \\  & Cooked & & & 31.97  & \(\pm\)0.15 & 12.12  & \(\pm\)0.15 & 91.89  & \(\pm\)0.27 \\ \hline \multirow{2}{*}{\(2\)H} & Raw & 6.54 & \(\pm\)0.17 & 27.15  & \(\pm\)0.14 & 9.57  & \(\pm\)0.30 & & \\  & Cooked & & & 30.47  & \(\pm\)0.01 & 10.82  & \(\pm\)0.13 & 92.71  & \(\pm\)0.36 \\ \hline \multirow{2}{*}{\(3\)H} & Raw & 6.66 & \(\pm\)0.15 & 29.36  & \(\pm\)0.51 & 11.38  & \(\pm\)0.70 & & \\  & Cooked & & & 31.18  & \(\pm\)0.04 & 11.93  & \(\pm\)0.05 & 93.74  & \(\pm\)0.18 \\ \hline \end{tabular}
\end{table}
Table 3: Dry matter and fat content of raw and cooked samples, pH of batters, and cooking yields (mean values \(\pm\) standard errors).
## 5 Experiments
### Model Implementation and Assessment Metrics  
The proposed framework was implemented using Python 3 and Pytorch backend on a machine equipped with an NVIDIA GeForce RTX 3080 GPU and 16 GB of memory for the experiments. The input video frame was resized to 224 \(\times\) 224 \(\times\) 3 dimensions to capture its characteristics from the ViT. The Adam optimizer [70] was used to train and optimize the model with a learning rate of 1e\({}^{-4}\), batch size 16, and a five-frame input sequence length. The hidden dimension in MLP in ViT was set to 128, 512, 1024 and 1024, for the UCSD, Avenue, Shanghai, and CHAD, respectively.  
The performance of the model was assessed using the area under the receiver operating characteristic (ROC) curve, following the other research such as [26; 49; 56; 64; 71; 72]. The AUC ROC was employed to determine the capability of the introduced method to discriminate between normal and abnormal frames. Accordingly, the existence of abnormalities in the recordings at the frame level was assessed following the assessment methodologies [73; 74; 75]. The true positive rate (TPR) against the false positive rate (FPR) curve constitutes the ROC curve. The TPR and FPR are computed using Equations (10) and (11), respectively.  
\[TPR=\frac{TP}{TP+FN} \tag{10}\]  
\[FPR=\frac{FP}{FP+TN} \tag{11}\]  
The abbreviations _TP_ and _FN_ stand for true positive and false negative, respectively, whereas _FP_ and _TN_ are abbreviations for false positive and true negative.
# An Improved Monte Carlo Reliability Analysis Method Based on BP Neural Network
## 4 Examples Verification
### Multivariate Response Surface Polynomial  
Example 4 comes from a vehicle side collision problem [33], which has random variables with seven-dimensional normal distribution. The specific distribution parameters are shown in Table 13, and its explicit structural performance function is defined as:  
\[G(X)=0.489x_{1}x_{4}+0.843x_{2}x_{3}-0.0432x_{5}x_{6}+0.0556x_{5}x_{7}+0.000786 x_{7}^{2}-0.75 \tag{16}\]  
For this polynomial response surface, the results calculated by different methods are shown in Table 14. Among them, the Improved BP-MCS algorithm needs 127 groups of sample points, which greatly reduces the calculation workload compared with the subset simulation (SS). Compared with the accelerated methods (AK-IS, AK-SS), the number is slightly larger, but it is still in a lower sample size range. The number of calls of surrogate model is reduced from 5 \(\times\) 10\({}^{6}\) to 132,466, which greatly reduces the calculation costs, and the relative error of failure probability is only 1.27%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Random Variables** & **Distribution** & **Mean** & **Standard Deviation** \\ \hline \(x_{1}\) & Normal & 1.38 & 0.3 \\ \(x_{2}\) & Normal & 1.38 & 0.3 \\ \(x_{3}\) & Normal & 1.38 & 0.3 \\ \(x_{4}\) & Normal & 1.38 & 0.3 \\ \(x_{5}\) & Normal & 0.3 & 0.06 \\ \(x_{6}\) & Normal & 0 & 10 \\ \(x_{7}\) & Normal & 0 & 10 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Random variable distribution of multivariable response surface polynomials.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & \(N_{\text{{FEM}}}\) & \(N_{\text{{call}}}\) & \(P_{f}\) & \(COV_{P_{f}}\) & \(\varepsilon\) \\ \hline MCS & 7 \(\times\) 10\({}^{4}\) & 7 \(\times\) 10\({}^{4}\) & 2.834 \(\times\) 10\({}^{-2}\) & 0.0221 & \\ Kriging [15] & 600 & 7 \(\times\) 10\({}^{4}\) & 3.086 \(\times\) 10\({}^{-2}\) & 0.0212 & 8.89\% \\ AK-MCS [31] & 530 & 7 \(\times\) 10\({}^{4}\) & 2.852 \(\times\) 10\({}^{-2}\) & 0.0221 & 0.64\% \\ AK-MCS-U [28] & 212 & 7 \(\times\) 10\({}^{4}\) & 2.841 \(\times\) 10\({}^{-2}\) & 0.0221 & 0.25\% \\ Direct BP-MCS & 93 & 7 \(\times\) 10\({}^{4}\) & 2.809 \(\times\) 10\({}^{-2}\) & 0.0222 & 0.88\% \\ Improved BP-MCS & 93 & 37,957 & 2.79 \(\times\) 10\({}^{-2}\) & 0.0223 & 1.55\% \\ \hline \hline \end{tabular}
\end{table}
Table 11: Reliability calculation results of nonlinear oscillator.  
Table 15 statistics the failure probability calculation time of the polynomial response surface, Direct BP-MCS, and Improved BP-MCS. When using Direct BP-MCS, its calculation time is as high as 36,521.2 s (about 10 h). When Improved BP-MCS is used, the calculation time is only 1364.1 s, which is about 1/27 of that of Direct BP-MCS. This shows that this method has a great reduction in time cost, but there is still a certain gap in calculation time compared with the explicit response surface polynomial.
## 4 Discussion
### Microorganisms as the Agents of Biodeterioration
#### 4.1.2 Aesthetic Changes Caused by Pigments  
The most noticeable aesthetic changes are colored patinas, which can be of bacterial, cyanobacterial, fungal, algal, or even archaeal origin [4]. Black crusts are common for fungi-infested limestone, infested with namely _Aspergillus versicolor_, _Penicillium brovicompatum_[51], and the _Ochroconis_ genera [8]. The black discoloration caused by fungi is often a consequence of strongly melanized cell walls. Melanin is a stress-protective pigment, which is beneficial for the survival of certain extremophilic fungi, among which belong the so-called \"black fungi\". Black fungi genera represent a heterogeneous taxonomic group, including orders within the classes Dothideomycetes and Eurotiomycetes [48]. Orange-colored pigments, carotenoids, serve the same purpose as melanin--the protection of the cell [48; 71]--but they are mainly excreted by other inhabitants of CHL, such as the algal _Tentepolhia_ genera [15] and some bacterial species, namely the following: _Staphylococcus aureus_, _Dietzia maris_, _Gordonia rubripertincta_, _Rhodococcus corynebacterioides_[4], _Rhodococcus cerastii_, and _Rhodococcus fascians_[7]. Pink discoloration, which was previously assigned to a non-biological origin only, was later found to be excreted by bacterial genera _Rubrobacter_, _Halobacillus_[4], _Microoccus_[54], and _Arthrobacter_[4; 7], and by taxons belonging to archaea, such as genera _Halobacterium_, _Halococcus_, and _Haloferax_[4]. Green patinas on CHL are a consequence of chlorophyll production by algae and cyanobacteria [1; 6; 39] or a consequence of different metabolite production by fungal genera such as _Aspergillus_ and _Penicillium_[51]. White coloration can occur due to a calcium-oxalate-producing genera that include mainly _Streptomyces_[54], _Aspergillus_, _Penicillium_, and _Colletotrichum_[21], or due to the growth of white-looking lichen with a fungus from the _Leprocaulon_ genera [6].  
Interestingly [PERSON] et al. [6] found that some of the white patches in the West Lake Cultural Landscape were transitional.
# New Retailing Problem for an Integrated Food Supply Chain in the Baking Industry
## 4 Model Formulation
### Manufacturer's Total Profit per Unit Time  
The manufacturer's total profit per replenishment cycle is calculated as follows:  
1. Sales revenue (SR): The manufacturer's sales revenue per replenishment cycle is expressed as \(SR=(1-\rho)[p_{2}S(Q)-g_{ck}(D-(\beta-\gamma)(p_{1}+p_{2})-S(Q))]\).
2. Wholesale value (WV): \(WV=w^{\prime}nQ\).
3. Setup cost (SC): The manufacturer's setup cost per replenishment cycle is \(SC=K\frac{D}{Q}\).
4. Quality degradation function (\(C_{QD}\)): Similar to [PERSON] et al. [61], the manufacturer's degradation function per replenishment is \(C_{QD}=p_{2}\Big{[}Q-\frac{D}{p(T)}(1-e^{-b(T)Q/D})\Big{]}\).  
Goodwill cost (GC): Goodwill cost of the manufacturer is \(GC=g_{ck}[(D-(\beta-\gamma)\)\((p_{1}+p_{2})-S(Q))]\).
6. Holding cost (HC): Based on [PERSON] et al. [59], the manufacturer's inventory level in a replenishment cycle. The manufacturer's holding cost is calculated as \(HC=\frac{h_{n}mk_{T}Q}{2}\Big{(}\frac{2-n}{P}+\frac{n-1}{D}\Big{)}\).
7. CASE I. Revenue-sharing contract The manufacturer's total profit function at in a replenishment cycle is expressed as \[\begin{array}{ll}TPF_{ck}(n,T)&=SR+WV-SC-PC-GC-HC-C_{QD}\\ &=-g_{ck}[(D-(\beta-\gamma)(p_{1}+p_{2})-S(Q))]-K\frac{D}{Q}-c_{ck}nQ+w^{\prime }nQ\\ &+(1-\rho)[p_{2}S(Q)-g_{ck}(D-(\beta-\gamma)(p_{1}+p_{2})-S(Q))]\\ &-p_{2}\Big{[}Q-\frac{D}{b(T)}(1-e^{-b(T)Q/D})\Big{]}-\frac{h_{n}mk_{T}Q^{2}}{ 2}\Big{(}\frac{2-n}{P}+\frac{n-1}{D}\Big{)},\end{array}\] (10)
8. CASE II. Buy-back contract The manufacturer's total profit function at in a replenishment cycle is expressed as \[\begin{array}{ll}TPF_{ck}(n,T)&=\beta[Q-S(Q)]-K\frac{D}{Q}-c_{ck}nQ+wnQ-g_{ck }[D-(\beta-\gamma)(p_{1}+p_{2})-S(Q)]\\ &-p_{2}\Big{[}Q-\frac{D}{b(T)}(1-e^{-b(T)Q/D})\Big{]}-\frac{h_{n}mk_{T}Q^{2}}{ 2}\Big{(}\frac{2-n}{P}+\frac{n-1}{D}\Big{)},\end{array}\] (11)
9. CASE III. Quantity-flexibility contract 1. Case 1: \(D-(\beta-\gamma)(p_{1}+p_{2})>(1-\delta)Q\) \[\begin{array}{ll}TPF_{ck}(n,T)&=wn(1-\delta)Q-K\frac{D}{Q}-c_{ck}n(1-\delta )Q\\ &-p_{2}\Big{[}Q-\frac{D}{b(T)}(1-e^{-b(T)Q/D})\Big{]}-\frac{h_{n}mk_{T}Q^{2}}{ 2}\Big{[}\frac{2-n}{P}+\frac{n-1}{D}\Big{]},\end{array}\] (12)
10. Case 2: \((1-\delta)Q<D-(\beta-\gamma)(p_{1}+p_{2})<Q\) \[\begin{array}{ll}TPF_{ck}(n,T)&=wnQ-K\frac{D}{Q}-c_{ck}nQ-p_{2}\Big{[}Q- \frac{D}{b(T)}(1-e^{-b(T)Q/D})\Big{]}\\ &-\frac{h_{n}mk_{T}Q^{2}}{2}\Big{(}\frac{2-n}{P}+\frac{n-1}{D}\Big{)},\end{array}\] (13)
11. Case 3: \(D-(\beta-\gamma)(p_{1}+p_{2})>Q\) \[\begin{array}{ll}TPF_{ck}(n,T)&=wnQ-K\frac{D}{Q}-c_{ck}nQ-g_{ck}[Q-S(Q)]-p_ {2}\Big{[}Q-\frac{D}{b(T)}(1-e^{-b(T)Q/D})\Big{]}\\ &-\frac{h_{n}mk_{T}Q^{2}}{2}\Big{(}\frac{2-n}{P}+\frac{n-1}{D}\Big{)},\end{array}\] (14)
## 2 Materials and Methods
### Preprocessing of Taxonomic Abundance Data  
To compare the taxonomic abundance among samples with different numbers of total short reads from NGS, the count-based taxonomic abundance table should be normalized. In EdgeR, the read count data is normalized using the \"trimmed mean of M values\" (TMM) method. TMM is designed to shift the log-fold-change of stable features, such as housekeeping genes (HKGs), to zero values. Recently, a robust normalization method using the geometric mean of pairwise ratios(GMPR) [27] has been proposed for taxonomic count tables. GMPR is a normalization method that modifies the calculation procedure of the relative log expression normalization (RLE) implemented in DESeq2 and EdgeR. These normalization methods may capture robust changes in taxonomic abundance among samples, but they are less sensitive to relative abundance changes for microbial species with low abundance. Robust normalizations can underestimate the compositional changes of minor components in the microbial community. As a simple normalization method, \"Total Sum Scaling (TSS)\" is often applied to the read-count based tables. TSS uses the total read count for each sample as the size factor. TSS normalization converts count-based taxonomic abundance data into compositional data. Compositional data reside in a simplex, and thus most of the statistical frameworks assuming a Euclidean space cannot be directly applied to the compositional data. To appropriately deal with such compositional data, our framework performed a centered log-ratio (CLR) transformation for the taxonomic compositional data in the microbiome. This preprocessing is used for non-parametric differential analysis in geological studies [28; 29], as well as microbiome studies [30]. This transformation function clr(X) is defined for the compositional data X as follows:  
\[X=(x_{1},x_{2},...,x_{D}) \tag{1}\]  
\[g(X)=(\prod_{i=1}^{D}x_{i})^{1/D} \tag{2}\]  
\[clr(X)=[\ln\frac{x_{1}}{g(X)},\ln\frac{x_{2}}{g(X)},...,\ln\frac{x_{D}}{g(X)}] \tag{3}\]  
where \(g(X)\) is the geometric mean of the composition \(x\), and \(D\) is the number of features (e.g., OTUs). This function transforms the relative taxonomic abundance from the simplex to the real space, and allows us to treat the data in real space.
## 1 Introduction
To the best of the author's knowledge, the steady-state and transient responses of an exponential-law based slant-cracked functionally graded rotor-bearing system to detect and understand the influence of the cracks have not been reported in the literature. Therefore, the principal aim of the present work is to study the natural frequencies, steady-state and transient time responses, and the corresponding frequency spectra of a slant cracked exponentially graded (EG) rotor-bearing system by considering the breathing effect of the slant crack. The organisation of this current research work is as follows. Primarily, an FG rotor-bearing system having an exponentially graded shaft is considered in the present work. The material properties are graded along the radial direction of the FG shaft by using exponential law, whereas exponential temperature distribution (ETD) law is used to simulate the temperature gradients across the cross-section of the FG shaft. Although [PERSON] and [PERSON] modelled a slant crack in a steel rotor-bearing system [26], the derivations and modelling of the slant-cracked EG rotor-bearing system are not available in the literature. Therefore, a two-nodded EG rotor element with and without a slant crack are formulated based on Timoshenko beam theory using the finite element method. Then, the stiffness matrix of a slant-cracked EG rotor element is developed by determining the local flexibility coefficients using Paris's equations. Transient and steady state vibration responses of EG rotor system have been simulated by considering the breathing slant crack in order to develop a crack detection method through frequency response. Finally, the influence of the crack parameters and temperature gradient on natural frequencies are investigated, and the effect of the crack depth, torsional frequency and temperature gradient on steady-state and transient responses of a slant-cracked EG rotor system is also analysed.
## 4 Case Study
### Experimentation and Testing Process
#### 4.1.3 Cognitive Emotion Recognition  
The proposed cognitive emotion recognition method was trained and tested. In order to verify the advantages of the proposed method using different methodologies (including ML-based methods, DL-based methods, and video-based machine learning methods), some competing methods with good performance (such as LBP + SVM, IL-VGG, PLBP + RF, etc.) were used for comparison. For the proposed method, the number of decision trees in RF was 100. The initial number of training samples k was set to 10, 20, 30, 40, 50, 60, 70 and 80, and then _180-k_ samples were selected through the sample selection criteria based on the uncertainty and complexity; the remaining 720 samples were used as test samples. For the competing methods, since some of these methods are based on static images, the first step was to extract the most representative image from each video sample. The 900 image samples were randomly divided into five groups on average, and 5-fold cross validation (CV) was carried out. In order to unify the conditions for comparison, the size of the training set was set to 180, and the size of the test set was set to 720. This also highlights the advantages of the proposed method when using small samples of data.
# An Improved Empirical Wavelet Transform and Its Applications in Rolling Bearing Fault Diagnosis
## 4 Simulated Signal Verification
### Case Study 1
After calculating the difference between the separated empirical mode and the corresponding component of the original signal, the mean square error is used to calculate the error rate. The formula is as follows:  
\[\text{rate\_Error}=\sqrt{\frac{\sum_{i=1}^{\text{N}}\left(\text{EM}_{\text{j} }-\text{s}_{\text{k}}\right)^{2}}{\text{N}}} \tag{19}\]  
where rate_Error is the error rate, EM\({}_{\text{j}}\) is the jth empirical model waiting for comparison, and s\({}_{\text{k}}\) is the corresponding empirical mode. Figure 9 shows the separation success rate and error rate of EWT and FEWT. The success rate of EWT decomposition is 7.14% and FEWT is 42.86%. The FEWT decomposition efficiency and success rate are higher. Since the EWT method only successfully separates the third component of the original signal, only the error rate of this component can be compared. From Figure 9b, it is known that the components decomposed by FEWT are more consistent with the original components. Therefore, the boundary of the proposed method is more reasonable.
# Shear Resistance Evolution of Geogrid Reinforced Expansive Soil Under Freeze-Thaw Cycles
###### Abstract  
Expansive soils have significant characteristics of expansion by water absorption, contraction by water loss. Under the freeze-thaw (F-T) cycles, the engineering diseases are more significant, and the serious geotechnical engineering incidents are induced extremely easily. The aim is to investigate the mechanical response characteristics of geogrid-reinforced expansive soils (GRES) under F-T cycles. Based on a series of large-scale temperature-controlled triaxial tests, influencing factors were considered, such as the number of F-T cycles, the geogrid layers, and the confining pressure. The results showed that: (1) Friction between the expansive soil and geogrid and the geogrid's embedded locking effect indirectly provided additional pressure, limited shear deformation. With the increase in reinforced layers, the stress-strain curve changed from a strain-softening to a strain-hardening type. (2) Elastic modulus, cohesion, and friction angle decreased significantly with increasing number of F-T cycles, whereas dynamic equilibrium was reached after six F-T cycles. (3) The three-layer reinforced specimens showed the best performance of F-T resistance, compared to the plain soil, the elastic modulus reduction amount decreases from 35.7% to 18.3%, cohesion from 24.5% to 14.3%, and friction angle from 7.6% to 4.5%. (4) A modified Duncan-Zhang model with the confining pressure, the F-T cycles, and the geogrid layers was proposed; the predicted values agreed with the measured values by more than 90%, which can be used as a prediction formula for the stress-strain characteristics of GRES under freeze-thaw cycling conditions. The research results can provide important theoretical support for the practical engineering design of GRES in cold regions.  
Keywords:expansive soils; geogrid; freeze-thaw cycles; reinforcement layers; shear resistance