Pore-Water Pressure Forecasting with Recurrent Neural Networks

Field monitoring · Recurrent neural networks · Next-hour prediction

Pore-water pressure (PWP) is a direct input to slope-stability analysis, but its response to rainfall can be nonlinear, site-specific, and delayed. This study compares a static multilayer perceptron with standard RNN, LSTM, and GRU models for predicting PWP one hour ahead from rainfall and monitoring histories. (Wei et al., 2021)

SiteA fully instrumented natural slope in Hong Kong

Data1,224 hourly rainfall and pore-pressure records

ForecastNext-hour PWP from 3–12 hours of input history

Research question

Do recurrent models provide more accurate and stable short-term PWP predictions than a static neural network, particularly when the groundwater response lags behind rainfall?

The comparison focuses on two representative piezometers. SP3 was installed at 2 m depth in less-permeable completely decomposed volcanic rock and showed a pronounced delayed response. SP8 was installed at 1 m depth in colluvium and responded more rapidly. SP4 and SP9 provided additional checks of GRU performance. (Wei et al., 2021)

Topographic map locating the monitored natural slope near Tung Chung and Hong Kong International Airport

Location of the approximately 25,000 m² monitored natural slope above the North Lantau Expressway in Tung Chung, Hong Kong. Fig. 3 in (Wei et al., 2021), after Evans and Lam (2003).

Topographic monitoring layout showing piezometers, tensiometers, rain gauges, and the SP3, SP4, SP8, and SP9 analysis locations

Monitoring layout and the four piezometers used in the model comparison and supplementary checks. Fig. 4 in (Wei et al., 2021), after Evans and Lam (2003).

Data and model design

The hourly record ran from June 8 to September 12, 2001, with gaps in the monitoring period. Inputs included hourly rainfall, PWP, and rainfall accumulated over 3, 6, and 12 hours. The first 75% of the time series was used for training and the final 25% for testing. Each architecture was trained 30 times, and the distributions of $R^2$ and RMSE were used for evaluation. (Wei et al., 2021)

The gated recurrent unit updates its state as

\[h_t=(1-z_t)\odot h_{t-1}+z_t\odot\widetilde{h}_t\]

Interpretation. The update gate $z_t$ controls how much of the previous state is retained and how much is replaced by the candidate state. This memory mechanism helps represent delayed rainfall–PWP responses that are difficult for a static MLP and can challenge a standard RNN.

Prediction performance

R² 0.96Mean GRU and LSTM performance at SP3, with RMSE 0.31 kPa

R² 0.89Mean GRU performance at SP8, with RMSE 0.63 kPa

43.23 vs. 99.48 sMean training time for single- versus double-layer GRU, with nearly unchanged accuracy

Location	Model	Mean R²	Mean RMSE	Mean training time
SP3	MLP	0.91	0.47 kPa	23.01 s
SP3	Standard RNN	0.91	0.47 kPa	28.77 s
SP3	LSTM	0.96	0.31 kPa	55.20 s
SP3	GRU	0.96	0.31 kPa	39.68 s
SP8	MLP	0.73	0.99 kPa	23.45 s
SP8	Standard RNN	0.87	0.70 kPa	28.99 s
SP8	LSTM	0.88	0.68 kPa	52.64 s
SP8	GRU	0.89	0.63 kPa	40.53 s

Mean test performance over 30 random training runs with a six-hour input window. Values are transcribed from Tables 3–4 in (Wei et al., 2021); the reported training times were measured on an Intel i7-8700 CPU with 16 GB RAM.

R squared and RMSE distributions for GRU, LSTM, standard RNN, and MLP predictions at piezometer SP3 using input windows from three to twelve hours

At SP3, the gated models remain accurate and stable across the tested input-window lengths, whereas the MLP varies more strongly. Cropped from Fig. 8 in (Wei et al., 2021).

R squared and RMSE distributions for GRU, LSTM, standard RNN, and MLP predictions at piezometer SP8 using input windows from three to twelve hours

SP8 presents a more difficult test for the static MLP; GRU and LSTM show narrower performance ranges. Cropped from Fig. 9 in (Wei et al., 2021).

Key findings and contribution

Temporal structure matters. At SP3, one observed PWP rise occurred about eight hours later than at SP8. LSTM and GRU were more robust than standard RNN where this lag was apparent. (Wei et al., 2021)
A simpler gated model was sufficient. A second GRU layer more than doubled mean training time in the reported experiment without a meaningful accuracy gain. (Wei et al., 2021)
Dropout was important. The model without dropout showed wave-like overfitting artifacts, while a dropout rate of 0.5 improved agreement with observations. (Wei et al., 2021)
Positive-pressure records were scarce. Positive PWP observations comprised only 1.2% and 2.9% of the SP3 and SP8 records, and the paper associates this scarcity with deviations in positive PWP prediction. (Wei et al., 2021)

Relationship to early warning

The authors position the findings as guidance for establishing landslide early-warning systems; the study itself evaluates one-hour-ahead PWP prediction using $R^2$ and RMSE. (Wei et al., 2021)

Scope and limitations

The case study uses one monitored natural slope and 1,224 hours of rainfall and PWP records, including periods with unavailable measurements. The paper identifies missing PWP data as a possible limit on prediction performance. Positive PWP observations account for only 1.2% and 2.9% of the SP3 and SP8 records, respectively, and the authors associate this scarcity with deviations at positive PWP values. The Min–Max normalization uses extrema from the complete dataset, and the paper notes that new data extending this range would require renormalization. (Wei et al., 2021)

Knowledge of pore-water pressure (PWP) variation is fundamental for slope stability. A precise prediction of PWP is difficult due to complex physical mechanisms and in situ natural variability. To explore the applicability and advantages of recurrent neural networks (RNNs) on PWP prediction, three variants of RNNs, i.e., standard RNN, long short-term memory (LSTM) and gated recurrent unit (GRU) are adopted and compared with a traditional static artificial neural network (ANN), i.e., multi-layer perceptron (MLP). Measurements of rainfall and PWP of representative piezometers from a fully instrumented natural slope in Hong Kong are used to establish the prediction models. The coefficient of determination (R2) and root mean square error (RMSE) are used for model evaluations. The influence of input time series length on the model performance is investigated. The results reveal that MLP can provide acceptable performance but is not robust. The uncertainty bounds of RMSE of the MLP model range from 0.24 kPa to 1.12 kPa for the selected two piezometers. The standard RNN can perform better but the robustness is slightly affected when there are significant time lags between PWP changes and rainfall. The GRU and LSTM models can provide more precise and robust predictions than the standard RNN. The effects of the hidden layer structure and the dropout technique are investigated. The single-layer GRU is accurate enough for PWP prediction, whereas a double-layer GRU brings extra time cost with little accuracy improvement. The dropout technique is essential to overfitting prevention and improvement of accuracy.