Number of exacerbations (calculated statistics) in COPD patients per year before and after vaccination.
\r\n\t
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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"4816",title:"Face Recognition",subtitle:null,isOpenForSubmission:!1,hash:"146063b5359146b7718ea86bad47c8eb",slug:"face_recognition",bookSignature:"Kresimir Delac and Mislav Grgic",coverURL:"https://cdn.intechopen.com/books/images_new/4816.jpg",editedByType:"Edited by",editors:[{id:"528",title:"Dr.",name:"Kresimir",surname:"Delac",slug:"kresimir-delac",fullName:"Kresimir Delac"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"51369",title:"Chronic Obstructive Pulmonary Disease (COPD): Clinical and Immunological Effects of Mono-Vaccination Against Influenza Using an Immunoadjuvant Vaccine of a New Class Versus Combined Administration S. pneumoniae, H. influenzae, and Influenza Vaccines",doi:"10.5772/64292",slug:"chronic-obstructive-pulmonary-disease-copd-clinical-and-immunological-effects-of-mono-vaccination-ag",body:'\nIn Russia, 27,300,000–41,200,000 acute upper and lower respiratory infections are reported annually. Patients with chronic obstructive pulmonary disease (COPD) are at higher risk of severe course, complications, and lethal outcomes of influenza. Therefore, influenza prevention in such patients is one of the most urgent tasks.
\nAbout 30% of COPD exacerbations are due to viral infections, and influenza A and B viruses are among the most common causes.
\nThe best approach to prophylaxis is provided by vaccination because it combines the advantages of specificity, efficacy, safety, and cost-effectiveness. The GOLD guidelines (Global Initiative for Chronic Obstructive Lung Disease) recommend that influenza vaccination preferentially with split or subunit vaccines must be integrated into treatment strategies for all COPD patients regardless of the disease stage. However, further studies are needed to evaluate the efficacy and immunogenicity of modern adjuvant influenza vaccines [1].
\nIt is not rarely that the risk of COPD exacerbation is associated not directly with the influenza virus as such, but rather with the development of bacterial superinfection, mainly caused by Streptococcus pneumoniae or Haemophilus influenzae type b [2–4].
\nIn the Russian Federation, both inactivated and live vaccines against influenza have been licensed [5]. Antigenic composition of these vaccines is modified annually to adopt current epidemic situation and WHO guidelines. Recently, an innovative new class of immunoadjuvant influenza vaccines has evolved. The use of these vaccines in COPD patients will be outlined below.
\nAccording to CPMP criteria (Committee for Proprietary Medicinal Products), a vaccine is considered immunogenic, if at least one of the assessments meets the indicated requirements:
\nSeroconversion rate (at least fourfold increase in anti-hemagglutinin antibody titre): over 40% for individuals aging 18–60 years and over 30% among individuals above 60 years.
Seroprotection rate (number of individuals with protective titre of at least 1:40): over 70% for individuals aging 18–60 years and over 60% in individuals above 60 years.
Mean titre increase after vaccination: ≥2.5 in individuals aging 18–60 years and ≥2 in individuals above 60 years.
Vaccination against influenza for COPD patients is included into the National Immunization Calendar of the Russian Federation.
\nS. pneumoniae, H. influenzae, M. catarrhalis, and influenza virus are the most common causes of COPD infective exacerbations [6]. The standard of care for COPD patients includes vaccination against influenza and pneumococcal infection. Several serotypes of H. influenzae are known, and COPD exacerbation may be caused by each of them, including H. influenzae type b. Vaccine against H. influenzae type b is now available; therefore, it is of interest to evaluate a combined vaccination against S. pneumoniae, H. influenzae, and influenza in COPD patients and the effects of these vaccines on exacerbation rate and pulmonary function tests.
\nIn adult COPD patients, the pioneer studies evaluating the therapeutic effect of PPV23 were performed in 2004. Elimination of S. pneumoniae from the sputum was observed in 52.9% cases, that is, at a lower rate compared to children. Other findings include increased levels of IgG against S. pneumoniae serotypes 3, 6B, 9N, 23F; decreased total IgE, and increased Wright’s phagocytic index [7].
\nImmunization of COPD patients with PPV23 contributed to a 2.2-fold decrease in exacerbation rate by 18 months; at 12 months post vaccination, the duration of acute episodes decreased 1.8-fold compared to the control group [8].
\nThough disputable, the preliminary results regarding therapeutic effects of vaccination against respiratory infections were thus obtained. The common controversy is whether it is possible to improve the respiratory function tests in COPD patients through vaccination.
\nStudy aim—to assess exacerbation rate, number of courses of antibiotic chemotherapy, pulmonary function, and immunological effects of mono-vaccination with a new immunoadjuvant influenza vaccine vs. combined vaccination against pneumococcal infection, Haemophilus type b infection, and influenza in COPD patients.
\nThe study enrolled 170 patients with grade 1, 2, 3, 4 COPD (age 30–80 years) who had signed informed consent according to the study protocol approved by the ethics committee of the Samara State Medical University (Russian Federation) and Research Institute of Pulmonology (Moscow, Russian Federation). The diagnosis was determined according to GOLD guidelines (2012) [9].
\nPatients were divided into four groups. Group I enrolled 50 patients with COPD who continued to receive basic therapy for the main disease and were vaccinated with commercially available vaccines against pneumococcal infection (Pneumo 23, France), H. influenzae type b infection (Hiberix, Belgium), and influenza (new immunoadjuvant vaccine Grippol® plus, Russian Federation). Vaccines were administered once intramuscularly into various parts of the body. Two patients from Group I did not complete the study per protocol (one patient died after a traffic accident, and one patient died from sudden massive pulmonary embolism). Therefore, the data from these patients were not included into final analysis, and it was based on 48 patients of Group I.
\nGroup II (control for patients who received complex vaccination against pneumococcal infection, Haemophilus type b infection, and influenza) consisted of 80 patients with COPD of similar grade, who were not vaccinated and received only basic therapy.
\nGroup III consisted of 20 COPD patients vaccinated against influenza with a new immunoadjuvant vaccine. Group IV (control for patients who received mono-vaccination against influenza with a new immunoadjuvant vaccine) enrolled 20 unvaccinated COPD patients. Groups II and IV were composed of patients who categorically rejected any vaccination, despite the information provided. Nevertheless, these patients gave their consent to participate in the study. All study patients were followed up for 1 year and subjected to function and immunological tests at baseline and at 12 months.
\nThe use of two control groups was associated with enrollment of patients in two various study centers. Each study center enrolled subjects either to Group I (group of complex vaccination and control group) or to Group III (group of mono-vaccination against influenza and control group). Another reason for the use of two control groups was the probability that baseline characteristics of the patients in Group 1 and Group 3 will not be well balanced, and their comparison with the total control group will be incorrect. Our study is not a direct comparison between the groups of complex vaccination and mono-vaccination. We just compare each of these groups with its own control.
\nAll study patients underwent a history taking (identification of risk factors for COPD, complaints for cough, sputum discharge, dyspnea of any grade worsened by physical exercise). To verify the diagnosis of COPD, all patients were subjected to pulmonary function tests and broncholytic test with 400 μg of salbutamol according to the standard techniques [8]. The study enrolled patients with Tiffeneau index forced expiratory volume in 1 s/forced vital capacity (FEV1/FVC) below 70%.
\nMen and women above 30 years of age.
Patients with mild/moderate/severe/extremely severe COPD.
Patient’s informed consent.
Age below 30 years.
Vaccination against pneumococcal infection within the previous 3 years.
Previous vaccination against H. influenzae type b infection.
Acute infectious diseases and tuberculosis.
Active phase of chronic virus hepatitis.
Mental disorders.
Renal or hepatic failure.
Malignancies.
Exacerbation of chronic diseases.
Hypersensitivity to vaccine components.
Severe complications of previous vaccination.
Pregnancy.
Autoimmune disorders.
Patients were followed up by general practice physicians, pulmonologists, or allergologists-immunologists in the outpatient context or in hospitals, if hospitalization was required. In cases of COPD exacerbation, if necessary, patients were hospitalized to departments of pulmonology.
\nPatients meeting inclusion/exclusion criteria were divided into four groups. Groups II and IV enrolled patients who categorically rejected any vaccination. Other patients were first recruited to Group I to undergo complex vaccination and then to Group III to be vaccinated against influenza using a new immunoadjuvant vaccine. Sample size was determined by the number of vaccines.
\nAll patients received basic bronchodilatory and anti-inflammatory therapies in accordance with the disease severity and GOLD guidelines (2012). At baseline, groups were well balanced for age, gender, disease severity, and scope of basic therapy, which remained unchanged throughout the study period. Vaccination was performed at remission in the outpatient context, follow-up period lasted for 12 months after vaccination.
\nPPV23 vaccine is a polyvalent pneumococcal vaccine manufactured by Sanofi aventis (France). It contains purified capsule S. pneumoniae polysaccharides of 23 serotypes. One dose of vaccine is 0.5 ml.
\nHiberix is a conjugated vaccine to prevent infections caused by H. influenzae type b (GlaxoSmithKline Biologicals s.a., Belgium). One dose contains 10 μg of purified capsule polysaccharide isolated from str. H. influenzae type b conjugated with 30 μg of tetanus toxoid.
\nGrippol plus vaccine (NPO Petrovax Pharm, Russia) is a trivalent polymeric subunit immunoadjuvant vaccine (Petrovax, Russia) containing protective antigens isolated from purified influenza type A and B viruses grown in chicken embryos. One immunization dose (0.5 ml) contains at least 5 μg of hemagglutinin of epidemiologically relevant influenza subtype A (H1N1 and H3N2) and type B viruses, and polyoxidonium immunoadjuvant 500 μg in sodium phosphate buffer. Vaccine is free of preservatives.
\nClinical efficacy of vaccination was assessed by the number of COPD exacerbations during the year before vaccination and after vaccination. COPD exacerbation was defined as increased dyspnea, cough, and sputum volume requiring medical advice and modification of current therapy documented by primary medical records.
\nVentilation function was investigated using a Spiro S-100 spirometer (Russian Federation). The following parameters were measured: forced vital capacity (FVC), forced expiratory volume in 1 s (FEV1), and a calculated ratio of these two parameters (FEV1%/FVC), that is, modified Tiffeneau test. Exercise tolerance was assessed using the 6-minute walk test (6MWT) according to the standard protocol.
\nThe levels of IgG antibodies against influenza virus strains were measured using standard HAI assay (hemagglutination inhibition assay) in accordance with the manufacturer’s instructions to the kit.
\nThe results were studied statistically using StatPlus 2009 Professional 5.8.4. Measures of central tendency and dispersion were chosen depending on the data distribution type. Continuous variables corresponding to normal distribution are presented as means (SD); variables differing from normal distribution as medians (interquartile distance). Categorical variables are presented as proportions (%) and absolute values.
\nThe choice of statistical test depends on the data distribution type and evaluation of dispersion equality. The hypothesis of data distribution normality was tested (Shapiro-Wilks test). In cases of normal distribution of data in each sample, dispersion is to be compared between two distributions (Levene’s test). If both criteria are met, Student’s t test is selected, if no, its non-parametric alternative is used (Mann-Whitney test). The same is applicable to paired tests for comparisons of changing variables (pairwise Student’s t test or Wilcoxon test for paired comparisons). Comparative analysis of categorical variables was performed using exact two-sided Fisher’s test. Differences were statistically significant at p < 0.05 [10].
\nProspective study design allows calculating the following statistics:\n
Number of patients with exacerbations per year before and after vaccination.
Absolute risk (AR) of exacerbation per year before and after vaccination.
Relative risk (RR) of exacerbation per year before and after vaccination.
Reduction of absolute risk (RAR) of exacerbation after vaccination.
Reduction of relative risk (RRR) of exacerbation after vaccination.
Chance of exacerbation.
Odds ratio (OR) for exacerbation after vaccination compared to no vaccination.
Number of patients needed to treat to prevent one additional bad outcome (NNTp).
About 95% CI of the difference of absolute risks (AR): the results are statistically significant, if 95% CI will not contain 0.
\nAbout 95% CI of the relative risk (RR): the results are statistically significant, if 95% CI will not contain 1.
\nAbout 95% CI for the odds ratio (OR): the results are statistically significant, if 95% CI will not contain 1.
\n\n
The clinical effects of vaccination (exacerbation rate) in COPD patients are characterized by groups in Table 1.
\nNumber of exacerbations (calculated statistics) in COPD patients per year before and after vaccination.
Both complex and mono-vaccination resulted in a statistically significant reduction of the number of COPD exacerbations. The risk of COPD exacerbation was reduced by 54% after complex vaccination vs. 30% after mono-vaccination (p > 0.05 for all comparisons).
\nNumber of courses of antibiotic chemotherapy (calculated statistics) in COPD patients per year before and after vaccination in the groups considered.
As compared to unvaccinated patients, complex vaccination reduced the risk of COPD exacerbation by 59 vs. 38% reduction after mono-vaccination vs. increase by 6% in unvaccinated patients.
\nIn the group of complex vaccination against pneumococcal, Haemophilus type b infection, and influenza, the chance of COPD exacerbation was 5% of that in unvaccinated patients (p < 0.05). In the group of mono-vaccination, the chance of COPD exacerbation was 25% of that without vaccination (p > 0.05).
\nTable 2 presents characteristics of the clinical effect of vaccination (i.e., number of courses of antibiotic chemotherapy) in different groups of COPD patients.
\n\nBoth complex and mono-vaccination led to statistically significant reduction in the number of antibacterial chemotherapy courses.
\nThe risk of antibiotic chemotherapy was reduced by 54% in the group of complex vaccination against pneumococcal, Hemophilus type b infection, and influenza vs. 30% in the group of mono-vaccination (p > 0.05 for all comparisons).
\nAs compared to no vaccination, complex vaccination reduced the risk of antibiotic chemotherapy in patients with COPD by 64%, whereas mono-vaccination reduced it by 35%.
\nIn the group of complex vaccination against pneumococcal, Hemophilus type b infection, and influenza, the chance of antibiotic chemotherapy was 8% of that in unvaccinated patients (p < 0.05). In the group of mono-vaccination, the chance of antibiotic chemotherapy was 21% of that in unvaccinated (p < 0.05).
\nIn COPD patients from Groups I and II, FVC changes did not undergo any statistically significant changes over 12 months (Table 3). In Group I (patients vaccinated against pneumococcal, Hemophilus type b infection, and influenza), forced expiratory volume in 1 s (FEV1) increased to 57.4% (2.0%) at 12 months vs. 53.9% (2.7%) at baseline (p < 0.05). In unvaccinated patients (Group II), these parameters remained unchanged: 54.1% (1.9%) at baseline vs. 50.4% (2.8%) at 12 months (p > 0.05), indicating that the rate of FEV1 decrease was lower in vaccinated COPD patients (Group I). Detailed characteristics of FEV1 changes in Groups I and II depending on the disease severity are given in Table 4, and Table 5 outlines the same for Tiffeneau index.
\nCOPD grade | \nAt baseline | \nAt 12 months | \n||
---|---|---|---|---|
Abs., ml | \n% | \nAbs., ml | \n% | \n|
1 (n = 3/n = 24) | \n3611 (466) | \n100.7 (3) | \n3724 (489) | \n104 (0.4) | \n
3608 (206) | \n97.8 (3.2) | \n3572 (176) | \n95.6 (2.9) | \n|
2 (n = 23/n = 25) | \n2943 (180) | \n78.9 (3.3) | \n2867 (169) | \n79.3 (3.3) | \n
2936 (173) | \n77.9 (4.1) | \n2918 (167) | \n76.9 (3.5) | \n|
3 (n = 18/n = 25) | \n2301 (129) | \n55.2 (2.8) | \n2173 (208) | \n53.3 (3.5) | \n
2311 (128) | \n55.2 (2.7) | \n2086 (96.2) | \n51.2 (2.6) | \n|
4 (n = 4/n = 6) | \n1854 (116) | \n46.6 (5.6) | \n2158 (119)& | \n55.8 (3.8)& | \n
1845 (129) | \n45.2 (5.1) | \n1778 (106) | \n43.3 (2.2) | \n|
Total (n = 48/n = 80) | \n2653 (119) | \n68.7 (2.9) | \n2602 (131) | \n68.3 (2.9) | \n
2648 (122) | \n67.9 (2.5) | \n2562 (131) | \n64.8 (2.2) | \n
FVC changes in COPD patients from Groups I and II over 12 months.
Data are presented as means (standard deviation).
Group I patients in the numerator, Group II patients in the denominator.
& p < 0.05—differences between Groups I and II (Student’s test).
COPD grade | \nAt baseline | \nAt 12 months | \n||
---|---|---|---|---|
Abs., ml | \n% | \nAbs., ml | \n% | \n|
1 (n = 3/n = 24) | \n2412 (236) | \n86.7 (1.6) | \n2597 (337) | \n90.5 (1.1)&& | \n
2399 (205) | \n85.8 (2.0) | \n2384 (136) | \n85.4 (1.2) | \n|
2 (n = 23/n = 25) | \n1954 (112) | \n66.1 (2.1) | \n1985 (109) | \n69.9 (2.6)& | \n
1959 (110) | \n66.4 (2.7) | \n1916 (102) | \n62.9 (1.4) | \n|
3 (n = 18/n = 25) | \n1274 (65.1) | \n39.1 (1.4) | \n1314 (101) | \n42.0 (2.2) | \n
1280 (69.3) | \n40.0 (1.3) | \n1204 (76.3) | \n37.2 (1.6) | \n|
4 (n = 4/n = 6) | \n876 (106.5) | \n26.9 (1.4) | \n951 (106.5) | \n28.6 (2.7) | \n
883 (115.5) | \n27.9 (1.2) | \n826 (97.2) | \n25.9 (1.0) | \n|
Total (n = 48/n = 80) | \n1638 (86.6) | \n53.9 (2.7) | \n1685 (95.4) | \n57.4 (2.0)& | \n
1642 (92.5) | \n54.1 (1.9) | \n1574 (94.4) | \n50.4 (2.8) | \n
FEV1 changes in COPD patients from Groups I and II over 12 months.
Data are presented as means (standard deviation).
Group I patients in the numerator, Group II patients in the denominator.
& p < 0.05; && p < 0.01—differences between Groups I and II (Student’s test).
COPD grade | \nAt baseline | \nAt 12 months | \n
---|---|---|
% | \n% | \n|
1 (n = 3/n = 24) | \n67.27 (1.95) | \n69.8 (0.1) | \n
66.34 (2.18) | \n68.4 (0.89) | \n|
2 (n = 23/n = 25) | \n67.14 (2.04) | \n69.9 (2.29)& | \n
66.85 (1.95) | \n64.24 (1.58) | \n|
3 (n = 18/n = 25) | \n56.68 (2.59) | \n62.39 (2.61) | \n
55.43 (2.12) | \n58.4 (2.53) | \n|
4 (n = 4/n = 6) | \n47.85 (6.69) | \n44.2 (4.95) | \n
47.38 (5.12) | \n45.84 (2.53) | \n|
Total (n = 48/n = 80) | \n61.62 (1.73) | \n64.93 (1.94)& | \n
60.98 (1.85) | \n59.13 (2.15) | \n
Tiffeneau index changes in COPD patients from Groups I and II over 12 months.
Data are presented as means (standard deviation).
Group I patients in the numerator, Group II patients in the denominator.
& p < 0.05—differences between Groups I and II (Student’s test).
One year post vaccination, vaccinated COPD patients (Group I) showed 6MWT results that were 75.2% (2.8%) of the desired values vs. 60.4% (2.3%) in Group II patients (p < 0.001). Detail characteristics of the dynamics of the 6-minute walk test depending on the disease severity are given in Table 6.
\nCOPD grade | \nAt baseline | \nAt 12 months | \n||
---|---|---|---|---|
Abs., m | \n% | \nAbs., m | \n% | \n|
1 (n = 3/n = 24) | \n440 (49.0) | \n86.1 (8.6) | \n450 (54.5) | \n92.8 (4.3) | \n
434 (52.8) | \n84.7 (9.1) | \n429 (41.2) | \n83.5 (4.2) | \n|
2 (n = 23/n = 25) | \n355 (13.1) | \n71.8 (2.4) | \n401 (15.8)*,&&& | \n81.2 (3.1)*, &&& | \n
351 (10.2) | \n70.9 (2.6) | \n324 (8.7)# | \n64.1 (1.2)# | \n|
3 (n = 18/n = 25) | \n314 (21.1) | \n64.0 (3.8) | \n338 (26.4) | \n69.7 (4.3)& | \n
319 (20.3) | \n64.1 (3.6) | \n296 (17.1) | \n59.4 (1.7) | \n|
4 (n = 4/n = 6) | \n230 (45.2) | \n47.4 (13) | \n266 (37.3) | \n54 (12.3) | \n
235 (40.3) | \n48.6 (10.3) | \n213 (10.5) | \n44.2 (2.3) | \n|
Total (n = 48/n = 80) | \n335 (12.6) | \n67.8 (2.4) | \n369 (14.5)&&& | \n75.2 (2.8)*, &&& | \n
332 (18.4) | \n66.3 (2.6) | \n305 (10.5) | \n60.4 (2.3) | \n
Dynamics of 6MWT in COPD patients from Groups I and II over 12 months.
Data are presented as means (standard deviation).
Group I patients in the numerator, Group II patients in the denominator.
* p ˂ 0.05 vs. baseline values in Group I (Student’s test).
# p < 0.05 vs. baseline values in Group II (Student’s test).
& p ˂ 0.05; &&& p < 0.001—differences between Groups I and II (Student’s test).
Detailed characteristics of spirometry data in COPD patients from Groups III and IV are presented in Table 7.
\nParameter | \nVaccinated against influenza (Group III, n = 20) | \nUnvaccinated (Group IV, n = 20) | \n|||
---|---|---|---|---|---|
At baseline | \nAt 12 months | \nAt baseline | \nAt 12 months | \n||
FVC | \nAbs. | \n1.62 (0.18) | \n1.71 (0.13) | \n2.05 (0.12) | \n1.88 (0.16) | \n
% | \n37.69 (3.61) | \n42 (2.74) | \n47.06 (2.9) | \n41.94 (3.05) | \n|
FEV1 | \nAbs. | \n1.13 (0.13) | \n1.17 (0.08) | \n1.48 (0.1) | \n1.38 (0.11) | \n
% | \n33.65 (3.43) | \n35.76 (2.16) | \n42.25 (2.76) | \n40.83 (3.46) | \n|
FEV1/FVC | \n% | \n52.7 (3.42) | \n46.46 (3.2)& | \n55.8 (2.18) | \n57.9 (2.66) | \n
Spirometry values in COPD patients vaccinated against influenza (Group III) and in unvaccinated control patients (Group IV).
Data are presented as means (standard deviation).
& p < 0.05—differences between Groups III and IV at 12 months (Student’s test).
The analysis of the 6-minute walk test results showed a trend to distance increase by 13 m (+3.7%) 1 year after mono-vaccination (p > 0.05, Student’s test).
\nThus, the study demonstrated statistically significant increase in FEV1 [57.4% (2.0%)] at 12 months after complex vaccination when compared to unvaccinated COPD patients [50.4% (2.8%)]. This FEV1 increase was 3.5%, that is, not statistically significant vs. baseline value, although the positive trend was observed.
\nThe group of mono-vaccination against influenza also demonstrated the positive trend of FEV1 increase, but the increase was only 2.11%, which is less than 3.5% in the group of complex vaccination.
\nIn the group of complex vaccination, patients demonstrated significantly improved 6MWT results at 12 months vs. baseline distance. In Group I, the increase was 7.4% (+34 m), that is, statistically significant (p < 0.05). In patients vaccinated against influenza, 6MWT increase approached trend levels of significance.
\nPreviously, we have reported the dynamics of specific antibodies against influenza virus in COPD patients after complex vaccination against S. pneumoniae, H. influenzae type b, and influenza [11].
\nCombined vaccination against pneumococcal, H. influenzae type b and influenza is accompanied by production of antibodies to these infections, which persist during 1 year (observation period), regardless of disease severity. In patients with stage 4 COPD, the level of antibodies to influenza virus (strains A/H1N1, A/H3N2 and B) in post-vaccination period was lower than in patients with stages 1, 2, and 3. Probably, these patients should be vaccinated against influenza twice. Despite the fact that patients with COPD had lower levels of post-vaccination antibodies than control, they demonstrated apparent clinical effect throughout 12 months, which was recorded as reduction of both exacerbation number and the need in antibacterial medications. Combined vaccination against bacterial and viral infections contributes to the achievement of antibody levels leading to the development of significant clinical effect in patients with COPD.
\nTable 8 demonstrates lists immunogenicity parameter of the new immunoadjuvant vaccine against influenza after mono vaccination of COPD patients.
\nNo statistically significant differences in immunogenicity were found between COPD patients and healthy participants vaccinated only against influenza, the latter, however, demonstrated a trend toward higher immune response to vaccination.
\nIn the comparative analysis of COPD patients, in whom antibodies to all three influenza virus strains were detected at arbitrarily protective titres (≥1:40) at 6 months after vaccination, and patients, in whom, despite vaccination, antibody titres were <1:40, COPD patients at risk of low response to vaccination were identified. These patients had a long history of COPD with frequent respiratory infections and COPD exacerbations requiring hospitalization and systemic glucocorticosteroids or antibiotic chemotherapy.
\nVaccine strains | \nSeroconversion, % (N ≥ 40%) | \nSeroprotection, % (N ≥ 70%) | \nMean geometric antibody titre (N ≥ 40) | \n||||
---|---|---|---|---|---|---|---|
6 months | \n12 months | \n6 months | \n12 months | \nAt baseline | \n6 months | \n12 months | \n|
A/H1N1/Brisbane/59/07 | \n60 ± 16 | \n40 ± 16 | \n58 ± 14 | \n67 ± 14 | \n20 (log2 4.32 ± 0.36) | \n30.64 (log2 4.94 ± 0.38) | \n33.64^p(log2 5.07 ± 0.28) | \n
A/H3N2/Uruguay/716/2007 | \n70 ± 15 | \n50 ± 16 | \n75 ± 13 | \n83.3 ± 11 | \n24.75 (log2 4.63 ± 0.63) | \n71.91 (log2 6.17 ± 0.62) | \n59.93 (log2 5.91 ± 0.38) | \n
B/Florida/4/2006 | \n30 [15; 45] | \n10 [1; 20] | \n100 ± 0 | \n100 ± 0 | \n46.94 (log2 5.55 ± 0.30) | \n84.38 (log2 6.4 ± 0.33) | \n59.9 (log2 5.91 ± 0.38) | \n
Immunogenicity parameters of the new immunoadjuvant vaccine against influenza after mono-vaccination of COPD patients (n = 15).
Marked values meet CPMP requirements.
During post-vaccination period, treating physicians and patients as well focus their attention on the main disease course. The clinical course of the disease may be characterized by number of COPD exacerbations and the need for antibiotic chemotherapy. Both complex vaccination against S. pneumoniae, H. influenzae type b, and influenza and mono-vaccination with a new immunoadjuvant influenza vaccine led to statistically significant reduction in the number of COPD exacerbations and of antibiotic chemotherapy courses.
\nOur study had some limitations, that is, its pilot character, absence of randomization and blinding, and small sample size. As follows from the study results, complex vaccination of COPD patients against bacterial and viral respiratory infections have more expressed beneficial effects on their functional status when compared to mono-vaccination against influenza. Further well-designed multicenter clinical studies devoid of these limitations are needed to refine the hypothesis. Nevertheless, based on the obtained results, widespread implementation of mono-vaccination against influenza with a new immunoadjuvant influenza vaccine, as well as complex vaccination against bacterial respiratory infections and influenza can be recommended for COPD patients, as vaccination is beneficial for their functional status, that is, improves FEV1 and 6-minute walk test results.
\nMono-vaccination of COPD patients using immunoadjuvant vaccines of a new class as well as combined vaccination against S. pneumoniae, H. influenzae, and influenza is associated with protective antibody titres. In our study, we evaluated immunogenicity of the new influenza immunoadjuvant vaccine administered as mono-vaccine to COPD patients in accordance with CPMP requirements. Immune response to vaccine strains of influenza virus was more intense and durable in initially seropositive patients compared to seronegative.
\nCombined vaccination against pneumococcal, H. influenzae type b and influenza is accompanied by production of antibodies to these infections. In patients with stage 4, COPD the level of antibodies to influenza virus (strains A/H1N1, A/H3N2 and B) in post-vaccination period was lower than in patients with stages 1, 2, and 3. Probably, these patients should be vaccinated against influenza twice. Combined vaccination against bacterial and viral infections contributes to the achievement of antibody levels leading to the development of significant clinical effect in patients with COPD.
\nInfluenza prophylaxis in COPD patients implies annual influenza vaccination of all individuals having no contraindications regardless of the disease severity. Influenza vaccine prophylaxis must be included into patient’s care plan and into the list of recommendations given by a pulmonologist at an outpatient visit or at discharge from hospital. If possible, simultaneous vaccination against S. pneumoniae, H. influenzae type b, and influenza is recommended as early as possible before the season of respiratory infections starts. Combined vaccination against respiratory infections has more significant effects on clinical characteristics and functional status of COPD patients and promotes production of specific antibodies not only against vaccine strains of influenza virus but also against S. pneumoniae and H. influenzae antigens contained in the corresponding vaccines.
\nChina has nearly 100,000 reservoir dams, of which earth-rock dams account for more than 95% [1, 2]. Most of these reservoir dams were built in the 1950s and 1970s. Due to economic and technical conditions at that time, the problem of dangerous reservoirs in China was outstanding [3]. According to statistics [4], from 1954 to 2018, 3541 reservoir dams broke in China. The “75·8” flood occurred in Henan in 1975, which led to the collapse of 2 large reservoirs in Banqiao and Shimantan (Figures 1 and 2), 2 medium-sized reservoirs in Tiangang and Zhugou, and 58 small reservoirs, causing heavy casualties and property losses [5]. In the twenty-first century, with the improvement of the dam safety management level and the comprehensive development of the reservoir’s risk elimination and reinforcement, the number of dam breaks has been significantly reduced, but due to the frequent occurrence of extreme weather events, dams’ breaching still occur frequently. On July 19, 2018, the Zenglongchang Reservoir in Inner Mongolia and the Sheyuegou Reservoir in Xinjiang on August 1, 2018, successively dams’ breaching [4] (Figures 3 and 4).
\nFinal breach of Banqiao dam.
Final breach of Shimantan dam.
Final breach of Zenglongchang dam.
Final breach of Sheyuegou dam.
Therefore, it is necessary to establish a mathematical model and numerical calculation method that reasonably simulates the process of overtopping and seepage failure collapse, improves the prediction accuracy of the flood flow process of earth-rock dam collapse, and provides theoretical and technical support for the evaluation of the consequences of dam collapse and the preparation of emergency plans. This article will briefly introduce the research progresses on the mechanisms and numerical models of earth-rock dams’ breaching, especially the latest research results of the author’s research team in recent years, and make suggestions for future research.
\nThe mathematical model of earth-rock dams’ breaching is generally divided into three categories [6]: The first category is the parameter model. Most of these models are based on statistical analysis of dam-break case data, and empirical formulas are used to calculate and obtain dam-break-related parameters. Although most models cannot consider the erosion characteristics of damming materials, but the parameter model formula is simple and fast to calculate and is also often used for rapid evaluation of the consequences of dams’ breaching. The second category is a simplified mathematical model based on the mechanism of failure. It is generally assumed that the shape of the fractured breach (rectangular, inverted trapezoidal, triangular, etc.) remains unchanged during the dams’ breaching. The method based on the flow shear stress and the critical shear stress of the dam material or the erosion formula of the dam material is used to calculate the breach development process; the weir flow is used (overtopping dam failure) or pore flow (seepage failure dam breaching) formulas are used to calculate the breach flow. The stability analysis of the breach slope mostly uses the limit equilibrium method; generally, the numerical calculation method based on time step iteration is used to simulate the breach development process and the breach flow process. The advantage of this type of model is that it considers the failure mechanism of earth-rock dams, and the calculation speed is relatively fast, which is the most widely used in the numerical simulation of earth-rock dams dam breaching process. The third category is a detailed mathematical model based on the failure mechanism. In recent years, a series of researches on one-dimensional, average two-dimensional, and three-dimensional mathematical models based on the hydrodynamic dam material erosion equation have made significant progress, which can simulate the dams’ breaching process of earth-rock dams in more detail. In order to deal with the diffuse overtopping flow composed of discontinuous mixed flow states, shock wave capturing methods such as approximate Riemann solution method and total variation declining (TVD) method are generally used, and finite volume method, level set method, and smooth particle hydrodynamic method are used to solve the governing equation. This type of model is a fast-developing simulation method in recent years, but it can only be used for the simulation of the overtopping collapse process of homogeneous dams or landslide dams. It has not been used to simulate the process of seepage and failure of earth-rock dams and the simulation of the process of overtopping failure of other types of earth-rock dams [6].
\nIn 1977, Kirkpatrick [7] proposed the first empirical formula for predicting peak outflow Qp\n, and then scholars from various countries proposed a series of models. With the continuous enrichment of dam failure case investigation data and the deepening of research, the dam failure parameter model has gradually evolved from the single-parameter model to a multi-parameter model, and the output results have increased from the original peak outflow of the breach to the final average width of the breach and the duration of the dam and can consider the shape of the dam body, reservoir capacity, dam material characteristics, etc. The peak outflow rate of breach is very important for the evaluation of the consequences of dam breaching. Therefore, domestic and foreign scholars have studied more. The commonly used parameter model of peak outflow rate is shown in Table 1.
\nModel | \nCase number | \nExpression | \n
---|---|---|
Kirkpatrick (1977) [7] | \n19 | \n\nQp\n = 1.268(hw\n + 0.3)2.5\n | \n
Soil Conservation Service (1981) [8] | \n13 | \n\nQp\n = 16.6hw\n\n1.85\n | \n
Hagen (1982) [9] | \n6 | \n\nQp\n = 0.54(hdS)0.5\n | \n
Singh and Snorrason (1984) [10] | \n28 | \n\nQp\n = 13.4hd\n\n1.89 or Qp\n = 1.776S\n0.47\n | \n
MacDonald and Langridge-Monopolis (1984) [11] | \n23 | \n\nQp\n = 1.154(Vwhw\n)0.412\n | \n
Costa (1985) [12] | \n31 | \n\nQp\n = 0.981(hdS)0.42\n | \n
Evans (1986) [13] | \n29 | \n\nQp\n = 0.72Vw\n\n0.53\n | \n
USBR (1988) [14] | \n21 | \n\nQp\n = 19.1hw\n\n1.85\n | \n
Froehlich (1995) [15] | \n22 | \n\nQp\n = 0.607Vw\n\n0.295\nhw\n\n1.24\n | \n
Walder and O’Connor (1997) [16] | \n18 | \n\nQp\n = 0.031 g\n0.5\nVw\n\n0.47\nhw\n\n0.15\nhb\n\n0.94\n | \n
Xu and Zhang\n1\n (2009) [17] | \n75 | \n\nQp\n = 0.175 g\n0.5\nVw\n\n5/6(hd\n/hr\n)0.199(Vw\n\n1/3/hw\n)−1.274\neB\n\n4\n | \n
Pierce et al. (2010) [18] | \n87 | \n\nQp\n = 0.0176(Vh)0.606or Qp\n = 0.038 V\n0.475 h\n1.09\n | \n
Thornton et al. (2011) [19] | \n38 | \n\nQp\n = 0.1202 L\n1.7856 or Qp\n = 0.863 V\n0.335\nhd\n\n1.833\nWave\n\n−0.663or\nQp\n = 0.012 V\n0.493\nhd\n\n1.205\nL\n0.226\n | \n
Lorenzo and Macchione (2014) [20] | \n14 | \n\nQp\n = 0.321 g\n0.258(0.07Vw\n)0.485\nhb\n\n0.802(overtopping) \nQp\n = 0.347 g\n0.263(0.07Vw\n)0.474\nhb\n\n−2.151\nhw\n\n2.992(seepage failure) | \n
Hooshyaripor et al. (2014) [21] | \n93 | \n\nQp\n = 0.0212 V\n0.5429\nh\n0.8713 or Qp\n = 0.0454 V\n0.448\nh\n1.156\n | \n
Azimi et al. (2015) [22] | \n70 | \n\nQp\n = 0.0166(gV)0.5\nh\n | \n
Froehlich\n2\n (2016) [23] | \n41 | \n\nQp\n = 0.0175kMkH\n(gVwhwhb\n\n2/Wave\n)0.5\n | \n
Mei Shiang et al. (2018) [24] | \n154 | \n\nQp = Vwg\n0.5\nhw\n\n−0.5(Vw\n\n1/3/hw\n)−1.58(hw\n/hb\n)−0.76(hd\n/h\n0)0.10e−4.55(homogeneous dam) \nQp = Vwg\n0.5\nhw\n\n−0.5(Vw\n\n1/3/hw\n)−1.51(hw\n/hb\n)−1.09(hd\n/h\n0)−0.12e−3.61 (core-wall dam) | \n
Parameter model of peak outflow rate.
The expression of parameter B\n4 is B\n4 = b\n3 + b\n4 + b\n5, for core-wall dam, concrete face rockfill dam or homogeneous dam, b\n3 is taken as −0.503, 0.591, or − 0.649, respectively; for overtopping or seepage failure, b\n4 is taken as −0.705 or − 1.039, respectively; for dam materials with high, medium, or low erosion rate, b5\n is taken as −0.007, −0.375, or − 1.362, respectively.
For overtopping dam failure, kM\n = 1.85; for seepage failure dam failure, kM\n = 1; when hb\n ≤ 6.1 m,kH\n = 1; when hb\n > 6.1 m, kH\n = (hb\n/6.1)1/8.
\nQp\n is the peak outflow of the breach; hw\n is the water depth above the bottom of the breach when the dam breaks; hd\n is the height of the dam; S is the reservoir capacity; Vw\n is the reservoir capacity above the bottom of the breach when the dam breaks; g is the gravity acceleration; hb\n is the depth of the dam breaks; hr\n is the reference dam height, take 15 m; V is the reservoir capacity at dam breaching; h is the water level at dam breaching; L is the length of the dam; Wave\n is the average width of the dam; kM\n and kH\n are coefficients.
In 1988, the US Bureau of Reclamation (USBR) [14] proposed the first empirical formula for predicting the final average width of the breach Bave\n, and then scholars from various countries put forward a series of models. The commonly used parameter model of the final average width of the breach is shown in Table 2.
\nModel | \nCase number | \nExpression | \n
---|---|---|
USBR (1988) [14] | \n21 | \n\nBave\n = 3hw\n\n | \n
Von Thun and Gillette\n1\n (1990) [25] | \n57 | \n\nBave\n = 2.5 hw\n + Cb\n\n | \n
Froehlich\n2\n (1995) [26] | \n22 | \n\nBave\n = 0.1803 K\n0(Vw\n)0.32(hb\n)0.19\n | \n
Xu and Zhang\n3\n (2009) [17] | \n75 | \n\nBave\n = 0.787(hb\n)(hd\n/hr\n)0.133(Vw\n\n1/3/hw\n)0.652\neB\n\n3\n | \n
Froehlich\n4\n (2016) [23] | \n41 | \n\nBave\n = 0.27kM\n(Vw\n)1/3\n | \n
Mei Shiang et al. (2018) [24] | \n154 | \n\nBave = hb\n(Vw\n\n1/3/hw\n)0.84(hw\n/hb\n)2.30(hd\n/h\n0)0.06e−0.90(homogeneous dam) \nBave = hb\n(Vw\n\n1/3/hw\n)0.55(hw\n/hb\n)1.97(hd\n/h\n0)−0.07e−0.09(core-wall dam) | \n
Parameter model of the final average width of the breach.
When S < 1.2335 × 106 m3, Cb\n = 6.096; when 1.2335 × 106 m3 ≤ S < 6.1676 × 106 m3, Cb\n = 18.288; when 6.1676 × 106 m3 ≤ S < 1.2335 × 107 m3, Cb\n = 42.672; when S ≥ 1.2335 × 107 m3, Cb\n = 54.864.
For overtopping dam failure, K\n0 = 1.4; for seepage failure dam breaching, K\n0 = 1.0.
\nhr\n is the dam height, which is 15 m; the expression of parameter B\n3 is B\n3 = b\n3 + b\n4 + b\n5, for core-wall dam, concrete face rockfill dam or homogeneous dam, b\n3 takes −0.041, 0.026 or 0.226; for overtopping or seepage failure, b\n4 = 0.149 or − 0.389, respectively; for dams with high, medium, or low erosion rate, b5\n is 0.291, 0.14, or 0.391, respectively.
For overtopping dam failure, kM\n = 1.3; for seepage failure dam breaching, kM\n = 1.0.
In 1984, MacDonald and Langridge-Monopolis [42] proposed the first empirical formula for predicting the duration of dam failure, and then scholars from various countries proposed a series of models. Commonly used dam-break duration parameter model is shown in Table 3.
\nModel | \nCase number | \nExpression | \n
---|---|---|
MacDonald and Langridge-Monopolis (1984) [11] | \n23 | \n\nTf\n = 0.0179(0.0261(Vwhw\n)0.769)0.364\n | \n
USBR (1988) [14] | \n21 | \n\nTf\n = 0.011Bave\n\n | \n
Froehlich (1995) [26] | \n22 | \n\nTf\n = 0.00254(Vw\n)0.53(hb\n)−0.9\n | \n
Xu and Zhang\n1\n (2009) [17] | \n75 | \n\nTf\n = 0.304Tr\n(hd\n/hr\n)0.707(Vw\n\n1/3/hw\n)1.228\neB\n\n5\n | \n
Froehlich (2016) [23] | \n41 | \n\nTf\n = 63.2(Vw\n/(ghb\n\n2))0.5\n | \n
Mei Shiang et al.\n2\n (2018) [24] | \n154 | \n\nTf = T\n0(Vw\n\n1/3/hw\n)0.56(hw\n/hb\n)−0.85(hd\n/h\n0)−0.32e−0.20(homogeneous dam) \nTf = T\n0(Vw\n\n1/3/hw\n)1.52(hw\n/hb\n)−11.36(hd\n/h\n0)−0.43e−1.57(core-wall dam) | \n
Dam-break duration parameter model.
Tr means the duration of the reference dam break, take 1 h; the expression of parameter B5 is B5 = b3 + b4 + b5, for core-wall dam, concrete face rockfill dam, or homogeneous dam, b3 takes −0.327, −0.674, or − 0.189; for overtopping or seepage failure, b4 = −0.579 or − 0.611, respectively; for dam materials with high, medium, or low erosion rate, b5 is −1.205, −0.564, or 0.579 respectively.
T0 means unit duration, take 1 h.
Due to the difficulties in obtaining the dam-break duration, the relatively low accuracy of the data, and the small number of samples, the dam-break duration model has a large deviation in the calculation of individual cases.
\nIn order to fully consider the dam type, dam breach mode, reservoir characteristics, and breach characteristics, the reservoir capacity (Vw\n) is above the bottom of the breach at the dam break, the water depth (hw\n) above the bottom of the dam at the dam break (hd\n), and the final depth of the rupture (hb\n). For other parameters, the method of statistical regression is used to obtain the results of the peak flow of the breach, the final average width of the breach, and the duration of the dam breach. From the above statistics, it can be seen that the parameter model can simulate the dam-break parameters simply and quickly, which is an efficient and rapid evaluation method, but the parameter model cannot provide the dam-break flood flow process line.
\nIn the 1960s, European and American scholars began to study a simplified mathematical model based on the mechanism of collapse based on hydraulics and sediment transport formulas. This model is also the most widely used mathematical model of earth-rock dams’ breaching. In 1965, from the US Bureau of Reclamation, Cristofano [27] established the first mathematical model of homogeneous dam overtopping failure. Afterward, scholars from various countries proposed a series of mathematical models for simulating earth-rock dam collapse [6, 28]. The most widely used is the NWS BREACH model developed by Fread from the National Weather Service [29]. In recent years, the Nanjing Hydraulic Research Institute and China Institute of Water Resources and Hydropower Research have conducted systematic research work on the mathematical model of earth-rock dams’ breaching, establishing NHRI-DB series and DB-IWHR series dam-break mathematical models, respectively. The commonly used simplified mathematical model of earth-rock dam breaching is shown in Table 4.
\nModel | \nShape of breach | \nThe flow of the breach | \nErosion formula | \nMechanical analysis | \nBreach mode | \nType of dam | \n
---|---|---|---|---|---|---|
Cristofano (1965) [27] | \nTrapezoid | \nWide crest weir formula | \nCristofano formula | \nBreach without lateral collapse | \nOvertopping | \nHomogeneous | \n
BRDAM (1981) [30] | \nParabolic | \nWide crest weir formula, vent flow formula | \nSchoklitsch formula | \nBreach without lateral collapse (overtopping), top collapse (seepage) | \nOvertopping or seepage | \nHomogeneous | \n
DAMBRK (1984) [31] | \nTrapezoid or rectangle | \nWide crest weir formula | \nEven flush | \nBreach without lateral collapse | \nOvertopping | \nHomogeneous | \n
BEED (1985) [32] | \nTrapezoid | \nWide crest weir formula | \nEinstein and Brown formula, Meyer-Peter-Mueller formula | \nCollapse laterally | \nOvertopping | \nHomogeneous | \n
NWS BREACH (1988) [29] | \nTrapezoid or rectangle | \nWide crest weir formula, vent flow formula | \nCorrection Meyer-Peter-Mueller formula | \nCollapse laterally (overtopping), top collapse (seepage) | \nOvertopping or seepage | \nHomogeneous, core wall | \n
HR BREACH (2002, 2009) [33, 34] | \nEffective stress method | \n1D stable non-uniform weir flow formula | \nSediment transport formula or erosion rate formula | \nSingle (two) side erosion, collapse laterally, stability analysis of core wall | \nOvertopping or seepage | \nHomogeneous earth dam, core wall | \n
FIREBIRD (2006) [35] | \nTrapezoid | \nUnsteady Saint-Venant equation | \nSediment transport formula or erosion rate formula | \nCollapse laterally | \nOvertopping | \nHomogeneous | \n
WinDAM/SIMBA (2005, 2006, 2010) [36, 37, 38] | \nRectangle | \nWide crest weir formula | \nErosion rate formula | \nBreach without lateral collapse | \nOvertopping | \nHomogeneous | \n
DLBreach (2013) [40] | \nTrapezoid | \nWide crest weir formula, vent flow formula | \nSediment transport formula or erosion rate formula | \nSingle (two) side erosion, collapse laterally, stability analysis of core wall, dam foundation erosion | \nOvertopping or seepage | \nHomogeneous, core wall | \n
Hong Kong University of Science and Technology model [39] | \nTrapezoid | \nWide crest weir formula, vent flow formula | \nErosion rate formula | \nCollapse laterally (overtopping), top collapse (seepage) | \nOvertopping or seepage | \nHomogeneous, landslide | \n
DB-IWHR series dam-break mathematical model of China Institute of Water Resources and Hydropower Research [41, 42, 43] | \nTrapezoid | \nWide crest weir formula | \nErosion rate formula | \nCollapse laterally | \nOvertopping | \nHomogeneous, core wall, landslide dam | \n
NHRI-DB series dam-break mathematical model of Nanjing Hydraulic Research Institute [44, 45, 46, 47, 48] | \nTrapezoid | \nWide crest weir formula, vent flow formula | \nSediment transport formula or erosion rate formula | \nShearing or dumping of the core wall, panel break, collapse laterally (overtopping), top collapse (seepage) | \nOvertopping or seepage | \nHomogeneous, core wall, face dam, landslide | \n
Simplified mathematical model of earth-rock dam breaching.
It can be seen from the above analysis that this type of model is mainly aimed at the two failure modes of earth-rock dam overtopping and seepage failure. By assuming the shape of the breach, different flow calculation formulas and erosion formulas are used to simulate the scouring of the dam material, and different simulation methods are used to analyze the vertical undercut and lateral expansion of the breach. Most of the models use iterative numerical calculation methods based on time steps to simulate the process of dam break and can output the parameters of dam break (such as the flow of the breach, the size of the breach, the water level of the reservoir, etc.) at each time step.
\nFor example, based on the overtopping breach mechanism of the clay-core wall dam, a mathematical model to simulate its breach process is proposed. The model is based on the shape of the dam body and the characteristics of the flood flow to determine the initial scoring position of the downstream slope during erosion. The flow formula of the wide crested weir is used to calculate the rupture flow. The mechanical equilibrium method is used to simulate the tipping and shear failure of the core wall; the model can also consider the erosion of the dam body on one side, the erosion on both sides, and the erosion of the dam foundation and the process of water and soil coupling during dam break.
\nBased on the mechanism revealed by the model test of the overtopping breach of the homogeneous cohesive earth dam, the author has established a mathematical model that can simulate its collapse process (Figure 5). The specific modules of the model are as follows.
\nSchematic diagram of the author’s model calculation process. (1) Breach formation, (2) Scarp formation, (3) Scarp widen, (4) Headcut scour, (5) Breach widen, (6) Breach fully formed.
This model is based on the shape of the dam body and the characteristics of the flow at the top of the crater to determine the formation position of the “dark ridge.” The traceable erosion formula that can consider the physical and mechanical characteristics of the dam material is used to simulate the movement of the “dark ridge.” The collapse of the dam body: choose a reasonable erosion formula of the dam material to simulate the development of the dam crest and the downstream slope failure, and use the limit equilibrium method to simulate the failure of the collapse slope. The model considers incomplete dam failure and erosion of the dam foundation, as well as erosion on one side and both sides of the dam body.
\nThe flow chart of the model calculation process of the collapse process of the homogeneous earth dam is shown in Figure 6.
\nCalculation flow chart of the process of overburden collapse of the homogeneous earth dam.
There are two major highlights of the NHRI-DB concrete-face dam-break mathematical model [47]: the adoption of total-load nonequilibrium transport equation (Eq. (1)) [72] to simulate the erosion process of sand gravels with a wide range of gradation and the establishment of an analogy to simulate the failure process of each concrete-face slab under various loads during the dam breaching process.
\nwhere t = time; x = longitudinal coordinate; A = cross-sectional flow area in the breach channel; Ct\n = actual total-load sediment concentration; Ct\n = sediment concentration at the equilibrium state; and L\ns = adaptation length characterizing the adjustment of sediment from a nonequilibrium state to equilibrium state.
\nIn the NHRI-DB core dam-break mathematical model [45], a hydraulic method was used to predict the initial scour position for high dam. A time averaged erosion equation was adopted to simulate the backward erosion of dam’s shoulder. The broad-crested weir equation (Eqs. (2) and (3)) [73, 74] was adopted to calculate the breach flow discharge. Furthermore, the sliding or overturning failure was adopted as the key mechanism for the core, which was judged based upon numerical analysis. The calculated results show that the proposed model gives reasonable peak outflow, final breach width, and failure time.
\nwhere Bb\n is the bottom width of the breach (m), H represents the difference “zs − zb\n” (m), in which zb\n is the elevation of the breach bottom (m), m is the side slope (horizontal/vertical) of the breach, c1\n and c2\n are the discharge coefficients with values of 1.7 m0.5/s and 1.3 m0.5/s [73], and ksm is the submergence correction factor for tailwater effects on weir outflow.
\nwhere zt\n is the tailwater level (m).
\nThe advantage of this type of model is that it can consider the failure mechanism of the earth-rock dam and can use a short calculation time to complete the simulation of the dam-break process; however, most models cannot really consider the water-soil coupling effect during the dam-break process.
\nIn order to fully describe the water-soil coupling effect in the process of dams’ breaching, in recent years, with the improvement of computer performance and the development of sediment science and computational fluid dynamics, a series of nonequilibrium dam material transport theory has emerged based on shallow water hypothetical detailed mathematical model for dam failure [49]. The commonly used detailed mathematical model of earth-rock dams’ breaching is shown in Table 5.
\nModel | \nDetermination method of breach shape | \nFlow of breach | \nDam material erosion | \nMechanical analysis | \nCalculation method | \n
---|---|---|---|---|---|
Wang and Bowles (2006) [50] | \nScour without sediment motion | \nShallow water equations | \nErosion rate formula | \nThree-dimensional collapse laterally | \nFinite different method | \n
Faeh (2007) [51] | \nTwo-dimensional Exner equations | \nShallow water equations | \nTraction load and suspended load formula | \nCollapse laterally | \nFinite volume method | \n
Wu et al. (2007, 2012) [52, 53] | \nOne- and two-dimensional nonequilibrium total sand transport equations | \nGeneral shallow water equations | \nTotal sand transport formula | \nCollapse laterally | \nFinite volume method | \n
Swartenbroekx et al. (2010) [54] | \nTwo-dimensional Exner equations | \nShallow water equations | \nTraction load formula | \nCollapse laterally | \nFinite volume method | \n
Li et al. (2011) [55] | \nTwo-dimensional nonequilibrium sediment transport equations (suspended load) | \nShallow water equations | \nEmpirical formulas of sediment carrying rate and Sedimentation rate | \nBreach without lateral collapse | \nFinite volume method | \n
Cao et al. (2011) [56] | \nTwo-dimensional nonequilibrium total sediment transport equations | \nGeneral shallow water equations | \nTraction load formula | \nCollapse laterally | \nFinite volume method | \n
Rosatti and Begnudelli (2013) [57, 58] | \nTwo-dimensional mass conservation and energy conservation equations (solid phases) | \nShallow water equations (liquid) | \nFloe concentration formula | \nBreach without lateral collapse | \nFinite volume method | \n
Juez et al. (2013, 2014) [59, 60] | \nOne- and two-dimensional Exner equations | \nSaint-Venant equations and shallow water equations | \n10 different erosion formulas | \nBreach without lateral collapse | \nFinite volume method | \n
Swartenbroekx et al. (2013) [61] | \nTwo-dimensional mass conservation and energy conservation equations (traction load) | \nShallow water equations (clean water) | \nErosion rate formula | \nBreach without lateral collapse | \nFinite volume method | \n
Guan et al. (2014) [62] | \nTwo-dimensional nonequilibrium sediment transport equations (traction load) | \nShallow water equations (pure water) | \nTraction load formula | \nCollapse laterally | \nFinite volume method | \n
Kesserwani et al. (2014) [63] | \nTwo-dimensional nonequilibrium sediment transport equations (suspended load) | \nShallow water equations | \nEmpirical formulas of sediment carrying rate and sedimentation rate | \nBreach without lateral collapse | \nIntermittent Galerkin method | \n
Razavitoosi et al. (2014) [64] | \nN-S equations (solid phases, non-Newtonian fluid) | \nN-S equations (liquid, non-Newtonian fluid) | \n/ | \nBreach without lateral collapse | \nSmoothed particle hydrodynamics method | \n
Marsooli and Wu (2015) [65] | \nThree-dimensional nonequilibrium sediment transport equations | \nN-S equations | \nTraction load and suspended load formula | \nBreach without lateral collapse | \nFinite volume method and volume of fluid | \n
Abderrezza et al. (2016) [66] | \nTwo-dimensional Exner equations | \nShallow water equations | \nTraction load formula | \nCollapse laterally | \nFinite volume method | \n
Cantero-Chinchilla et al. (2016) [67] | \nOne-dimensional nonequilibrium sediment transport equations | \nSaint-Venant equations, vertical momentum equation | \nTraction load and suspended load formula | \nBreach without lateral collapse | \nFinite volume method | \n
Cristo et al. (2016, 2018) [68, 69] | \nTwo-dimensional mass conservation and energy conservation equations (solid phase) | \nShallow water equations (liquid) | \nTraction load formula | \nBed collapse algorithm | \nFinite volume method | \n
YAN Zhikun et al. (2019) [70] | \nTwo-dimensional nonequilibrium sediment transport equations | \nGeneral shallow water equations | \nTotal sand transport formula considering bed slope | \nBed collapse algorithm | \nFinite volume method | \n
Detailed mathematical model of earth-rock dams’ breaching.
It can be seen from the above statistics that this type of model is mainly based on the continuity equations of water flow (Eq. (4)), momentum equations (Eq. (5)), and energy equations (Eq. (6)), coupled with the sediment movement equation, and the finite volume method and other numerical simulation methods are used to discretely solve the governing equations
\nIn Yan Zhikun’s model [70], based on the continuity equations of water flow, momentum equations, and nonequilibrium sediment transport equations, a planar two-dimensional mathematical model of dam rupture along the depth average is proposed. The sand capacity and the collapse mechanism of the two-dimensional slope during the dam-break process. The fully coupled method is used to convert the hydrodynamic equation and the nonequilibrium sediment transport equation into a shallow water equation with source terms and is based on the finite volume method under a rectangular grid. Discrete processing, using conservative, non-negative water depth numerical reconstruction format to make the model have second-order accuracy in the space–time direction, using HLLC [71] approximate Riemann solver to calculate grid boundary flux, SGM (Surface Gradient Method) format to calculate water surface gradient source terms, semi-implicit format. For the bottom bed friction term, the explicit gradient calculation of the source term of the concentration gradient is used to numerically solve the control equation.
\nSuch models can achieve detailed simulation of the dam-break process, but the calculation speed is slow, and it can only be used for the numerical simulation of the overtopping dams’ breaching. However, this method can fully consider the coupling effect of water-soil coupling in the process of dam failure and can simulate complex boundary conditions, which is the development direction of numerical simulation of earth-rock dams’ breaching.
\nEarth-rock dams’ breaching mechanism and dam-break process simulation are the foundation of dam-break disaster assessment and emergency response. They involve fluid mechanics, sediment kinematics, soil mechanics, and other disciplines. They are complex water-soil coupling problems. After decades of research and exploration, various mathematical models of dams’ breaching have been developed and made a series of innovative achievements, which provide theoretical support for improving the accuracy of flood disaster prediction of earth-rock dams. It is suggested that in the future, research efforts should be intensified on the mathematical model of the detailed simulation of the earth-rock dam breaching process, focusing on the application of visualization technology in the simulation of the dam-break process and accelerating the development of a universal and friendly simulation of the earth-rock dams’ breaching and the visual calculation of the disaster-causing process software.
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