esa-sceva/satcom-chunk-collection huggingface dataset:
# Downlink Training Design for FDD Massive MIMO Systems in the Presence of Colored Noise
## 6 Physical Channel Models
The channel covariance matrices in the azimuth and elevation directions are given in (47) and (48), respectively,  
\[\left[\mathbf{R}_{\rm h,A}\right]_{i,j}=\frac{1}{\sqrt{2}\alpha_{\rm A}}\int _{\theta-\pi}^{\theta+\pi}e^{-\frac{\sqrt{2}}{\alpha_{\rm A}}(x-\theta)}e^{ \frac{-j\pi\pi}{\lambda}(i-j)\sin(x)}\mathrm{d}x, \tag{47}\]  
\[\left[\mathbf{R}_{\rm h,E}\right]_{i,j}=\frac{1}{\sqrt{2}\alpha_{\rm E}}\int _{\phi-\pi}^{\phi+\pi}e^{-\frac{\sqrt{2}}{\alpha_{\rm E}}(x-\phi)}e^{\frac{-j \pi\pi}{\lambda}(i-j)\sin(x)}\mathrm{d}x, \tag{48}\]  
where \(\theta\) is the angle of arrival of \(k\)-th user in the azimuth direction and \(\alpha_{\rm A}\) denotes the angular spread in the azimuth direction. The angular spread in elevation direction, denoted by \(\alpha_{\rm E}\), and the angle of arrival in elevation direction, denoted by \(\phi\), are given by (49) and (50), respectively [22]  
\[\alpha_{\rm E}=\frac{1}{2}\Bigg{(}\arctan\bigg{(}\frac{D+s}{h}\bigg{)}-\arctan \bigg{(}\frac{D-s}{h}\bigg{)}\Bigg{)}, \tag{49}\]  
\[\phi=\frac{1}{2}\Bigg{(}\arctan\bigg{(}\frac{D+s}{h}\bigg{)}+\arctan\bigg{(} \frac{D-s}{h}\bigg{)}\Bigg{)}, \tag{50}\]  
where \(s\) denotes the radius of the scattering ring in meter and parameter \(D\) denotes the users distance from the BS and \(h\) represents the BS height. Note that the narrow angular spread in the azimuth direction provides a low-rank structure for the channel covariance matrix, which implies a strong spatial correlation. For the ULA, the spatial channel correlation \(\mathbf{R}_{\rm h}\) can be modelled as [33]  
\[\left[\mathbf{R}_{\rm h}\right]_{i,j}=\frac{1}{2\alpha_{A}}\int_{\theta- \alpha_{A}}^{\theta+\alpha_{A}}e^{\frac{-j\pi d}{\lambda}(i-j)\sin(x)}dx, \tag{51}\]  
where \(\alpha_{\rm A}\) denotes the angular spread in the azimuth direction. The following section presents several results that characterize the FDD performance in MaMi systems with RZFBF precoding in the ULA and UPA configurations. Figure 2: Illustration of a UPA with azimuth and elevation directions based on \(x,y,z\) coordinates.
## 3 Results and Discussion
### Damage Variable  
Quantitative analysis of changes in the mechanical properties of granite under different hot-cold impacts can be undertaken using the generalized damage variable \(D\):  
\[D=1-\frac{W_{T}}{W_{0}} \tag{6}\]  
where \(W_{\rm T}\) and \(W_{0}\) are the mechanical properties (shear strength and cohesion) of the granite before and after the heat-cold impact, respectively. Compared to conventional damage variables, if D is negative, it indicates that thermal hardening of the rock is occurring at this time.  
Based on the experimental results, the damage to coarse- and fine-grained granite after various high-temperature and cold-shock treatments was calculated, as shown in Figure 18. The figure shows that, overall, the degree of damage to granite increases significantly with increasing heat treatment temperature, reaching a maximum at 600 \({}^{\circ}\)C. In addition, under liquid nitrogen cold shock, the damage characteristics of the rock are more pronounced. For example, at 600 \({}^{\circ}\)C, the cohesion damage of coarse-grained granite under high-temperature liquid nitrogen cold shock is 0.2, significantly higher than the 0.12 observed under high-temperature water cold shock. In addition, fine-grained granite exhibits more significant damage under high-temperature cold shock than coarse-grained granite. For example, at 400 \({}^{\circ}\)C, the maximum damage value of fine-grained granite under high-temperature water cold shock is 0.11, while under high-temperature liquid nitrogen cold shock it is 0.23. As mentioned in Section 3.2.1, the effect of high temperature on  
Figure 17: Schematic diagram of particle crack structure in granite after high-temperature treatment: (a) 25 \({}^{\circ}\)C, (b) 400 \({}^{\circ}\)C, (c) 600 [51].  
granite is the result of the competition between thermal hardening and thermal damage. From Figure 18, it can be seen that the transition from thermal hardening to thermal damage is closely related to temperature, cold-shock method, and particle size, with the transition temperature occurring earlier for liquid nitrogen cold shock than for water cold shock. The degree of damage to granite resulting from high-temperature cold shock varies with different mechanical parameters. Taking fine-grained granite as an example, if the damage level of granite is assessed on the basis of its cohesion change, it is significantly higher than the results obtained using other mechanical parameters. Therefore, relevant mechanical parameters should be reasonably selected to assess the fracture effect of dry hot rock reservoirs.  
Figure 18: Damage variables of granite under different cooling methods: (**a**) coarse-grained granite after high-temperature water-cooled impact; (**b**) coarse-grained granite after high-temperature liquid-nitrogen-cooled impact; (**c**) fine-grained granite after high-temperature water-cooled impact; (**d**) fine-grained granite after high-temperature liquid-nitrogen-cooled impact.
# A Performance Analysis of Internet of Things Networking Protocols: Evaluating MQTT, CoAP, OPC UA
## 3 An Overview on IoT Communication Protocols and Frameworks
### Dds  
The _Object Management Group (OMG) Data Distribution Service (DDS)_[19] is a middleware connectivity framework and API standard for data-centric connectivity, that targets direct communication between devices. Its purpose is to distribute data to other devices while interfacing with an IT infrastructure.  
DDS provides low-latency data connectivity, extreme reliability, and a scalable architecture, that fits well business and mission-critical IoT require. DDS was first introduced to overcome limitations of client/server architectures such as CORBA, COM+/DCOM. A main difference of DDS in comparison to AMQP and to MQTT is decentralization. DDS supports 1 to N communication. A second relevant difference is that DDS provides direct communication support, without a broker. A third difference is the support for automatic discovery of devices.  
With DDS, \"real-time\" is in the order of milliseconds. DDS offers powerful ways to filter and select exactly which data goes where, and \"where\" can be thousands of simultaneous destinations. Some devices are small, so there are lightweight versions of DDS that run in constrained environments.  
To allow such control, instead of relying on a hub-and-spoke broker model such as AMQP and MQTT, or on a client/server model such as CoAP and OPC UA, DDS implements direct device-to-device \"bus\" communication with a relational data model, coined _DataBus_. This data-centric messaging bus model connects publishers and subscribers directly. Detailed QoS policies controls the information flow, and the application matches publishers and subscribers based on topics and on QoS.
## 4 Experiment and Results
### Model Performance
#### 4.4.2 Performance with Loss Functions  
Experiments are performed using different loss functions for classification and regression tasks. For classification, Cross Entropy (CE) loss and Kullback-Leibler (KL) divergence loss are examined, while Concordance Correlation Coefficient (CCC) loss and Mean Absolute Error (MAE) loss are considered for regression. Configurations combining these loss functions are assessed to determine their effectiveness in the joint network's learning. Experiments explored the effects of different loss functions on the joint model's performance. The results, shown in Table 4, indicate that the combination of Cross-Entropy (CE) and Concordance Correlation Coefficient (CCC) loss achieved the highest performance, with a WA of 72.66% and a UA of 73.72%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Features**} & \multirow{2}{*}{**Feature Encoder**} & **Weighted** & **Unweighted** \\  & & **Average** & **Average** \\  & & **(WA)** & **(UW)** \\ \hline Log Mel-Spectrogram & DCNN & 59.67 & 60.17 \\ MFCC & 1 DCNN+BiLSTM & 57.63 & 58.61 \\ Short-term Features & 1 DCNN+BiLSTM & 53.47 & 56.09 \\ Raw PCM & Wav2 Vec 2.0 & 68.96 & 68.15 \\ Raw PCM & HuBERT & 68.37 & 68.19 \\ Combined Log Mel-Spectrogram & & & \\ + MFCC + STF + Raw & Parallel Model w/Wav2 Vec 2.0 & 68.94 & 68.42 \\ Combined Log Mel-Spectrogram & & & \\ + MFCC + STF + Raw & Parallel Model w/HuBERT & 68.73 & 68.42 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Baseline performance on the non-joint model.
# A Sensor Data-Driven Decision Support System for Liquefied Petroleum Gas Suppliers
## 5 Consumption Forecasts
### Medium-Term LPG Consumption Prediction  
Medium-term prediction supports the supplier's strategic planning at the company level from a longer perspective, e.g., three months or half a year. When setting the perspective at the company level, what matters is not the gas consumption on a given day per single customer, but rather the predicted total gas capacity that will be consumed within a given period of time. Thanks to this information, it is possible to anticipate and mitigate, e.g., a situation when the gas demand for a given period would exceed the available reserves. This allows for planning increased purchases in advance and for preparing appropriate agreements with partners regarding the provision of storage space and gas-transporting rolling stock.  
Prediction at the delivery area level or even that of the whole company can be broken down into predictive tasks defined for each tank similarly to the short-term prediction problem. However, while short-term prediction models can be based on recent trends and local features, e.g., temperature forecast or gas consumption in the last days, medium-term prediction models have to be based on more general attributes.  
In the case of a medium-term approach, where the prediction horizon is at least three months, it is not possible to retrieve the temperature values that are the basis for prediction from a weather forecast. However, having the temperature measurements from the last few years, it is possible to calculate climate-like temperature as a mean of the available values of each day of a year. This way, the generated predictor models the consumption dependency on a general climate information. Such an approach may result in large error values for short-term prediction, when current temperature values can significantly differ from the long-term average. However, a total relative error within a longer period may be reasonable.  
Referring to the workflow presented in Section 4, similar to the short-term LPG consumption prediction, the medium-term LPG consumption prediction is generated within the process in which the data transformation and modeling are performed.
## 2 Background and Related Work
### Vanilla RNN  
This is the very basic form of a Recurrent Neural Network. Figure 1 shows the internal structure of the Vanilla RNN. Mathematically, Equations (1) and (2) represent its time sequencing behavior. The input feature vector \(x_{t}\) is associated with the nonrecurrent weight matrix \(W_{hx}\), and the activations from previous time step \(h_{t-1}\) are associated with recurrent weight matrix \(U_{hh}\). The output vector \(y_{t}\) is the associated weight matrix \(W_{yh}\). \(f1\) is a nonlinear function like a _tanh_ or _sigmoid_ nonlinearity. \(f2\) can be a softmax output nonlinearity.  
\[h_{t}=f1\left[U_{hh}h_{t-1}+W_{hx}x_{t}+b_{h}\right] \tag{1}\] \[y_{t}=f2\left[W_{yh}h_{t}+b_{y}\right] \tag{2}\]
# Evaluation of the Consistency of Three GRACE Gap-Filling Data
## 2 Materials and Methods
### Consistency Analysis in the Spatial Domain
More than 81% of the rRMS values estimated between any two of the three datasets are less than 1.0, with the ratio reaching 94% in some cases. The datasets are strongly correlated when larger RMS values (e.g., \(>\)5 cm) exist in the EWH series, suggesting good agreement on the seasonal patterns of variation. However, the gap-filling signals recovered from IGG might be higher than those recovered from SSA and QF, which was inferred similarly in Section 3.2. In contrast, the RMS and correlation coefficients are heterogeneous at sites with weak hydrological signals, showing poor consistency. As a result, we recommend that these three gap-filling datasets be utilized with caution in regions with weak hydrological signals.
# Unlocking Efficiency in Fine-Grained Compositional Image Synthesis: A Single-Generator Approach
## 4 Experiments and Results  
### Dataset and Training Method  
Our main results were obtained using the CelebAMask-HQ dataset [68], which is a large-scale face image dataset consisting of 30,000 high-resolution images accompanied by fine-grained segmentation masks for facial attributes. This dataset is well-suited to our fine-grained compositional image synthesis task. To ensure a fair benchmark comparison with SemanticStyleGAN, we adopted the same pre-processing method. Specifically, we used the first 28,000 facial images and their corresponding segmentation masks for training. The segmentation masks include thirteen semantic parts: Background, skin, eyes, eyebrows, nose, mouth, ears, hair, neck, clothing, eyeglasses, hats and earrings. Prior to training, we resized both the images and segmentation masks to 256 \(\times\) 256 pixels and normalized them within the range of \([-1,1]\).  
We also attempted to use the same optimization settings as SemanticStyleGAN, whenever possible, to ensure a fair comparison. For training, we employed the Adam optimizer with \(\beta=(0,0.99)\). In SemanticStyleGAN, a single learning rate of 0.002 was used. However, we observed that this value is too high when applied to the LSTM module with the Adam optimizer, as it leads to gradient spikes and disrupts the training process. Consequently, we introduced a separate learning rate of 0.0001 exclusively for the LSTM module to mitigate this issue.  
To regularize the training process, we applied path regularization [10] on the generator and \(R1\) regularization on the discriminator every 4 and 16 iterations, respectively. The weight factors for \(\mathcal{L}_{mask}\) and \(\mathcal{L}_{KL}\) were set to 100 and 0.0001, respectively. As we explicitly modeled the relationships between the parts using the LSTM module, we observed that style mixing had a detrimental effect on the training. This is expected, as style mixing assumes independent styles for the parts, which contradicts the function of the LSTM module. Therefore, we did not utilize style mixing during training.  
Our model was trained using a single RTX3090 GPU, with a batch size of 16 and gradient accumulation every two iterations, resulting in an effective batch size of 32. We set the maximum number of training steps to 150,000, with each iteration taking approximately 4 s.
# Panoptic Segmentation-Based Attention for Image Captioning
## 3 Captioning Models
### Up-Down Attention Model  
We adopt the framework of the up-down attention model [6] with our segmentation-region/detection-region features. This model is composed of an attention LSTM which generates the attention weights and a language LSTM which generates words. Their hidden states are denoted by \(h_{t}^{1}\) and \(h_{t}^{2}\), respectively.  
Given \(k\) image regions, the features of these regions \(\mathbf{v}\) are given by:  
\[\mathbf{v}=\{v_{1},...,v_{k}\},v_{i}\in\mathbb{R}^{D}. \tag{5}\]  
The input to the attention LSTM is the concatenation of the mean-pooled image feature, the previous hidden state of the language LSTM, and the previous generated word:  
\[x_{t}^{1}=[\bar{I},h_{t-1}^{2},Ew_{t-1}] \tag{6}\]  
where the mean-pooled image feature \(\bar{I}\) provides the attention LSTM with a global content of the image. Note that, differently from [6] where \(\bar{I}=\frac{1}{k}\sum_{i}^{k}v_{i}\) is the average feature of the detected regions, in this paper, \(\bar{I}\) is the average feature of the uniform grid of the image regions. In the baseline detection-based attention model, the image features \(\mathbf{v}\) are the features of detection regions. In order to obtain fine-grained representation of the images, the image features \(\mathbf{v}\) in our method are the features of segmentation regions. The definitions of detection/segmentation regions are illustrated in Sections 4.1 and 4.2, and the image features \(\mathbf{v}\) are described in Section 5.  
The input to the language LSTM is the concatenation of the attention weighted image feature and the previous hidden state of the attention LSTM:  
\[x_{t}^{2}=[I_{t},h_{t}^{1}] \tag{7}\]where the attention weighted image feature \(I_{t}\) is the weighted sum of \(v_{i}\):  
\[a_{t}^{i} =W_{a}^{T}\tanh(W_{av}v_{i}+W_{ah}h_{t}^{1}) \tag{8}\] \[\mathbf{\alpha}_{t} =\text{softmax}\left(\mathbf{a_{t}}\right)\] (9) \[I_{t} =\sum_{i=1}^{k}\alpha_{t}^{i}v_{i} \tag{10}\]  
where \(\alpha_{t}^{i}\) is the normalized attention weights, \(W_{a}\in\mathbb{R}^{A}\), \(W_{av}\in\mathbb{R}^{A\times D}\), and \(W_{ah}\in\mathbb{R}^{A\times d}\); \(A\) is the dimension of the attention layer. For the sake of simplicity, we denote \(\{a_{t}^{1},...,a_{t}^{k}\}\) by \(\mathbf{a_{t}}\) and denote \(\{\alpha_{t}^{1},...,\alpha_{t}^{k}\}\) by \(\mathbf{\alpha}_{t}\).  
Then, the hidden state of the language LSTM is used to generate the distribution of the next word following (2) and \(h_{t}\) is replaced with \(h_{t}^{2}\) following [6]. The other parts of the model remain the same with the definition in Section 3.1.  
Reinforcement training [28] is also introduced to directly optimize the CIDEr [40] metric. For a sampled sentence \(\mathbf{w}\), a reward function \(r(\mathbf{w})\) denoting the CIDEr score of \(\mathbf{w}\) is used to measure the quality the sentence. With this reward, the probability of the sampled captions with a higher CIDEr score is increased by reinforcement training following [28]. Therefore, we can directly optimize the CIDEr score by reinforcement learning.
## 3 Green's Function Formulation of the Problem
The Green's functions in the relevant layers are  
\[G(\rho,\,\varphi,\rho^{{}^{\prime}},\phi^{{}^{\prime}})=\frac{i}{4}\,H_{0}^{(1 )}(k_{b}|\vec{\rho}-\vec{\rho}^{{}^{\prime}}|)+\sum_{n=-\infty}^{\infty}R_{n} H_{n}^{(1)}(k_{b}\rho)\,e^{in(\phi-\phi^{{}^{\prime}})},\rho>r_{1} \tag{9}\]  
and, for respective indices \(\ell=2,3\) and \(4\),  
\[G(\rho,\,\phi,\rho^{{}^{\prime}},\phi^{{}^{\prime}})=\sum_{n=-\infty}^{\infty} \Bigl{[}T_{\ell\,n}\,H_{n}^{(1)}(k_{\ell}\,\rho)+S_{\ell\,n}\,J_{n}(k_{\ell}\, \rho)\Bigr{]}\,e^{in(\phi-\phi^{{}^{\prime}})},r_{\ell}<\rho<r_{\ell+1} \tag{10}\]  
and  
\[G(\rho,\,\phi,\rho^{{}^{\prime}},\phi^{{}^{\prime}})=\sum_{n=-\infty}^{\infty} T_{5\,n}\,J_{n}(k_{5}\,\rho)\,e^{in(\phi-\phi^{{}^{\prime}})},\rho<r_{4} \tag{11}\]  
The unknown wave amplitude coefficients \(R_{n},T_{2n},S_{2n},T_{3n},S_{3n},T_{4n},S_{4n}\) and \(T_{5n}\) in the above expressions can be obtained by imposing the continuity and the jump conditions  
\[G(\rho=\rho^{{}^{\prime}}+0,\,\phi,\,\rho^{{}^{\prime}},\,\phi^{{}^{\prime}})- G(\rho=\rho^{{}^{\prime}}-0,\,\rho^{{}^{\prime}},\phi^{{}^{\prime}})=0 \tag{12}\]  
and  
\[\frac{\partial G}{\partial\rho}(\rho=\rho^{{}^{\prime}}+0,\,\phi,\,\rho^{{}^{ \prime}},\phi^{{}^{\prime}})-\frac{\partial G}{\partial\rho}(\rho=\rho^{{}^{ \prime}}-0,\,\rho^{{}^{\prime}},\phi^{{}^{\prime}})=-\frac{1}{\rho^{{}^{\prime }}}\,e^{-in\phi^{{}^{\prime}}} \tag{13}\]  
on each layer surface \(S\), respectively, Ref. [26]. The resulting expressions, when continuity and jump conditions are applied, are as follows:  
\[H_{0}^{(1)}(k_{1}|x-y|)=\sum_{n=-\infty}^{\infty}H_{n}^{(1)}(k_{1}\rho_{>})\,J_{n }(k_{1}\rho_{<})\,e^{in(\phi-\phi^{\prime})} \tag{5}\]0  
\[H_{0}^{(1)}(k_{1}|x-y|)=\sum_{n=-\infty}^{\infty}H_{n}^{(1)}(k_{1}\rho_{>})\,J_{n }(k_{1}\rho_{<})\,e^{in(\phi-\phi^{\prime})} \tag{5}\]1  
and, for respective indices \(\ell=1,2\) and \(3\),  
\[H_{0}^{(1)}(k_{1}|x-y|)=\sum_{n=-\infty}^{\infty}H_{n}^{(1)}(k_{1}\rho_{>})\,J_{n }(k_{1}\rho_{<})\,e^{in(\phi-\phi^{\prime})} \tag{5}\]2\[H_{0}^{(1)}(k_{1}|x-y|)=\sum_{n=-\infty}^{\infty}H_{n}^{(1)}(k_{1}\rho_{>})\,J_{n }(k_{1}\rho_{<})\,e^{in(\phi-\phi^{\prime})} \tag{5}\]3  
and  
\[H_{0}^{(1)}(k_{1}|x-y|)=\sum_{n=-\infty}^{\infty}H_{n}^{(1)}(k_{1}\rho_{>})\,J_{n }(k_{1}\rho_{<})\,e^{in(\phi-\phi^{\prime})} \tag{5}\]4  
\[H_{0}^{(1)}(k_{1}|x-y|)=\sum_{n=-\infty}^{\infty}H_{n}^{(1)}(k_{1}\rho_{>})\,J_{n }(k_{1}\rho_{<})\,e^{in(\phi-\phi^{\prime})} \tag{5}\]5  
where derivatives are considered with respect to the entire argument. The values of the scattered and transmitted wave amplitude coefficients appearing in Equations (14)-(19) will be determined alphanumerically in numerical implementations.
# Effect of Cement Content on the Deformation Properties of Cemented Sand and Gravel Material
## 3 Results and Discussion
### Volumetric Strain at the Initial Dilatancy Point  
The volumetric strain at the initial dilatancy point is referred to as the peak volumetric strain \(\varepsilon_{\rm vd}\) in this study and decreases with increasing cement content and decreasing confining pressure, as shown in Figure 13. It can be expressed as  
\[\varepsilon_{\rm vd}=\lambda_{2}(\sigma_{3}/Pa)+d_{2}, \tag{14}\]  
where \(\lambda_{2}\) is a dimensionless parameter related to the cement content and the slope of lines; \(d_{2}\) is a dimensionless parameter related to the cement content and the vertical intercept. The curves fitted by Equation (14) are shown in Table 8. Values of R\({}^{2}\) that are greater than 0.96 indicate that the calculated results of Equation (14) fit the experimental results well.  
The peak volumetric strain \(\varepsilon_{\rm vd}\) is also affected by the cement content, and Figures 14 and 15 shows the test values of \(\lambda_{2}\) and \(d_{2}\) under different cement contents with the cement contents of 20, 40, 80, and 100 kg/m\({}^{3}\). As can be seen from Figure 14, with increasing \(Cc\), \(\lambda_{2}\) gradually decreases. When \(Cc\) tends to the cement content of the roller compacted concrete, \(\lambda_{2}\) is close to 0, which indicates that the compaction of the CSG material increases and the shear shrinkage decreases with the increasing cement content. The parameter \(\lambda_{2}\) can be expressed as  
\[\lambda_{2}=a_{2}{\rm e}^{-c_{2}(Cc/Cc_{0})}, \tag{15}\]  
where \(a_{2}\) and \(c_{2}\) are the fitting coefficients of the relationship between \(\lambda_{2}\) and \(Cc\).  
Figure 13: The relationship between the peak volumetric strain \(\varepsilon_{\rm vd}\) and confining pressure \(\sigma_{3}\).  
As can be seen from Figure 15, the parameter \(d_{2}\) decreases with the increase of the cement content, which can be expressed as follows:  
\[d_{2}=l_{2}\mathrm{e}^{-m_{2}(Cc/Cc_{0})}, \tag{16}\]  
where \(l_{2}\) and \(m_{2}\) are the fitting coefficients of the relationship between \(d_{2}\) and \(Cc\).  
The curves fitted by Equations (15) and (16) are shown in Figures 14 and 15, respectively. Values of R\({}^{2}\) that are greater than 0.96 indicate that the calculated results of Equations (15) and (16) fit the experimental results well. When \(Cc\) is close to 0, \(d_{2}\) in Equation (16) is close to \(l_{2}\), the peak volumetric strain increases, and CSG material presents an obvious shear shrinkage phenomenon. When \(Cc\) increases, \(d_{2}\) gradually tends to 0, and CSG material firstly exhibits a small shear shrinkage followed by obvious dilatancy.  
By substituting Equations (15) and (16) into Equation (14), the peak volumetric strain of CSG material with a specific cement content and confining pressure is expressed as:  
\[\varepsilon_{\mathrm{vd}}=a_{2}\mathrm{e}^{-c_{2}(Cc/Cc_{0})}(\sigma_{3}/Pa)+ l_{2}\mathrm{e}^{-m_{2}(Cc/Cc_{0})}. \tag{17}\]