Experimental Study on the Nonlinear Behavior of a Sailing Container Ship under Landslide-Induced Surges

Surges induced by rock landslides that enter water at a high speed are extremely destructive. ,e initial surge height and spread characteristic are important references used in disaster precaution and risk assessment. In this study, twenty groups of orthogonal experiments of landslide-induced impulse wave were conducted, the details of the self-propulsion of ships were designed, the values of the propeller, rudder, and shafting were calculated, and the model of the propeller and rudder was processed. ,e validity of the model system was verified from a turning test, zig-zag maneuver test, and free attenuation test. ,e interactions between landslides and water and between landslide-induced wave and ships are analyzed by performing an orthogonal model test and determining the difference among the initial wave heights of landslide surges caused by different landslide volumes. ,e model test can compare and analyze the influences of different landslide volumes and navigation positions on the nonlinear behavior of ships, thereby proposing control methods and measures for safe sailing in waters with landslide-induced surges and providing a theoretical basis for disaster prevention and reduction in the channel of a reservoir area or a hydraulic structure.


Introduction
e height of waves can range from tens of meters to over 100 m when the water rushing to the opposite bank or to water-retaining structures is stirred up by large surges such as a large landslide body from the reservoir bank rushing into the reservoir at a high speed [1][2][3].Simultaneously, the shape and depth of a river channel in a reservoir area are extremely complicated, and the time that a surge wave reaches the shore varies.Some surge waves will rise, whereas others will exhibit reflection and refraction, thereby generating extremely complex fluctuations on the water surface of the entire reservoir area [4,5].Landslideinduced surges may cross the dam crest and may destroy hydraulic buildings and threaten the safety of dams and downstream properties.Rocky soil from landslides may block rivers, particularly in severe cases [6].erefore, the effect of landslide-induced surge on ships should be taken into account.
In recent years, extensive analytical investigations have been performed to study the motions of extremely large ships during tsunami, and an effective floating tsunami protection wharf was established [7][8][9].To investigate the motions of a tsunami, Makino and Koba [10] proposed a new method based on the big data of a vessel.e big data of a ship refer to a collective data group that consists of the data sent from the ship's journey and the details of the ship's journey.A number of numerical simulations investigated vessel motions and considered several feasible scenarios to evaluate the progress of appropriate discrete-event simulation-based ship evacuation processes [11,12].e time-domain Rankine source method was developed to solve motion of ship advancing with steady forward speed in waves [13,14].e authors reviewed the progress of ship antiroll tanks and developed a quasi-linear theory for "rectangular" antirolling tanks [15,16].e motion characteristics of ships were studied with four degrees of freedom, and the near-field and far-field disturbances in Green's function by Faltinsen and Michelsen [17], Fein et al. [18] and Scullen and Tuck [19].Sen [20] evaluated the effects of nonlinear terms on the calculation results of the motion response of a ship.Bulian and Cercos-Pita addressed ship dynamics in presence of sloshing, coupled with a 3D weakly compressible smoothed-particle hydrodynamics [21].Wu and Hermundstad [22] used nonlinear time-domain equations to calculate ship motion response and wave load.Aniel-Quiroga et al. studied the interaction between tsunami waves and coastal structures as these are the first to receive the tsunami's energy [23].e probability of invasion was lowered for the Gulf of Alaska and Hawaii [24,25].Silva and Soares [26] described a nonlinear strip theory model in the time domain of ship motions with six degrees of freedom.Neves and Rodríguez [27] introduced a third-order mathematical model to illustrate the intense parametric excitation related to cyclic changes in the restoration features of a vessel.
Recently, some experimental tests have been performed to investigate the characteristics of landslide-induced waves and ship motions.Ataie-Ashtiani and Nik-Khah [28] analyzed the wave period, amplitude, and energy caused by surges by conducting 120 sets of model tests.Fritz et al. [1] considered the effects of different characteristic parameters on surges through three-dimensional physical tests and analyzed the flow field characteristics caused by surges.de Carvalho and Antunes do Carmo [29] investigated the influencing factors and pressure magnitude on a reservoir bank of landslide-induced surges by conducting model tests.Some investigations have been performed based on basic theory.Sayed and Hamed [30] assessed the reaction of a two degree-of-freedom quadratic coupling system with the effects of parametric and harmonic excitations.Heller and Hager [5] analyzed the waveform characteristics of the pulse waves generated by landslide-induced surges based on nonlinear theory.A ship model resistance test was conducted to study the motion of the ship model in ice floes [31].
In the ree Gorges Reservoir, the volume of 24 million soil slid into the channel river, cut off the river, and caused a landslide-induced wave that is more than 20 m high that capsized some ships, thus causing significant economic losses.e interaction between a landslide-induced wave and a ship is seldom studied. is paper investigates the propagation law of landslide-induced surges in complex curved river channels, strengthens the early warning and prevention of geological disasters in reservoir areas, and explores the nonlinear effects of landslide-induced surges on the primary degree-of-freedom motion response of a ship based on a series of landslide surge tests.
e safe navigation range of ships in the reservoir area is also evaluated.

River Channel Model.
is study is based on the situation of a river wharf section in the ree Gorges Reservoir.
e river channel model adopts a geometric scale of 1 : 70 to simulate the river section, which is from the 36 km mileage to the 330 km mileage of the channel river, and the length is approximately 6 km.
e model was constructed using a section method, and the river bottom terrain was produced.
e generalized model can analyze the dynamic changes of a landslide body.e landslide body was built with a certain ratio that adopted a number of stones with different specifications according to survey data.e friction coefficient is reduced owing to the pressure reduction between stones and particles when fine particles slide between the stones.Figure 1 shows the topographic drawing of the channel.In the model test, the channel model was built according to the actual scale ratio, as shown in Figure 2.

Ship Model.
According to the survey data, owing to the rapid development of the local economy, a container ship is the primary ship type around the region of landslides.Last year, the containerized freight volume was 1.152 million tons, and the trend is gradually increasing.Such an external environment imposes increasingly higher requirements on the tonnage of ships and the navigation capacity of waterways.e ship type is a 3500T container ship in the model test.e survey data are shown in Figure 3.
e ship model was designed at a scale of 1 : 70 based on geometric similarity, similar gravity, and similar motion.
e ship model was self-navigating and made of wood boards, wooden strips, and fiber-reinforced plastic (FRP).
e longitudinal and transverse skeletons of the ship were first produced following the design drawings of the ship.Subsequently, the outer and inner plates of the ship were cut, bent, and fixed by bonding.e ship was coated with glass FRP to waterproof it.Finally, the completed ship model was verified and painted.e data are shown in Table 1.ese data include the primary dimensions of the container ship, revolutions per second, torque and thrust values, rudder dimensions, etc.
e motive power of a sailing ship depends on the motor, the motor was linked to the propeller by the shafting, rotational speed of propeller count on the value of different voltages.e primary parameters of the motor are shown in Table 2.
e design of the shafting was based on the design specifications of the ship, and the diameter of the shafting is not less than the calculated results, as follows: where d indicates the diameter of the shafting, K indicates a coefficient, K � 1.26, N e indicates the power of the shafting, n e indicates the speed of the shafting, and σ b indicates the tensile strength of the material.
2 Advances in Civil Engineering e design of the propeller should not only satisfy the requirements of installation, but should also satisfy the requirements of design speed.According to the parameters of the ship and the empirical formula, the specific parameters of the propeller are shown in Table 1, and the propeller geometry is shown in Figure 3.
e size of the rudder area will affect the maneuverability of the ship.If the rudder area is maintained within a reasonable range, the navigation resistance of the ship will not increase, and the navigation stability of the ship will be maintained.According to the empirical formula, the calculation is as follows: ( According to the rules of shipbuilding, the total area of the rudder is not less than that calculated using the following formula: e specific parameters of the rudder are shown in Table 1.e rudder geometry is shown in Figure 4. Figure 4 shows the photograph of the ship model, propeller geometry, rudder geometry, and the details of the self-propulsion.

Arrangement of Channel and Measuring Points.
In accordance with the second point of Article 10, Chapter 2 of the Regulations on Navigation Safety of the Water Traffic Control Area of the ree Gorges Water Control Project (2016), a ship should rely on the channel on the starboard side when navigating the ree Gorges Reservoir.During the test, the ship model may exhibit a large amplitude sway under landslide surges, which causes yaw, collision, stranding, and other accidents.To ensure a successful test, the final route was set to 0.5 m from the right side of the centerline of the channel and 3.5 m from the shore.
Five experiments were performed for each group; the first experiment was to determine the position of the initial    impulse wave and to affix the wave gauges.
e second experiment was to determine the position of the container ship and to improve the accuracy of the measurement.e others were to acquire the height of the initial wave and the motion values of the ship about the roll and pitch; subsequently, the average values of those data were calculated as the experimental values of the results of the group.
In the model test, monitoring point no. 2 is the intersection of the landslide track extension line and the navigation line.Monitoring point no. 3 is the intersection of the middle section of the curve and the navigation line.Monitoring point no. 1 is located on a straight segment.e distance from the first point to the second point is equal to the distance between the second and third points, as shown in Figure 5. e sliding blocks are according to the actual situation of the landslide and are composed of different sizes, as shown in Figure 6.

Test Conditions
e design of the rocky landslide model adopts a singlefactor test for the plan.Considering that the horizontal velocity component of landslide body is larger, the energy exchange between the landslide and the water is sufficient.An angle of 40 °was selected for the landslide to enter the water.e water has three levels: 145, 155, and 175 m, during the operation of the ree Gorges Reservoir.Combined with the actual water level during operation and the depth of the river, the river channel is generally processed for testing and other elements.e water level for the model test was set to 0.74 m based on the scale ratio conversion.e ship sails along the prefabricated route at a constant speed of 0.7 m/s and passes through position nos. 1, 2, and 3 to investigate the surges of two landslides with different volumes in the water and the influence of complex motions on the response of the ship.e first landslide has a length of 1 m, a width of 0.5 m, and a thickness of 0.6 m. e second landslide has a length of 1 m, a width of 1.5 m, and a thickness of 0.4 m. e water is still, and wind is absent during the test.
e model test consists of 45 groups, and the typical conditions of the test for four groups are provided in Table 3.

Experimental Verification of Landslide-Induced Wave.
In order to verify the correctness of the model test, this paper selects the same experimental model and test parameters as that of the Heinrich [32].
e landslide body size is 0.5 m * 0.5 m. e angle of slope is 45 degrees, and the depth of water is 0.4 m. e landslide body slides under the action of gravity.e experimental results coincide with that of Heinrich basically.
erefore, this paper establishes the experimental model which can simulate landslide-induce wave accurately (Figure 7).

Turning Test.
To verify the validity of the model test, the maneuverability of the ship is decided by the steering, turning, collision avoidance, and other behaviors, which are closely related to the ship's rotary performance.erefore, the rotary performance of the ship is the only standard to measure the maneuverability of the ship.e rotary test was performed in the laboratory of Chongqing Jiaotong University.e experimental tank is 50 m long and 30 m wide.
e rotary program was written using Visual Basic language, and a Differential Global Positioning System (DGPS) was equipped within the ship to capture its position information during navigation.
In order to obtain the higher accuracy of the position, the position system of DGPS and the differential technology were used in the process of the model test.A GPS receiver was placed on the reference station for observation.Based on the precise coordinates of the reference station, the corrected data from the reference station to satellite were calculated; the accurate data were sent out promptly, and the corrected data were observed and received by the reference station.
e information of trajectory was corrected, thus improving the accuracy of the positioning.
At the beginning of the model test, the angle of the rudder was controlled zero, the ship was maintained in a straight line,    It can be seen from Figure 9 that the general trend of trajectory is consistent, the error is less than 10%, and the model test meets the requirements of accuracy, so it can provide the guarantee for the results of the model test.However, there is no symmetry with respect to y displacement value, and the main reasons are as follows: Firstly, the model test was carried out in the pool of Chongqing Jiaotong University.As a result, it was difficult to achieve the ideal situation of no wind and no flow.Secondly, the actual loading condition of container ship was carried   Advances in Civil Engineering out in the process of model test that was not up to fully loaded condition.irdly, the interaction between propeller and rudder affected the efficiency of the rudder.Lastly, the process of steering was linear; the actual situation was in inconsistent with it; the response of ship model to the rudder deflection was very slow and so it becomes difficult to determine the suitable frequency of hydrodynamic forces.
As we can see from Figure 10, with the increase of rudder angle, the heading angle increases gradually, the differences between two cases are very small, and the time history curves of the heading angle and rudder angle agree well with the requirements of the standards for ship maneuverability resolution [33,34].It contains the 1st and 2nd overshoot angle.e response of ship to the first rudder angle is in good agreement with the first overshoot angle. is shows that ship model has better maneuverability.

Free Attenuation Test.
e degrees of freedom of the motion of the ship in the vertical plane exhibit the recovery characteristic.e ship model deviates from the position of equilibrium under an external loading.When the external force disappears, the ship will return to the original position, which depends on its own recovery characteristic.Under the free state, the roll motion and pitch motion of the ship are attenuated in static water.
e natural period and dimensionless damping coefficient can be obtained by analyzing the attenuation curve; subsequently, the accuracy of model test can be verified.e decay curve of roll motion is shown in Figure 11, and the decay curve of pitch motion is shown in Figure 12.

Propagation Characteristics of Landslide Surge.
e wave height and landslide surge cycle were measured using an ultrasonic wave acquisition analyzer designed and developed by the Southwest Transportation Science Research Institute of Chongqing Jiaotong University.Seven measuring points, which measure the initial surge and the surge along the path, were established.e straight road, curve, and river section areas were the primary measurement areas.Among the measuring points, measuring point no. 1 is the center point Model test Henrich [32] Figure 7: Comparison between Heinrich [32] and experimental free surface at 0.6 s.
-1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 y-displacement (m) x-displacement (m)   Figure 13 shows that a certain delay occurs in the landslide data, under different volumes, with the same entrance angle into the channel model of 0.74 m. e landslideinduced surge is irregular and asymmetric under the two operating conditions.e surges are spread incompletely during the early stage of landslide entry into the water.Over time, the front edge of the surges becomes steep and the water level rises and reaches its maximum value within an extremely short time.e wave height decreases rapidly and becomes a small-amplitude oscillation, and the water surface gradually returns to the stationary state after the landslide surge reaches a high peak.
e landslides with different volumes are accompanied by considerable energy loss as they enter the water.e lost energy is transformed into the heat energy and kinetic energy of the water.e height of the first wave caused by the landslide is different.e volume of the large landslide is twice that of the small landslide.e height of the first wave generated by the large landslide is thrice that of the small landslide.e height of the first wave caused by the landslide body that entered the water increases with landslide volume.When the landslide that enters the water has a different volume, the time that the first wave Advances in Civil Engineering height reaches its peak varies.When the landslide volume is large and the speed of the spreading surges caused by the landslide entering the water is fast, the water waves spreading along the coast and the influential scope of the disaster are expanded.

Influence of Different Navigation Positions on Ship Motion
Response.
e rectangular landslide block enters the water with a length of 1 m, a width of 0.5 m, and a thickness of 0.6 m when the ship passes the river's monitoring points 1, 2, and 3 at a constant speed of 0.7 m/s.e self-developed ship attitude acquisition device measures the rolling motion and pitch motion amplitudes of the ship and subsequently compares and analyzes the relevant provisions of the Inland River Ships Statutory Inspection Technical Regulations to determine the safe navigation range of the ship.
As shown in Figure 14, the shapes of the rolling motion curve at three locations are similar and a time difference of the maximum peak period node exists.e ship model sailed to different positions, and the maximum amplitude of the rolling motion satisfied the requirements of the rules.e landslide-induced surges carried most of the energy to the vicinity of the ship and generated the maximum hydrodynamic pressure on the ship.e landslide body enters the water when the ship sails to position no. 1. e landslide surge is centered on the entry point of the landslide body, scatters and propagates around it, and interacts with the ship.e ship has a rolling motion amplitude of 4 °, and it continues to sail forward.e ship acquires a large rolling motion amplitude after encountering the secondary wave of the landslide surge and the reflected wave on the opposite bank, with a maximum value of 6 °. e ship depends on its own recovery torque and recovery damping and gradually returns to a stable state.e landslide surge occurs suddenly when the ship sails to position no.2, and the ship has a large rolling motion amplitude with a maximum value of 11 °.
Moreover, the motion amplitude of the ship is gradually reduced when the ship encounters an initial high peak surge.
e landslide body enters the water at a high speed when the ship travels to position no.3. A chasing state occurs between the landslide-induced surge and the sailing ship.Energy decreases gradually with an increase in the propagation distance of the wave surges, which has a minimal effect on the ship's rolling motion amplitude.
e rolling motion amplitude of the ship exhibits a small fluctuation and is relatively stable.
As shown in Figure 15, a landslide occurs when the ship sails to position nos. 1, 2, and 3. e ship model sailed to those different positions, and the maximum amplitude of the pitching motion satisfied the requirements of the rules.e maximum rolling direction of position nos. 1 and 2 is different and noticeable and is attributed to the difference in the force position of the ship depending on the landslide surge.
e landslide surge acts on the stern of the ship when the ship sails at position no. 1, and the maximum pitch value is 1.8 °. e landslide surge acts on the tail of the ship when the ship sails at position no.2, and the maximum pitch value is 1.25 °. e speed of the landslide surge is less than that of the ship when the ship sails to position no.3. e ship sails in still water to generate waves caused by its traveling.After the reflection onto the bank wall, a small amplitude effect is observed on the ship's pitch.e labels are length, width, and thickness in sequence, such as the length is 1 m, the width is 0.5 m, the thickness is 0.6 m.

8
Advances in Civil Engineering when the surges caused by different numbers of landslides are transmitted to the vicinity of the ship.e time history curve of the ship's rolling motion contains two peaks.e first peak is reached when the initial surge propagates to the ship's navigation position and interacts with the ship.e maximum amplitude of the rolling motion is 10.5 °, and the reverse effect of the landslide surge is not initiated.e second peak occurs when the landslideinduced surge impacts the soil bank slope.e water depth becomes shallow and narrow, the wave energy gathers, and the surge wave spreads slowly.At this point, a wave propagates at a slightly slower speed, and its latter peak cannot catch up.A certain degree of water wall is formed after the reflection across the opposite shore, which interacts with the ship.e maximum rolling motion amplitude is 8.5 °, and the ship's rolling amplitude decreases with time.
e secondary damage of the ship caused by the landslideinduced surge and the violent shaking degree of the ship under the landslide-induced surge should be considered during a real voyage.e shifting of the ship's load, which changes the overall center of gravity of the ship and causes it to tilt, should be prevented.
e stability of the ship increasingly deteriorates, and the ship's recovery torque becomes smaller than the external moment of the landslide, thereby causing the ship to overturn.
As shown in Figure 17, the ship experiences landslide surges caused by different landslide bodies that enter the water during its voyage.e maximum amplitude of the pitching motion of the ship model satisfied the requirements of the rules.e change in the ship's pitch undergoes occurrence, development, and decay processes with remarkable changes in the pitching motion amplitude of the ship.
e propagation speed of the landslide surges is relatively fast, the interaction with the ship is early, and the maximum longitudinal amplitude is 1.75 °when a large number of landslide bodies enter the water.e interaction time with the ship is delayed, and the maximum longitudinal amplitude is 1.25 °when a small number of landslide bodies enter the water.e effect of landslide surges caused by different numbers of landslides on the ship's pitching motion exhibits a single-peak effect.e impact of the initial surge on the ship should be considered during the ship's navigation.e ship stall caused by a huge landslide surge, which deviates from the channel, pushes the ship toward the shore, and causes the ship to overturn and sink, should be investigated.e primary engine should be started, the bow direction should be adjusted appropriately, and the spread direction of the landslide-induced surge should be forwarded when a sudden landslide occurs during the voyage.e minimum cross section of the bow should be swayed toward the landslide-induced surges to divert their direction from the two sides of the hull.e hull's own streamline can effectively disperse the impact of landslide-induced surges, thereby maximizing the ship's protection and is conducive to preventing the tilting or tipping over of the ship on one side owing to landslide-induced surges.

Discussion and Conclusions
Based on field investigations, literature review, and model tests, this study obtained the characteristics of a ship when landslide-induced surges occur, and the impact of these surges on the ship's motion response.e emergency situation of maintaining safe navigation when a landslide entered the water was assumed, which was conducive to engineering feasibility demonstration and governance.e conclusions are summarized as follows: (1) e waveform of the landslide-induced surge exhibited evident asymmetry, wherein the peak was large and the trough was small with strong nonlinearity.e height of the wave decreased rapidly after the first wave of landslide-induced surge, and the wave energy decreased gradually with increased propagation distance.

Advances in Civil Engineering
(2) e aspect ratio reduced when the volume of the landslide body was large, and the first wave height of the landslide-induced surge was high.When the number of landslides was large, the speed of landslide-induced surges was high.(3) e landslide-induced surge exerted the greatest impact on the ship when it passed position no.2, followed by position no. 1, and finally, position no.3.In an actual navigation, the distance from the landslide point should be controlled, the impact of landslide-induced surges on the ship should be reduced, and the collision of the ship with coastal fixed structures and different degrees of damage under landslide-induced surges should be prevented.(4) When the number of landslides was large, the impact on the motion response of a sailing ship was considerable.In engineering practice, the landslide volume should be controlled to prevent the impact of the first wave and secondary wave peaks on the ship.e secondary damage of landslide-induced surges to the ship should be considered, and a warning system for landslide-induced surge disasters should be constructed to reduce the damage to ships.
(5) A ship should be stagnated appropriately, the double anchors should be dropped, and the long anchor chain should be loosened to ensure the ship's stability, decrease the extent of rolling and pitch motions of the ship, and mitigate the impact of landslide-induced surges on the ship when large-scale landslide-induced surges occur during a voyage.e ship should wait for the gradual return of tranquility on the river surface and avoid dangerous water areas.procedures as part of tsunami preparation," Journal of Simulation, vol.

Figure 1 :
Figure 1: Topographic drawing of the channel.
and a signal was sent to change the rudder angle.Next, the ship model started to enter the rotational motion, and the position information was recorded by DGPS during the model test.When the ship entered a stable state of rotation, the diameter of rotation was recorded.e data of the turning test in the state of 15 °, 25 °, and 35 °are shown in Figure 8. e results of turning test conformed to the basic requirements of ship model.e turning test results of different rudder angles are shown in Table 4 .

4. 3 .
Zig-Zag Maneuver Test.To verify the validity of the model test and to study the maneuvering state of the ship model in the water area, the zig-zag maneuver test was performed.e voltage of the primary engine of the ship was

Figure 5 :
Figure 5: Route and layout of measuring points.

igure 8 :
Trajectory in the turning test recorded by DGPS.

igure 9 :
Trajectory in the zig-zag maneuver test recorded by DGPS.6Advances in Civil Engineering of the area where the landslide enters the water.e data acquisition system collects the wave height and period data from different areas.e acquisition time is generally 200 s, and the frequency is 50 Hz.Two types of landslide bodies enter the water during the test.e large landslide volume has a length of 1 m, a width of 1.5 m, and a thickness of 0.4 m. e small landslide volume has a length of 1 m, a width of 0.5 m, and a thickness of 0.6 m.

Figure 16
shows the effect of different numbers of landslides on the ship's motion response after the landslides enter the water.e maximum amplitude of the rolling motion of the ship model satisfied the requirements of the rules.e landslide-induced surge spreads into the channel and interacts with the ship after a large number of landslide bodies (length � 1 m, width � 1.5 m, and height � 0.4 m) enter the water.e waveforms differ slightly

Figure 14 : 3 Figure 13 :
Figure 14: Time history curve of the rolling motion of the ship under different navigational positions.

Figure 15 :Figure 16 :
Figure 15: Time history curve of the pitching motion of the ship under different navigation positions.

Figure 17 :
Figure17: Time history curve of the pitching motion of the ship under different numbers of landslides.e labels are length, width and thickness in sequence, such as the length is 1 m, the width is 0.5 m, and the thickness is 0.6 m.

Table 1 :
Primary parameters of the ship.

Table 2 :
Primary parameters of motor.

Table 3 :
Operating of the test.
Number Angle of entering water ( °) Water depth (m) Speed (m/s) Position of ships Landslide volume (L × B × D (m))

Table 4 :
Turning test data.