A multiobjective steepest descent method with applications to optimal well control

Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms.     

Heat tracing to examine seasonal groundwater flow beneath a low-gradient stream in rural central Illinois,USA

The thermal profile of a streambed is affected by a number of factors including: temperatures of stream water and groundwater, hydraulic conductivity, thermal conductivity, heat capacity of the streambed, and the geometry of hyporheic flow paths. Changes in these parameters over time cause changes in thermal profiles. In this study, temperature data were collected at depths of 30, 60, 90 and 150 cm at six streambed wells 5 m apart along the thalweg of Little Kickapoo Creek, in rural central Illinois, USA. This is a third-order low-gradient baseflow-fed stream. A positive temperature gradient with inflection at 90-cm depth was observed during the summer period. A negative temperature gradient with inflection at 30 cm was observed during the winter period, which suggests greater influence of stream-water temperatures in the substrate during the summer. Thermal models of the streambed were built using VS2DHI to simulate the thermal profiles observed in the field. Comparison of the parameters along with analysis of temperature envelopes and Peclet numbers suggested greater upwelling and stability in temperatures during the winter than during the summer. Upwelling was more pronounced in the downstream reach of the pool in the riffle and pool sequence.     

Assessment of Submarine Groundwater Discharge (SGD) as a Source of Dissolved Radium and Nutrients to Moorea (French Polynesia) Coastal Waters

Previous work has documented large fluxes of freshwater and nutrients from submarine groundwater discharge (SGD) into the coastal waters of a few volcanic oceanic islands. However, on the majority of such islands, including Moorea (French Polynesia), SGD has not been studied. In this study, we used radium (Ra) isotopes and salinity to investigate SGD and associated nutrient inputs at five coastal sites and Paopao Bay on the north shore of Moorea. Ra activities were highest in coastal groundwater, intermediate in coastal ocean surface water, and lowest in offshore surface water, indicating that high-Ra groundwater was discharging into the coastal ocean. On average, groundwater nitrate and nitrite (N + N), phosphate, ammonium, and silica concentrations were 12, 21, 29, and 33 times greater, respectively, than those in coastal ocean surface water, suggesting that groundwater discharge could be an important source of nutrients to the coastal ocean. Ra and salinity mass balances indicated that most or all SGD at these sites was saline and likely originated from a deeper, unsampled layer of Ra-enriched recirculated seawater. This high-salinity SGD may be less affected by terrestrial nutrient sources, such as fertilizer, sewage, and animal waste, compared to meteoric groundwater; however, nutrient-salinity trends indicate it may still have much higher concentrations of nitrate and phosphate than coastal receiving waters. Coastal ocean nutrient concentrations were virtually identical to those measured offshore, suggesting that nutrient subsidies from SGD are efficiently utilized.     

Submergence and Herbivory as Divergent Causes of Marsh Loss in Long Island Sound

Tidal marsh degradation has been attributed to a number of different causes, but few studies have examined multiple potential factors at the same sites. Differentiating the diverse drivers of marsh loss is critical to prescribing successful interventions for conservation and restoration of this important habitat. We evaluated two hypotheses for vegetation loss at two marshes in Long Island Sound (LIS): (1) marsh submergence, caused by an imbalance between sea-level rise and marsh accretion, and (2) defoliation associated with herbivory by the purple marsh crab, Sesarma reticulatum. At our western LIS site, we found no evidence of herbivory: crabs were scarce, and crab-exclusion cages provided no benefit. We attribute degradation at that site to submergence, a conclusion supported by topographic and hydrologic data showing that loss of vegetation occurred only in wetter parts of the marsh. In contrast, at our central LIS site, our observations were consistent with herbivory as a driving force: There were substantial populations of Sesarma, crab-exclusion cages allowed plants to thrive, and vegetation loss took place across a variety of elevations. We also analyzed soil conditions at both sites, in order to determine the signatures of different degradation processes and assess the potential for restoration. At the submergence site, unvegetated soils exhibited high bulk density, low organic content, and low soil strength, posing significant biogeochemical challenges to re-colonization by vegetation. At the herbivory site, unvegetated soils had a characteristic “riddled-peat” appearance, resulting from expansion and erosion of Sesarma burrow networks. The high redox potential and organic content of those soils suggested that revegetation at the herbivory site would be likely if Sesarma populations could be controlled before erosion leads to elevation loss.     

Destructive near-fault strong ground motion from the 2016 Kumamoto prefecture,Japan, M7.3 earthquake

The sequence of the 2016 Kumamoto, Japan, earthquake, which included an initial M6.5 foreshock on April 14, followed by a larger M7.3 mainshock on April 16, and subsequently occurred high aftershock activity, caused significant damage in Kumamoto and neighboring regions. The near-field strong motion record by strong motion network (K-NET and KiK-net) and the intensity meter network demonstrated clearly the characteristics of the strong ground motion developed by the shallow (H = 12 km), inland earthquake comprising short-time duration (<15–20 s) but large (>1G) ground accelerations. The velocity response spectra of the near-fault motion at Mashiki and Nishihara showed large levels (>300–550 cm/s) in the short-period range (T = 1–2 s), several times larger than that of the near-field record of the destructive 1995 Kobe earthquake (M7.3) and that of the 2004 Mid-Niigata earthquake (M6.8). This period corresponds to the collapse vulnerability of Japanese wooden-frame houses, and is the major cause of severe damage during the Kumamoto earthquake. The response spectra also showed extremely large levels (>240–340 cm/s) in the long-period (T > 3 s) band, which is potentially disastrous for high-rise buildings, large oil storage tanks, etc. to have longer resonant period. Such long-period motion was, for the most parts, developed by the static displacement of the fault movement rather than by the seismic waves radiating from the source fault. Thus, the extreme near-fault long-period motion was hazardous only close to the fault but it attenuated very rapidly away from the fault.     

Two-dimensional landslide dynamic simulation based on a velocity-weakening friction law

Surprisingly, hypermobility (high velocity and long run-out) is a remarkable feature of large landslides and is still poorly understood. In this paper, a velocity-weakening friction law is incorporated into a depth-averaged landslide model for explaining the higher mobility mechanism of landslides. In order to improve the precision of the calculation, a coupled numerical method based on the finite volume method is proposed to solve the model equations. Finally, several numerical tests are performed to verify the stability of the algorithm and reliability of the model. The comparison between numerical results and experimental data indicates that the presented model can predict the movement of landslide accurately. Considering the effect of velocity-weakening friction law, the presented model can better reflect the hypermobility of landslide than the conventional Mohr–Coulomb friction model. This work shows that the application of a universal velocity-weakening friction law is effective in describing the hypermobility of landslide and predicting the extent of landslides.     

Undrained creep failure of a drainage canal slope stabilized with deep cement mixing columns

This paper presents an analysis of the slope failure of a Suvarnabhumi drainage canal during construction. The Suvarnabhumi drainage canal project includes a large drainage canal with a road on both sides. The width of the bottom of the drainage canal is 48.0 m, the depth of the drainage canal is 3.0 m, and the length of the drainage canal is 10.5 km. Because the project was constructed on very soft Bangkok clay, deep cement mixing (DCM) columns were employed to increase the stability of the excavated canal. The failure of the drainage canal slope occurred 25 days after the end of excavation. The field monitoring data show that lateral movement of the canal slope continuously increased with time, which caused failure due to the instability of the canal slope. The time-dependent deformation and undrained creep behavior of very soft clay was suspected to be the cause of the canal failure. A laboratory investigation of undrained creep behavior and a finite element analysis (FEA) using the soft soil creep (SSC) model were performed to confirm the causes of the canal failure. The results indicate that very soft clay specimens that are subjected to deviator creep stress levels of 70 and 100 % of the peak strength failed by creep rupture within 60 days and 8 min, respectively. The factor of safety for the canal slope, which was obtained from the FEA, shows significant reduction from the initial value of 1.710 to 1.045 within 24 days after the end of excavation due to the effect of undrained creep. This paper also describes a solution method that is applied to a new section of the canal. Field monitoring and an FEA of the new trial section were performed to prove the effectiveness of the solution method.     

Landslide and debris flow initiated characteristics after typhoon Morakot in Taiwan

Typhoon Morakot brought extreme rainfall and initiated numerous landslides and debris flows in southern Taiwan in August of 2009. The purpose of this study is to identify the extreme rainfall-induced landslide frequency-area distribution in the Laonong River Basin in southern Taiwan and debris flow-initiated conditions under rainfall. Results of the analysis show that debris flows were initiated under high cumulative rainfall and long rainfall duration or high rainfall intensity. The relationship of mean rainfall intensity and duration threshold could reflect debris flow initiation characteristics under high rainfall intensity in short rainfall duration conditions. The relationship of cumulative rainfall and duration threshold could reflect debris flow initiation characteristics under high cumulative rainfall in long rainfall duration. Defining rainfall events by estimating rainfall parameters with different methodologies could reveal variations among intermittent rainfall events for the benefit of issuing debris flow warnings. The exponent of landslide frequency-area distribution induced by Typhoon Morakot is lower than that induced by the Chi-Chi earthquake. The lower exponent of landslide frequency-area distribution can be attributed to the transportation and deposition areas of debris flow that are included in the landslide area. Climate change induced high rainfall intensity and long duration of precipitation, for example, Typhoon Morakot brought increased frequency of debris flow and created difficulty in issuing warnings from rainfall monitoring.     

Comprehensive analyses of the initiation and landslide-generated wave processes of the 24 June 2015 Hongyanzi landslide at the Three Gorges Reservoir,China

Reservoir landslides pose a great threat to shipping safety, human lives and properties, and the operation of the hydropower station. In this paper, the 24 June 2015 Hongyanzi landslide at the Three Gorges Reservoir is considered as an example to study the initiation mechanism and landslide-generated wave process of a reservoir landslide. The finite difference method and limit equilibrium analysis are used to analyze the deformation and failure characteristics of the Hongyanzi slope. Simulation results show that a large deformation (about 358 mm) happens in the shallow deposits under intermittent rainfall condition, and the slope is in a limit state. At the same time, continuous rapid drawdown of the water level (about ?0.55 m/day during 8–24 June 2015) reduced the support and accelerated the drainage of the water for the bank slope. A coupling effect of intermittent rainfall and rapid drawdown of the water level was the triggering factor of the 24 June Hongyanzi landslide. Landslide-generated wave process was simulated using a fluid–solid coupling method by integrating the general moving object collision model. Simulation results show that the landslide-generated wave is dominated by the impulse wave, which is generated by sliding masses entering the river with high speed. The maximum wave height is about 5.90 m, and the wave would decay gradually as it spreads because of friction and energy dissipation. To prevent reservoir landslides, the speed for the rising or drawdown of the water level should be controlled, and most importantly, rapid drawdown should be avoided.     

Present-day oxidative subsidence of organic soils and mitigation in the Sacramento-San Joaquin Delta,California, USA

Subsidence of organic soils in the Sacramento-San Joaquin Delta threatens sustainability of the California (USA) water supply system and agriculture. Land-surface elevation data were collected to assess present-day subsidence rates and evaluate rice as a land use for subsidence mitigation. To depict Delta-wide present-day rates of subsidence, the previously developed SUBCALC model was refined and calibrated using recent data for CO₂ emissions and land-surface elevation changes measured at extensometers. Land-surface elevation change data were evaluated relative to indirect estimates of subsidence and accretion using carbon and nitrogen flux data for rice cultivation. Extensometer and leveling data demonstrate seasonal variations in land-surface elevations associated with groundwater-level fluctuations and inelastic subsidence rates of 0.5–0.8 cm yr^–1. Calibration of the SUBCALC model indicated accuracy of ±0.10 cm yr^–1 where depth to groundwater, soil organic matter content and temperature are known. Regional estimates of subsidence range from <0.3 to >1.8 cm yr^–1. The primary uncertainty is the distribution of soil organic matter content which results in spatial averaging in the mapping of subsidence rates. Analysis of leveling and extensometer data in rice fields resulted in an estimated accretion rate of 0.02–0.8 cm yr^–1. These values generally agreed with indirect estimates based on carbon fluxes and nitrogen mineralization, thus preliminarily demonstrating that rice will stop or greatly reduce subsidence. Areas below elevations of –2 m are candidate areas for implementation of mitigation measures such as rice because there is active subsidence occurring at rates greater than 0.4 cm yr^–1.