Development of Indicator for Piled Pier Health Evaluation in Vietnam Using Impact Vibration Test Approach

Abstract

Vietnam’s seaport system currently includes 298 ports with 588 wharves (a total length of approximately 92,275 m), which is vital in developing Vietnam’s marine economy. The piled pier, a type of wharf structure, is widely used and accounts for up to 90%, while the remaining 10% is made up of other types of wharf structures, such as gravity and sheet pile quay walls. Most wharves have been operating for over 10 years and some for even more than 50 years. Noticeably, wharves are highly vulnerable and degrade rapidly due to many factors, especially heavy load impacts and severe environmental conditions. Additionally, wharves have a higher risk of deterioration than other inland infrastructure, such as buildings and bridges. Consequently, determining a wharf’s health is an important task in maintaining normal working conditions, extending its lifecycle, and avoiding other severe damage that could lead to dangers to the safety of vehicles, facilities, and humans. Moreover, regulated quality inspections usually include only simple inspections, e.g., displacement, settlement, geometric height, and tilt; the visual inspection and determination of dimensions by simple length-measuring equipment; concrete strength testing by ultrasonic and rebound hammers; and the experimental identification of the chloride ion concentration, chloride diffusion coefficient, corrosion activity of rebar in concrete, and steel thickness. These testing methods often give local results depending on the number of test samples. Therefore, advanced diagnostic techniques for assessing the technical condition of piled piers need to be studied. The impact vibration test (IVT) is a powerful non-destructive evaluation method that indicates the overall health of structures, e.g., underground and foundation structures, according to official standards. Hence, the IVT is expected to help engineers detect the potential deterioration of overall structures. It is fundamental that, if a structure is degraded, its natural frequency will be affected. A structure’s health index and technical condition are determined based on this change. However, the IVT does not seem to be widely applied to piled piers, with no published standard; hence, controversial issues related to accuracy and reliability still remain. This motivates the present study to recommend an adjusted factor (equal to 1.16) for the health index (classified in official standards for other structures) through numerical and experimental approaches before officially applying the IVT method to piled piers. The current work focuses on the health index using the design natural frequency, which is more practical in common cases where previous historical data and the standard natural frequency are unavailable. This study also examines a huge number of influencing factors and situations through theoretical analysis, experience, and field experiments to propose an adjusted indicator. The results are achieved with several assumptions of damages, such as the degradation of materials and local damages to structural components. With the proposed adjusted indicator, the overall health of piled piers can be assessed quickly and accurately by IVT inspections in cases of incidents, accidents due to collisions, cargo falls during loading and unloading, or subsidence and erosion due to natural disasters, storms, and floods.

1. Introduction

During the operation stage, a wharf/berth (piled pier type), mainly made of concrete, is subjected to heavy loads and works under severe environmental conditions such as strong waves, erosion, and collision force with ships, which lead to a quick occurrence of degradation, affecting activities of the port, especially the corrosion of rebar [1,2,3]. Wharves frequently work in saltwater environments; one of the leading causes of damage is chloride intrusion into concrete structures, seriously reducing the bearing capacity of structural components. It should be noted that rebar corrosion is a widespread and severe problem in concrete in port structures and other structures, such as bridges [4]. Many port structures in Vietnam have been corroded and damaged after 20–25 years, and even severely degraded after only 10–15 years of use. The damage caused by corrosion is especially significant and severe, leading to repair work costs for these wharves being up to 30–70% of the construction investment. In addition to deterioration due to corrosion, large loads due to ship docking, port crane movements and the impact of crane leg loads during loading and unloading, and the operation of heavy trucks cause a higher probability of damage, with greater effects of fatigue in wharves than other structures. Large deformation can lead to a requirement for the stoppage of the operations of loading and unloading equipment. Therefore, inspections need to be conducted regularly using the optimal survey time, cost, and accuracy approaches. This is also a life-extending measure serving as a basis for the structure’s maintenance, repair, and reinforcement works. It is noted that other damages can also occur because of other special loads, such as explosive loads and earthquakes, as mentioned in [5,6,7]. Moreover, the conditions during the operation stage of the wharf can change suddenly; hence, the determination of its overall health condition is an essential task [8]. Noticeably, one of the three main components of a piled pier is its deck, which is more adversely affected by dynamic loads and even impact loads than other structures like bridges [9]. Furthermore, the port is required to meet and receive larger ships than those accounted for in the original design in several cases; thus, the assessment of the technical condition of the wharf becomes more urgent than ever.

Up to now, not including inland waterway ports, 298 ports in Vietnam’s seaport system have been constructed in coastal provinces from the northern to southern regions, where Hai Phong (50 ports), Ba Ria-Vung Tau (48 ports), Ho Chi Minh City (40 ports), Dong Nai (18 ports), and Khanh Hoa and Can Tho (17 ports) are the localities with the most significant numbers of ports. Among the components of ports, the reality in Vietnam has also proven that the deterioration rate of wharves becomes significantly higher than that of the components on the mainland side due to far greater effects of severe environmental conditions. Moreover, wharves are commonly located in areas with steep banks and weak or complex soils, where the possibility of subsidence and landslides frequently occur. Furthermore, wharves receive incoming and outgoing ships and load and unload goods using an extensive industrial equipment system. Hence, wharves must withstand various heavy loads, especially large horizontal ones. Many ports have been in service since the 1950s along rivers, estuaries, and coastal areas directly exposed to natural disasters, storms, floods, and changes in water levels, flow, waves, and seawater environment. Consequently, local damage, soil erosion, intrusion, and material corrosion (leading to a reduction in material properties) can occur. For example, some authors pointed out the typical deformation sequence of a wharf, including cumulative deformation (the corrosion of steel and concrete piles and the cracking of the superstructure) and sudden deformation (damage of the superstructure and damage or falling of the wharf due to uplift pressure caused by waves) [10,11].

Additionally, ports completed with a status different from the design, accidents due to collisions, and falling goods during loading and unloading are potential risks that can occur. Therefore, accurately determining a wharf’s health in Vietnam and in the world is an essential task that helps extend to its lifecycle under acceptable working conditions, avoid other severe damage, and ensure safety during its operation.

The port operation takes place continuously; hence, destructive evaluation methods seem inefficient compared to non-destructive approaches. Out of the non-destructive evaluation methods, the impact vibration test (IVT) method has been increasingly applied to evaluate structures’ overall health and technical condition, i.e., wharves and other structure types such as piers and columns. In the IV method, a structure’s health level and technical characteristics are quantified hierarchically by the health index. The health index (κ_o) is the ratio between the structure’s natural frequency at the time of measurement and its initial natural frequency (i.e., based on the design or the survey right after the structure construction process was finished).

There are three approaches for estimating the health index, wherein their initial natural frequencies correspond to (1) the measured natural frequency at the previous inspection, (2) the standard natural frequency, and (3) the design value of the natural frequency (based on the initial design). The initial measured natural frequency and previous standard natural frequency of ports in Vietnam are unavailable due to many factors, and the measurement work’s enormous cost is one of the main reasons for this. This situation may also be seen in other countries. Therefore, only the third approach mentioned above seems suitable for determining the health index. According to “Structure Management and Maintenance Standard—Underground Structure and Foundation Structure—Japan”, structure health is classified into four levels [12], as shown in

Table 1. The health index in the technical condition (health) evaluation.

Health Index (κo)	Level of Evaluation	Situation/Solution
κo ≤ 0.70	A1	Structures undergo dangerous deformation due to external forces at any time. Detailed inspection needs to be conducted for repairs and reinforcement.
0.70 < κo ≤ 0.85	A2	The reduction in the structure’s natural frequency needs to be monitored.
0.85 < κo ≤ 1.00	B	No severe damage is observed on structures. Structures work in a good health condition.
1.00 < κo	S	Structures work in an excellent health condition.

.

The IVT method was explained by [12] to effectively assess the health of substructures and pile foundation structures. Several previous studies [12,13,14,15,16,17,18,19,20,21] have introduced the theory, procedure of its field experiments, and measured data processing methods, especially the solutions creating impact vibration forces for IVT investigations. However, no study has clearly examined the issues affecting the determination of the health index of wharves or developed an indicator for wharf health evaluations using the IVT method. Additionally, no standard has been published related to the health index in the IVT method for wharves, unlike official standards for other structures like foundations. This motivates the present study to focus on the aforementioned problems by exploring numerical and experimental IVT approaches.

In the present study, it should be noted that the natural frequency based on the design is computed in the model without considering the crane weight or products located on the wharf surface. In addition, the tilt and settlement (affecting the stability conditions), as well as defects such as cracking, peeling, and delamination, are not taken into account in the numerical simulation.

2. Research Objectives

The primary purpose of the present study is to recommend an indicator for wharf health evaluation in Vietnam using the IVT approach. To achieve this goal, the following objectives are pursued: (1) determining a range for the natural frequency through numerical simulations (based on the design) considering different dynamic spring stiffnesses (equal to 2, 3, 4, and 4.5 times the static spring stiffnesses); (2) conducting field IVT experiments to identify the natural frequency and health index of the wharves, then, providing an initial evaluation; (3) performing numerical simulations of the wharves to determine their natural frequency and health index, taking to account several typical damages assumed based on experience; and (4) performing a comprehensive comparison between the health index determined from (3) with actual working conditions to recommend an indicator for wharf health evaluation in Vietnam.

3. Field Experimental and Numerical Simulation Work

With the aim of a comprehensive evaluation, typical wharves from northern, central, and southern Vietnam are analyzed as shown in

Table 2. Several typical ports considered in Vietnam.

No	The Names of Wharves	Level by Crane	Level by Height	Load of 103 DWT Ship	Height (m)	Age (Years)	Location
1	Tan Vu No.1	II	II	20	13.45	14	Northern Vietnam
2	Tan Vu No.2	II	II	20	13.45	14
3	Tan Vu No.3	II	II	20	13.45	12
4	Tan Vu No.4	II	II	20	13.45	12
5	Tan Vu No.5	II	II	20	13.45	11
6	Nam Dinh Vu	I	II	50	14.00	0
7	Mipex	I	I	40	17.70	3
8	Lach Huyen	Special	I	80	19.50	5
9	Nghi Son	II	I	30	17.00	5	Central Vietnam
10	Cua Lo	II	I	30	16.5	5
11	Tan Cang QN	II	I	30	16.7	19
12	Hiep Phuoc	I	I	50	19.5	10	Southern Vietnam
13	Cai Mep Ha	III	II	10	12.4	2
14	CMIT	I	I	60	19.7	13
15	SITV	Special	Special	80	22	12
16	Gemarlink	Special	Special	200	21.5	2
17	Cai Cui	II	I	20	15.7	17

. It can be seen that almost all these ports are classified into level II to level “special”, while the loads of ships range from 20.000 to 200.000 DWT. All examined ports have already been in service with an age of less than 20 years. The field experimental works, numerical simulation works, and initial evaluation are presented in Section 3.1, Section 3.2, Section 3.3, respectively.

3.1. Field Experimental Works for New Wharves

Due to the limitations of the times, costs, and effects of the experimental arrangement on the operation, the IVT field inspections are conducted only on the Tan Vu, Lach Huyen, Hiep Phuoc, SITV, and Gemarlink ports (new ports). The procedure of the IVT test is shown in Figure 1 and Figure 2. In contrast, solutions for creating a horizontal impact force are listed in Figure 3, and several images in Figure 4 illustrate the experimental works in the field. It is noted that other detailed information about the ITV field experiment can also be seen clearly in the author’s previous studies.

Five plans are employed to create a horizontal impact force to impart on the wharf structure as follows (see Figure 3): (Plan 1)—the first way: a load weight is supported by a suitable steel frame, in which the load weight generally ranges from 10 to 50 kg or larger; the second way: a weight hanger can also be installed using a mobile crane with enough reach, and the hanger is 2 m higher than the floor elevation; (Plan 2)—the tugboat is utilized to provide the horizontal impact force; (Plan 3)—the horizontal impact force is produced by a vessel; (Plan 4)—the horizontal impact force is created using a movable gantry crane; and (Plan 5)— impact forces are established using a movable gantry crane.

In order to identify the natural frequency types that can appear in the measured data (e.g., from the structure, electric, anchor line, or win), the exclusion method is used to determine the search frequency. Moreover, the data range is used to extract the natural frequency, as shown in Figure 5, in which the structure’s vibration is minimally affected by the impact force, leading to only natural vibration in this range. After that, the Seismo Signal software is employed to conduct Fourier transform to transform the signal from the time domain (an example is shown in Figure 5) to the frequency domain (several examples are indicated by the graphs on the left side in Figure 6) to obtain field experiment data. After that, the main natural frequency of the wharves can be determined by the natural frequencies, as in [12,15,17,18,19,20,21], at 90° (π/2), as shown by the sub-tables on the right of Figure 6 (the tabular information in Figure 6 is used to determine the natural frequency corresponding to a 90° phase angle). Consequently,

Table 3. Typical natural frequencies from actual measured data for new ports.

No.	The Names of Berths	Natural Frequency per Measurement Time (Hz)
		1st	2nd	3rd
1	Tan Vu	1.30	1.1342	1.221
2	Lach Huyen	1.049	1.428	1.135
3	Hiep Phuoc	1.709	1.709	1.831
4	SITV	1.953	2.014	1.519
5	CMIT	1.709	1.953	1.726
6	GEMARLINK’s Segment No.1 (GEM 1)	1.586	1.648	1.684
7	GEMARLINK’s, Segment No.2 (GEM 2)	1.641	1.641	1.587
8	GEMARLINK’s, Segment No.3 (GEM 3)	1.802	1.647	1.886

lists the natural frequencies of the wharves, which are new structures that have just been put into operation.

3.2. Numerical Simulation Works for All Wharves

The determination of the design natural frequency of the wharves is performed using the ITV method, in which numerical simulations (i.e., a dynamics analysis model) can be conducted in finite element software such as SAP, Midas Civil, Ansys, and Abaqus. Other detailed information on the models can be seen in detail in the authors’ past studies [13,14,15]. It should be noted that the boundary conditions are spring-bearing connections (with the pile model working simultaneously with the ground), and the stiffness of the spring bearings is determined through the dynamic spring stiffness. Models are systems consisting of horizontal beams, longitudinal beams, and plate elements, wherein the connection between the pile and the foundation are spring connections, as shown in Figure 7.

Generally, to comprehensively investigate twenty wharves, three groups of models for IVT with differences in their dynamic spring stiffnesses are examined for each wharf, i.e., this stiffness is equal to 3 times (3K), 4 times (4K), and 4.5 times (4.5K) the static spring stiffness. For each case, both models with their static spring stiffness calculated using the results from the Standard Penetration Test (SPT index) [10,11] and Plasticity Index (I_L) [22] are examined in the absence of field horizontal load pile testing. However, the model with the use of spring stiffness from I_L should be only utilized if the SPT is not conducted.

Table 4. Natural frequencies according to the design of several typical berths in Vietnam.

No.	The Names of Berths	Transverse Natural Frequencies of Berth Segments (Hz)
		3KSPT	4KSPT	4.5KSPT	3KIL	4KIL	4.5KIL
1	Tan Vu, No.1	0.9913	1.0292	1.0444	0.9984	0.9484	0.9984
2	Tan Vu, No.2	0.8834	0.9194	0.9339	0.9353	0.9373	0.9497
3	Tan Vu, No.3	1.0924	1.1177	1.1278	1.0944	1.1178	1.1272
4	Tan Vu, No.4	1.1751	1.2046	1.2162	1.1814	1.3266	1.3354
5	Tan Vu, No.5	1.4461	1.5328	1.5693	0.9000	0.9307	0.8978
6	Nam Dinh Vu, Stage 2	1.2397	1.2967	1.3197	1.3962	0.9950	1.3962
7	Mipec	0.9564	0.9928	1.0074	1.0327	1.0647	1.0770
8	Lach Huyen	1.0169	1.0496	1.0624	1.0204	1.0440	1.0533
9	Nghi Son	1.0924	1.1177	1.1278	1.0539	1.0872	1.1008
10	Cua Lo	1.1981	1.2373	1.2527	-	-	-
11	Quy Nhon New	0.7619	0.7786	0.7853	-	-	-
12	Hiep Phuoc	-	-	-	0.9363	0.9090	0.9170
13	Cai Mep Ha	2.0956	2.1968	2.2381	2.6439	2.7313	2.7663
14	SITV	1.4191	1.4191	1.4983	-	-	-
15	CMIT	-	-	-	0.8647	0.8808	0.8872
16	GEMARLINK Berth, Segment No.1 (GEM 1)	0.8852	0.9165	0.9295	-	-	-
17	GEMARLINK Berth, Segment No.2 (GEM 2)	0.8996	0.9312	0.9440	-	-	-
18	GEMARLINK Berth, Segment No.3 (GEM 3)	0.8769	0.9085	0.9213	-	-	-
19	Cai Cui	0.9707	1.0180	1.0377	-	-	-

lists the natural frequencies (in Hz) for all the numerical simulation cases.

It can be seen from Table 4 that the natural frequency of the wharves increases with a rise in the spring stiffness. Among the wharves examined, three ports, including SITV, CMIT, and Gemarlink, are located within regions with very weak ground conditions. Consequently, the natural frequencies of the wharves from the 4.5K-SPT model are more significant, from 5 to 6%, than those from the 3 K-SPT model. This difference is only 3% for the soft soil in the Hai Phong port area (Lach Huyen, Tan Vu, Mipec, and Nam Dinh Vu). Additionally, under a change in the dynamic spring stiffness (3K, 4K, and 4.5K models) with the same wharf, the gaps between the natural frequencies from the model with the spring stiffness calculated from the SPT are higher than the cases using I_L.

3.3. An Initial Evaluation Based on Experiments and Numerical Simulations for New Wharves

Two groups of wharves are included in the present study, however, the health index or comparison of their frequencies is conducted considering new wharves. No degradation is assumed for these new wharves, e.g., in material, dimension, or foundation. This is why the difference between the natural frequency obtained from the design (numerical simulation for a new structure) and the measurement on the wharf just put into operation can be indicated clearly.

Table 5. The health index κ_o for new ports in Vietnam.

No.	Names of Berths	Natural Frequency Based on the Official Design		Natural Frequency Measured		Health Index
		SPT	IL	Minimum (M)	Average (A)	SPT		IL
						M	A	M	A
1	Tan Vu No.1	0.937	0.991	1.14	1.23	1.14	1.22	1.14	1.23
2	Lach Huyen	0.968	1.020	1.08	1.24	1.03	1.18	1.08	1.24
3	Hiep Phuoc	-	0.936	-	-	1.83	1.87	-	-
4	SITV	1.419	-	1.07	1.29	-	-	1.07	1.29
5	CMIT	-	0.865	-	-	1.98	2.08	-	-
6	Gem 1	-	0.885	1.79	1.85	-	-	1.79	1.85
7	Gem 2	-	0.900	1.76	1.80	-	-	1.76	1.80
8	Gem 3	-	0.877	1.88	2.03	-	-	1.88	2.03

indicates that the average measured natural frequency is equal to approximately 1.18 to 2.0 times the frequency based on the design using the IVT model for the case of the 3K model. If the dynamic spring stiffness is calculated according to the reference [22], the natural frequency is commonly more considerable than those following references [23,24]. However, considering experience and previous recommendations for wharves located in the regions with very weak soil conditions, the 4.5K-SPT model should be applied, e.g., to the ports on the Cai Mep and Thi Vai rivers (where the soft ground thickness is greater than 30 m). Additionally, the thickness of the soft soil around the Lach Huyen port is less than 20 m, so the 3KSPT model should be considered.

4. Development of an Indicator for Wharf Health Evaluation in Vietnam

4.1. Evaluation Criteria of Wharf Evaluation

A discussion related to the evaluation criteria is provided here following the previous studies below:

Firstly, according to [10,11]:

The typical deformation sequences of wharves include two components: (1) cumulative deformation is mainly due to pile corrosion and the performance deterioration of concrete. This deformation starts with steel pile corrosion, and then further deformations will start and develop; and (2) sudden deformation is mainly divided into two types with a short duration: deformations and the deterioration of performance, the collapse or subsidence of berths, and the cracking of concrete structures.

In consideration of the degradation of structures, wharves are classified into four levels: (1) the performance of structures has been seriously reduced; (2) the performance of structures has been reduced; (3) the performance of structures is not reduced, but several deformations are occurring; and (4) there is no deformation, the wharf operates under a good condition.

Moreover, the classification of testing items according to their importance is divided into Types I, II, and III. Type 1 includes components directly affecting the performance of the wharf (especially its structural safety), i.e., the displacement or settlement of the entire wharf and deformation of and changes in the superstructure, main structure, foundation structure, and wave-absorbing structure. Type 2 represents items and materials affecting the performance of the wharf, including inspection for material damage. For Type 2, this performance deterioration will not directly and immediately impact the entire wharf, but it will affect the wharf performance without repair work for a long time. Finally, Type 3 is the test for auxiliary parts which influence the wharf’s activities. If damage to auxiliary works is not repaired promptly, accidents can occur, and the operation’s safety can be affected.

Furthermore, according to the results of the features’ assessment, wharves can be classified into four categories, i.e., Type A, B, C, and D. In particular, the structure belongs to Type A when its performance has been degraded, then repair work must undertaken promptly. In addition, it is necessary to increase the frequency of periodic inspections to determine the appropriate time for repair and reinforcement if the structure is categorized into Type B (the wharf’s functionality is rapidly deteriorating). Interestingly, structures of Type C have no deformations related to the degradation of the structure’s performance, but periodic inspection is still required. Finally, abnormalities are not found, and the structure’s features are still maintained according to its design requirements.

It should be noted that the classification above refers to the evaluation criteria of structural performance degradation in periodic and regular inspections for wharves according to the importance of a class I structure. This evaluation is for the main components of wharves, such as edges, surfaces, beams, slabs, and piles.

Secondly, according to [25,26], the technical status index for components of the wharf is determined based on the group of defects detected, i.e., with Groups 1, 2, and 3 corresponding to small, large, and serious defects represented by the value of the safety factor (a), i.e., this factor indicates characteristics for the statuses of defects in all components inspected. Particularly, if a structure belongs to Group 1, it can work under normal conditions (a = 0.8 ÷ 1.0), whereas a structure with Group 3 is no longer able to work (a ≤ 0.4). Finally, for Group 2, the ability to work is limited (a = 0.6 ÷ 0.8) or no longer available (a = 0.4 ÷ 0.6), depending on the defect characteristics and operation ability. In order to calculate the safety factor (a), structures are divided into n groups, each of which has the same type of components, denoted as a. Then, the safety factor is determined using Equations (1) and (2) [25,26], where i (from 1 to n) is the serial number of the components of the structure (the serial number of the group) listed in [25,26] and b is the mass factor of the group. In particular, during the inspection, the main components of the wharf need to be checked, i.e., piles, the structures above both beams and slabs, the bottom region, and the connection of the roof and the shore corresponding to mass coefficients (b) of 0.5, 0.35, 0.05, and 0.1. Additionally, a_i is the safety factor of a group of the same type of components, a_j is the safety factor of each element, j (from 1 to n) is the number of components in a group with the same type i, and m is the number of components in a group with the same type i.

$$a_n={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{a}_i{b}_i}}{{\displaystyle \sum _{i=1}^n{b}_i}}}$$

(1)

$$a_i={\displaystyle \frac{{\displaystyle \sum _{j=1}^n{a}_j}}{m}}$$

(2)

Based on the above explanation, requirements, and recommendations from references [10,11,25,26] for wharves, the technical statuses based on the characteristics of the defects of the main components are shown in

Table 6. Technical status according to defects of main components of the piled piers.

Status	Group 1: Normal Working Conditions	Group 2: Limited Working Conditions
Bottom area in front of the structure: a depth reduction due to dredging, sedimentation, and erosion.	The local depth change tolerance does not exceed 0.5 m on a section with a length of 0.25 L.	Determined through calculation of the structure’s bearing capacity.
Reduction in the compressive strength of the concrete of the pile and reduction in the steel pile thickness (corrosion)	≤10%	>20%
Reduction in the compressive strength of the concrete of the beam and deck	≤20%	>30%
General and local deformation, slope landslides	Change the depth at the wharf location within the allowable threshold.	The soil under the wharf is eroded.

. In contrast, the health classification and technical conditions are illustrated in

Table 7. Health classification and technical conditions of the piled piers.

Status	Type S	Type C	Type B	Type A
Bottom area in front of the structure: a depth reduction due to dredging, sedimentation, and erosion.	No	≤ 0.5 m	Determined through calculation of the structure’s bearing capacity.	Dangerous defects causing collapse.
Reduction in the compressive strength of the concrete of the pile and reduction in the steel pile thickness (corrosion).	No	≤10%	>20%	Dangerous defects.
Reduction in the compressive strength of the concrete of the beam and deck	No	≤20%	>30%	Dangerous defects.
General and local deformation, slope landslides	No	Change the depth at the wharf location within the allowable threshold.	The soil under the wharf is eroded.	Dangerous defects.

.

4.2. Health Index of Wharves

In order to develop an indicator for wharf health evaluation in Vietnam using the IVT method, several assumptions are proposed. Namely, degradation in the properties of concrete properties with the cases of 10% and 20% for beams and slabs + 10% for piles; 20% and 30% for beams and slabs + 20% for piles; and 30% and 40% (dangerous level) for beams, slab, and piles. Additionally, the degradation level of the elastic modulus E_c according to the compressive strength f’_c [27] is calculated based on Euro Code 2. An example of the performance degradation of M600 concrete is shown in

Table 8. Several cases of deterioration of M600 concrete material properties.

No	Compressive Strength Loss of Concrete (%)	Ec (kN/m2)	f’c (kN/m2)
1	0	37,500,000	32,639.2
2	10	36,333,231	29,375.3
3	20	35,071,817	26,111.3
4	30	33,694,629	22,847.4
5	40	32,171,895	19,583.5
6	50	30,459,465	16,319.6

. Moreover, the slope erosion is assumed to be 10%, 20%, and 30% for the cases (the percentage of erosion is calculated according to the length of the embedded pile in the soil). In the numerical simulation with the IVT method, this is the loss of the elastic bearing connection. It should be noted that erosion often occurs on wharves along the coast and on islands, especially under high flow rates and significant water level differences.

Thereafter, many numerical simulations with the aforementioned cases of degradation are carried out. Figure 8 below shows an example of the IVT model for a wharf without erosion (Figure 8a) and with erosion (Figure 8b). It should be noted that classification according to importance level or capacity scale and structural scale based on the recommendations of [28] affects the selection of the design water level, increasing the construction depth and design life, as well as the stability requirements and the rate of structural deterioration. The importance coefficient taken into the evaluation can be referred to reference [29], wherein these factors are 1.25, 1.2, 1.15, and 1.1, corresponding to levels 1, 2, 3, and 4.

Consequently, the horizontal natural frequencies (main frequency) are obtained, as shown in

Table 9. The horizontal natural frequencies (in Hz) of piled piers with hypothetical cases/damage.

No.	The Name of Berth	Natural Frequency When Scour Loses Spring Support along the Outermost Row of Piles (Hz)							Natural Frequency When Concrete Strength Decreases (Hz)
		10%	20% (Beam, Deck), 10% (Pile)	20%	30% (Beam, Deck), 20% (Pile)	30%	40%	50%	1 m	2 m	3 m
1	Tan Vu No.1	0.991	0.980	0.980	0.967	0.967	0.953	0.937	0.918	0.897	0.801
2	Tan Vu No.2	0.883	0.874	0.863	0.863	0.862	0.850	0.836	0.820	0.792	0.726
3	Tan Vu No.3	1.092	1.078	1.078	1.062	1.062	1.045	1.024	1.001	0.975	0.913
4	Tan Vu No.4	1.175	1.160	1.160	1.143	1.143	1.124	1.103	1.078	1.030	0.914
5	Tan Vu No.5	1.446	1.433	1.427	1.418	1.411	1.401	1.382	1.359	1.327	1.264
6	Nam Dinh Vu, Stage 2	1.240	1.227	1.226	1.212	1.212	1.195	1.177	1.155	1.131	1.029
7	Mipec	0.956	0.945	0.945	0.933	0.933	0.919	0.904	0.886	0.902	0.857
8	Lach Huyen	1.017	1.009	1.009	1.001	1.000	0.991	0.980	0.967	0.967	0.911
9	Nghi Son	1.092	1.078	1.078	1.062	1.062	1.045	1.024	1.001	0.976	0.913
10	Cua Lo	1.198	1.184	1.183	1.168	1.167	1.150	1.129	1.106	1.074	1.015
11	Quy Nhon New Port	0.762	0.752	0.752	0.741	0.741	0.728	0.714	0.698	0.707	0.646
12	Cai Mep Ha	2.096	2.074	2.071	2.049	2.046	2.022	1.991	1.955	1.996	1.915
13	SITV	1.419	1.403	1.402	1.385	1.384	1.365	1.342	1.316	1.346	1.285
14	GEM 1	0.885	0.882	0.882	0.878	0.878	0.874	0.869	0.863	0.855	0.828
15	GEM 2	0.900	0.895	0.894	0.889	0.889	0.883	0.876	0.868	0.860	0.827
16	GEM 3	0.877	0.873	0.873	0.869	0.868	0.864	0.859	0.852	0.844	0.815
17	Cai Cui	0.971	0.961	0.960	0.949	0.949	0.937	0.922	0.906	0.926	0.865

. It is emphasized that the results in Table 9 are for the case of the 3K-SPT model [12,16]. Thereafter, the health indexes of hypothetical cases are provided in

Table 10. The health indexes of wharves with hypothetical cases/damage.

No	The Name of Berth	Health Index
		Compressive Strength Loss of Concrete							Elastic Support Loss along the Outermost Row of Piles Due to Erosion
		10%	20% (Beam, Deck), 10% (Pile)	20%	30% (Beam, Deck), 20% (Pile)	30%	40%	50%	1 m	2 m	3 m
1	Tan Vu No.1	0.99	0.99	0.98	0.98	0.96	0.95	0.93	0.90	0.81	0.73
2	Tan Vu No.2	0.99	0.98	0.98	0.98	0.96	0.95	0.93	0.90	0.82	0.74
3	Tan Vu No.3	0.99	0.99	0.97	0.97	0.96	0.94	0.92	0.89	0.84	0.75
4	Tan Vu No.4	0.99	0.99	0.97	0.97	0.96	0.94	0.92	0.88	0.78	0.70
5	Tan Vu No.5	0.99	0.99	0.98	0.98	0.97	0.96	0.94	0.92	0.87	0.83
6	Nam Dinh Vu, Stage 2	0.99	0.99	0.98	0.98	0.96	0.95	0.93	0.91	0.83	0.77
7	Mipec	0.99	0.99	0.98	0.98	0.96	0.95	0.93	0.94	0.90	0.86
8	Lach Huyen	0.99	0.99	0.98	0.98	0.97	0.96	0.95	0.95	0.90	0.85
9	Nghi Son	0.99	0.99	0.97	0.97	0.96	0.94	0.92	0.89	0.84	0.75
10	Cua Lo	0.99	0.99	0.97	0.97	0.96	0.94	0.92	0.90	0.85	0.81
11	Quy Nhon New Port	0.99	0.99	0.97	0.97	0.96	0.94	0.85	0.93	0.85	0.77
12	Cai Mep Ha	0.99	0.99	0.98	0.98	0.96	0.95	0.93	0.95	0.91	0.87
13	SITV	0.99	0.99	0.98	0.98	0.96	0.95	0.93	0.95	0.91	0.87
14	GEM 1	1.00	1.00	0.99	0.99	0.99	0.98	0.98	0.97	0.94	0.91
15	GEM 2	0.99	0.99	0.99	0.99	0.98	0.97	0.97	0.96	0.92	0.89
16	GEM 3	1.00	1.00	0.99	0.99	0.99	0.98	0.97	0.96	0.93	0.90
17	Cai Cui	0.99	0.99	0.98	0.98	0.96	0.95	0.93	0.95	0.89	0.82

. Interestingly, the structure is under good working conditions following [12] (as shown in

Table 11. The assessment of wharves according to reference [1].

No	The Name of Berth	Level of Evaluation
		Compressive Strength Loss of Concrete							Elastic Support Lossy along the Outermost Row of Piles Due to Erosion
		10%	20% (Beam, Deck), 10% (Pile)	20%	30% (Beam, Deck), 20% (Pile)	30%	40%	50%	1 m	2 m	3 m
1	Tan Vu No.1	B	B	B	B	B	B	B	B	A1	A1
2	Tan Vu No.2	B	B	B	B	B	B	B	B	A1	A1
3	Tan Vu No.3	B	B	B	B	B	B	B	B	A1	A1
4	Tan Vu No.4	B	B	B	B	B	B	B	B	A1	A1
5	Tan Vu No.5	B	B	B	B	B	B	B	B	B	A1
6	Nam Dinh Vu, Stage 2	B	B	B	B	B	B	B	B	A1	A1
7	Mipec	B	B	B	B	B	B	B	B	B	B
8	Lach Huyen	B	B	B	B	B	B	B	B	B	B
9	Nghi Son	B	B	B	B	B	B	B	B	A1	A1
10	Cua Lo	B	B	B	B	B	B	B	B	A1	A1
11	Quy Nhon New Port	B	B	B	B	B	B	B	B	A1	A1
12	Cai Mep Ha	B	B	B	B	B	B	B	B	B	B
13	SITV	B	B	B	B	B	B	B	B	B	B
14	GEM 1	B	B	B	B	B	B	B	B	B	B
15	GEM 2	B	B	B	B	B	B	B	B	B	B
16	GEM 3	B	B	B	B	B	B	B	B	B	B
17	Cai Cui	B	B	B	B	B	B	B	B	B	A1

). However, it seems unsuitable and consistent with the overall assessment of structural deterioration.

Noticeably, the assessment levels in Table 11 are all grade B (for material strength loss), which is inconsistent with the requirements listed in Table 7 based on references [10,11,12,25,26]. Thus, the recommendations are suggested below with suitable consideration:

-

If the material strength loss is less than 10% for piles and 20% for beams and slabs, the structure works under normal conditions in group 1 according to [25,26] and type B following [12]. Then, the structure will be in a good working condition.

-

If the material strength is reduced by 20% for piles and 30% for beams and slabs, according to references [25,26], the structure has already been degraded. Therefore, the structure works under poor conditions, and it belongs to group A2 according to reference [12], group 2 according to references [25,26], and type B according to references [10,11].

-

If the material strength loss is greater than 30% along with erosion, landslides, etc., the structure belongs to group A1 [12], group 2 with major defects—inability to work [25,26], and type A according to [10,11].

-

If material strength is reduced by 40%, the structure is degraded to a dangerous situation (the health index is equal to or lesser than 0.7); thus, the structure will belong to group A1 [12], group 3 with severe defects [25,26], and type A according to [10,11].

4.3. Development of an Indicator for Wharf Health Evaluation in Vietnam

The reference [30] also showed that a dynamic analysis based on numerical simulations can be carried out to determine the natural frequency. However, the results can differ from the frequency obtained from the field experiment. This is because the natural frequency is influenced by stiffness and mass, wherein the structure’s cross-sectional inertia and elastic modulus influence the stiffness. In addition, when numerical simulations are performed, the element dimensions are not based on the actual field conditions at the scene.

Table 12. Comparison of the health indexes.

No	Name	Factor K with a Compressive Strength Loss of Concrete (20% in Beam and Deck, 10% in Pile)	Compared to 0.85
1	Tan Vu No.1	0.988	1.16
2	Tan Vu No.2	0.976	1.15
3	Tan Vu No.3	0.987	1.16
4	Tan Vu No.4	0.987	1.16
5	Tan Vu No.5	0.986	1.16
6	Nam Dinh Vu, Stage 2	0.989	1.16
7	Mipec	0.988	1.16
8	Lach Huyen	0.992	1.17
9	Nghi Son	0.987	1.16
10	Cua Lo	0.988	1.16
11	Quy Nhon New Port	0.987	1.16
12	Cai Mep Ha	0.989	1.16
13	SITV	0.988	1.16
14	GEM 1	0.988	1.16
15	GEM 2	0.996	1.17
16	GEM 3	0.994	1.17
17	Cai Cui Berth	0.995	1.17

shows the vital classification based on the health index, in which 0.85 is a critical value that needs to be considered. Then, a comparison of the health indexes considering a threshold of 0.85 is conducted. Consequently, by taking into account the cumulative deformation due to the material strength loss, the correction factor is recommended as 1.16.

Additionally, the smallest importance level of the wharf is 1.15 (level 4 is ignored), as explained in Section 4.2. Consequently, a factor of 1.16 is selected as the adjusted health index for evaluating the wharf, as shown in

Table 13. The health index in the technical condition (health) evaluation.

Health Index (κo)	Level	Situation/Solution
κo ≤ 0.81	A1	Structures undergo dangerous deformation due to an external force at any time. Detailed inspection needs to be conducted for repairs and reinforcement.
0.81 < κo ≤ 0.98	A2	The reduction in the structure’s natural frequency needs to be monitored.
0.98 < κo ≤ 1.16	B	No severe damage is observed in structures. Structures work in a good health condition.
1.16 < κo	S	Structures work in an excellent health condition.

below (the value of κ_o shown in Table 1 is multiplied by 1.16 to obtain a new range applied to the wharf).

5. Conclusions

A comprehensive study was conducted to evaluate wharves’ health using both field experiments and numerical simulations of hypothetical damage cases. Several conclusions can be given as follows:

(1)

The IVT is a highly effective method with simple theory and short experiment durations. This significantly helps with the maintenance, quality management, and safety management during the operation stage of a wharf.

(2)

A set of natural frequencies of twenty wharves, including both new and old structures, are provided in this work through numerical simulations. Moreover, ITV field tests are also conducted on five wharves to evaluate their correlation with the design in terms of the natural frequency and the health index with the current requirement of the classification of structures.

(3)

Hypothetical cases of damage are considered in the numerical simulation. Based on that, the present study develops an indicator with an adjusted health index of 1.16 to classify the health or condition of the wharf. This factor is recommended in the case of cumulative deformation due to the strength loss of material.

(4)

The spring stiffness in the IVT model calculated through SPT obtains a higher accuracy than that from I_l.

(5)

Although hypothetical cases of damage are considered, several damages can occur simultaneously, or other damages can be available. Further studies on the aforementioned issues should be conducted.