CN103074895B - A kind of foundation pit anchor unsticking safe evaluation method - Google Patents

Abstract

The invention discloses a kind of foundation pit anchor unsticking safe evaluation method, the method comprises the following steps: the structure of (1) accident tree; (2) determination of minimal cut set; (3) determination of elementary event probability; (4) quantitative analysis; (5) preventive damage control is formulated.The analytical method that the present invention adopts expert survey and accident tree method to combine, the given probability of foundation pit anchor unsticking accident bottom event, calculate the top event probability that such engineering accident occurs, the sensitiveness of each elementary event is sorted, analyze the main latency causing foundation pit anchor engineering unsticking failure damage, carry out safety evaluation report, for the risk management of system and the formulation of preventive action provide theoretical foundation.

Description

A kind of foundation pit anchor unsticking safe evaluation method

Technical field

The invention belongs to Safety Evaluation Technology field, relate to a kind of foundation pit anchor unsticking safe evaluation method.

Background technology

Safety evaluation is to realize for the purpose of engineering and security of system, identification and analysis is carried out to the danger existed in engineering, system and adverse factor, judge its possibility had an accident and the order of severity, proposition Security Countermeasures are advised, thus provide scientific basis for engineering, the system formulates precautionary measures and administrative decision.The program of safety evaluation mainly comprises: the preparatory stage, dangerous, adverse factor identification and analysis, and qualitative, quantitative evaluation proposes Safety Measures, forms safety evaluation conclusion and suggestion, establishment safety evaluation report.

Safe evaluation method conventional in construction project has expert evaluation method, Monte Carlo simulation approach, mathematics method, event tree method (ETA), accident tree method (FTA), analytic hierarchy process (AHP) (AHP) etc.

Event tree analysis (FaultTreeAnalysis, be called for short FTA) be comprehensive identification and the powerful of measure of risk, the method using be concerned about result event as top event, find out all direct factors and reason that cause this result event to occur and the intermediate event being in transition, till accident elementary event; And by based on the risk factor of the Sensitivity Analysis decision-making system of accident tree minimal cut set and the elementary event contribution degree for top event.

Bolt support is concealed work, add that the character of the soil body is complicated and changeable, anchor bolt works occurs that the phenomenon that disease is even had an accident is of common occurrence, brings great potential safety hazard to engineering construction, and serious even causes engineering interruption, casualties and bring great economic loss.Based on the advantage of FTA method, domestic more existing scholars are introduced into foundation pit anchor engineering field, but be only limitted to the research of method and thinking, how to provide the probability of accident tree bottom event, calculate the probability of top event, remain the insoluble problem that FTA is applied to the analysis of pit failure tree.

Summary of the invention

The object of the invention is to the defect overcoming the existence of above-mentioned technology, a kind of foundation pit anchor unsticking safe evaluation method is provided, adopt the analytical method that expert survey and accident tree method combine, the given probability of foundation pit anchor unsticking accident bottom event, calculate the top event probability that such engineering accident occurs, the sensitiveness of each elementary event is sorted, analyze the main latency causing foundation pit anchor engineering unsticking failure damage, carry out safety evaluation report, for the risk management of system and the formulation of preventive action provide theoretical foundation.

Its concrete technical scheme is:

A kind of foundation pit anchor unsticking safe evaluation method, comprises the following steps:

(1) structure of accident tree

Extensive analysis causes the relation between the intermediate event of top event cause and elementary event, and arranged, then from top event, according to the method for Deductive method, layer by layer deeply, by the refinement gradually of each influence factor, until all factors are the elementary event being difficult to refinement again, and according to the logical relation that each factor is determined between them to top event generation role, form accident tree;

(2) determination of minimal cut set

Minimal cut set adopt descending method try to achieve, the method is down carried out step by step along accident tree from top event, if run into and door, then with door below all incoming events all arrange on a same row; If run into or door, then or door below all incoming events all come on same row, by that analogy, step by step down, until till being all bottom event, the bottom event set obtained like this is called that boolean shows cut set, after the absorption Merging of Boolean algebra, just can obtain minimal cut set, and the elementary event comprised in minimal cut set is called the basic reason event of accident;

(3) determination of elementary event probability

Elementary event probability of happening is determined by expert survey:

Geological conditions is constantly change, the operation of engineering also can change the geological environment of surrounding conversely, therefore the probability of happening of each elementary event is without statistics, also cannot be drawn by design formulas, herein according to existing geologic information, tentatively be a unit with 10 years, adopt expert survey to provide experience estimate to the probability of happening of each elementary event within 10 years, carry out risk profile.

Key step is: a, to there being 20 of foundation pit anchor relevant professional knowledge or engineering experience experts to investigate; B, the academic title according to each expert, the corresponding weight of specialty setting; C, the judgement each expert done are weighted cumulative according to the weight of correspondence, and what finally obtain is exactly the most probable value of required target;

(4) quantitative analysis

Mainly comprise calculating two aspects of top event probability and each elementary event sensitivity coefficient:

A top event probability of happening utilizes minimal cut set to calculate;

If each other without the elementary event repeated in each minimal cut set, the probability of happening of top event is:

In formula, r is minimal cut set ordinal number; I is elementary event ordinal number; q _iit is the probability of i-th elementary event; N _gfor least partition assembly count in system; G _rbe r minimal cut set;

If minimal cut set has repeated events each other, when namely minimal cut set intersects, adopt method---the recursion method intersecting and turn to disjoint products will occurred in minimal cut set:

$T=F\left(1\right)+F\left(2\right)+\·\·\·\·\·\·+F\left(N_K\right)=\underset{i=1}{\overset{N_K}{\mathrm{\Σ}}}F\left(I\right)$

Wherein

F(I)＝C(I)K(I)，

K (I)=K _i, wherein, for L _isupplementary set,

N _kfor the sum of accident tree minimal cut set.

B elementary event sensitiveness sorts

Elementary event sensitivity coefficient: wherein, Q is probability of happening and P (T), the q of top event _ibe the probability of happening of i-th bottom event, sorted by elementary event sensitivity coefficient, the percentage contribution of elementary event for top event can be disclosed;

(5) preventive damage control is formulated

On the basis of qualitative or quantitative analysis, the preventible complexity of the minimal cut set that accident may be caused to occur according to each or the combination of minimum path sets elementary event and importance degree, in conjunction with practical capacity, draw up concrete, practicable preventive action, and be put to carry out.

Compared with prior art, beneficial effect of the present invention is:

(1) the present invention is according to the principle of accident tree, on the basis of reason and characteristic analyzing Foundation Pit of Bolt Support system generation unsticking accident, has built its accident tree graph.

(2) the present invention adopts the method that expert investigation and accident tree combine, and provides the experience estimate of each elementary event probability of happening, and the probability obtaining Foundation Pit of Bolt Support structure unsticking is 0.17023.Known with reference to underground construction risk probability classification standard, such event belongs to sporadic accident.

Accompanying drawing explanation

Fig. 1 is anchor pole unsticking accident tree.

Detailed description of the invention

Below in conjunction with the drawings and specific embodiments, technical scheme of the present invention is described in more detail.

The mathematical description of 1 accident tree

If x _irepresent the state variable of bottom event and top event respectively with φ, all only get 0 or 1 two states.Top event state φ determined by bottom event state X in accident tree completely, namely

φ＝φ(X)(1)

In formula 1, X=(x ₁, x ₂..., x _n), claim the structure function that φ (X) is FTA.Wherein i=1,2 ..., n, n are the sum of bottom event.

When top event T occurs, be namely equivalent to φ=1, the bottom event state that state is corresponding is therewith component, subsystem fault state, is equivalent to x _i=1.

Work as x _ionly get 0, when 1, be respectively with the structure function of door (condition and door) or door (conditioned disjunction door)

$\mathrm{\φ}\left(X\right)=\underset{i=1}{\overset{n}{\mathrm{\Π}}}{x}_i---\left(2\right)$

$\mathrm{\φ}\left(X\right)=1-\underset{i=1}{\overset{n}{\mathrm{\Π}}}(1-x_i)---\left(3\right)$

The construction of 2 foundation pit anchor unsticking accident tree

With reference to domestic and international foundation pit anchor unsticking cause of accident, and in conjunction with the mechanism of accident, determine that accident tree top event is foundation pit anchor unsticking accident, then to start with grouting body interface unsticking and be in the milk body and soil layer interface unsticking two aspects from the body of rod and analyze, layer by layer deeply, by the refinement gradually of each influence factor, until all factors are the elementary event being difficult to refinement again, and according to the logical relation that each factor is determined between them to top event generation role.The fault tree graph set up is shown in Fig. 1.Accident tree top event is foundation pit anchor unsticking accident, and intermediate event has two: the body of rod and grouting body interface unsticking and be in the milk body and soil layer interface unsticking.These two intermediate events are analyzed, layer by layer deeply, by the refinement gradually of each influence factor, until all factors are the elementary event being difficult to refinement again, and according to the logical relation that each factor is determined between them to top event generation role.

for with door, represent only as all incoming event E1, E2 ..., when En occurs, outgoing event just occurs.

for conditioned disjunction door, represent incoming event E1, E2 ..., En has at least an event to occur, and when satisfying condition event a, outgoing event just can occur.

for or door, represent have an incoming event E1 at least, E2 ..., when En event occurs, outgoing event occurs.

The each Event Description of fault tree is in table 1.

Symbol implication in table 1 accident tree

The analysis of 3 foundation pit anchor unsticking accident tree

The determination of 3.1 minimal cut sets

Minimal cut set is in fact the contingent approach of accident, and represent the danger of system, minimal cut set is more, and system is more dangerous.In the minimal cut set of accident tree, have 1 cut set to occur, top event just occurs.The cut set that elementary event is fewer, more easily occurs, and the possibility had an accident by this approach is larger, therefore the cut set few to elementary event answers emphasis to take preventive measures.

The present invention adopts descending method to solve the minimal cut set of accident tree.The method is down carried out step by step along accident tree from top event, if run into and door, then with door below all incoming events all arrange on a same row; If run into or door, then or door below all incoming events all come on same row.By that analogy, step by step down, until till being all bottom event.The bottom event set obtained like this is called that boolean shows cut set, just can obtain minimal cut set to be after the absorption Merging of Boolean algebra: { X ₄, { X ₁, { X ₂, { X ₃, { X ₁₀, X ₁₁, { X ₈, { X ₁₂, X ₁₃, X ₁₆, { X ₁₄, X ₁₅, X ₁₇, { X ₇, { X ₉, { X ₅, { X ₆.

As can be seen here, the possible approaches of Foundation Pit of Bolt Support structural system generation unsticking accident has 12 kinds, the elementary event that each minimal cut set comprises does not only have 1 to 3 not etc., that is, when only having 1 to 3 elementary events to occur simultaneously will there is unsticking accident in system, illustrate that the occurrence condition of such accident is easy to meet, the possibility that accident occurs is larger.

3.2 expert survey determination elementary event probability of happening

Table 2 Weight of Expert determines table

Because the probability of happening of each elementary event is without statistics, also cannot be drawn by design formulas, therefore, the present invention adopts expert survey to provide experience estimate to the probability of happening of each elementary event within 10 years.This is because geological conditions is constantly change, the operation of engineering also can change the geological environment of surrounding conversely, therefore, according to existing geologic information, tentatively is that a unit carries out risk profile with 10 years.By to there being 20 of foundation pit anchor relevant professional knowledge or engineering experience experts to investigate, and set corresponding weight according to the academic title, specialty etc. of each expert, then the judgement it done is weighted cumulative according to the weight of correspondence, and what finally obtain is exactly the most probable value of required target.

According to table 2, adopt each Weight of Expert of following formulae discovery.

$W_k=\underset{i=1}{\overset{4}{\mathrm{\Σ}}}{U}_i{V}_{\mathrm{ij}}---\left(4\right)$

In formula: W _kfor the scoring weight of kth position expert; U _i, V _ijimplication in table 2.As calculated, the weight distribution of 20 experts is in table 3.

Table 3 Weight of Expert distribution table

Weight of Expert is interval	0.8～1	0.7～0.8	0.6～0.7	0.4～0.6
					Expert's number	2	8	7	3

The operation hazard assessment method that probability of happening employing U.S. Green strategic point nurse (K.J.Graham) of elementary event and golden Buddhist nun (G.F.Kinney) propose, it is a kind of simple semi-quantitative assessment method of personnel's danger when having operation in potentially danger environment.The possibility score value of event of causing danger is in table 4.According to anchor bolt works concrete condition, ignore last 2 kinds of possibilities (extremely impossible and in fact impossible), front 5 kinds of possibilities are only discussed.In order to not make differential probability be greater than 1, its value is multiplied by 0.009 respectively.

Table 4 is caused danger the possibility score value of sexual behavior part

The possibility that accident occurs	Fractional value
		Can expect completely	10
Quite may	6
		May but infrequently	3
Possibility is little, completely surprisingly	1
		Very impossible, it is contemplated that	0.5
Extremely impossible	0.2
		Actual impossible	0.1

The determination of final elementary event probability of happening adopts following formula:

$P_i=\left(\underset{k=1}{\overset{20}{\mathrm{\Σ}}}{W}_k{Q}_{\mathrm{kl}}\right)/\underset{i=1}{\overset{20}{\mathrm{\Σ}}}{W}_k---\left(5\right)$

In formula: P _irepresent the final expert evaluation value of i-th elementary event probability of happening, Q _kifor kth position expert is to the assessed value of i-th elementary event probability of happening.

According to investigation result, the probability of happening that employing formula (4), (5) calculate each event is as shown in table 5:

Table 5 elementary event probability tables

Elementary event	X 1	X 2	X 2	X 4	X 5	X 6	X 7	X 8	X 9
										The probability of happening	0.0165	0.0278	0.0017	0.024	0.0012	0.021	0.021	0.0348	0.0219
Elementary event	X 10	X 11	X 12	X 13	X 14	X 15	X 16	X 17
										The probability of happening	0.030	0.011	0.025	0.004	0.0022	0.0132	0.0129	0.025

The probability calculation of 3.3 top events

If each other without the elementary event repeated in each minimal cut set, the probability of happening of top event is:

In formula, r is minimal cut set ordinal number; I is elementary event ordinal number; q _iit is the probability of i-th elementary event; N _gfor least partition assembly count in system; G _rbe r minimal cut set.

For convenience of the top event probability calculating soil anchor system accident tree, simplify as follows: 1. the probability of each elementary event is designated as q respectively _i; 2. all the minimal cut sets containing an event (are designated as G ₁), the minimal cut set containing 2 events (is designated as G ₂), the minimal cut set containing 3 events (is designated as G ₃) separately consider.

G ₁, G ₂, G ₃without any common factor, therefore the probability of happening of top event T can be reduced to

P(T)＝P(G ₁)+P(G ₂)+P(G ₃)(7)

The object of such simplification is that this three part is independent mutually, facilitates probability calculation.Can be found out by formula (6), G ₁each part is independent mutually, again due to only containing an event, the probability of happening addition contained by them is got final product P (G ₁)=0.1699; G ₃have 2 minimal cut sets, be respectively { X ₁₂, X ₁₃, X ₁₆, { X ₁₄, X ₁₅, X ₁₇, each minimal cut set contains 3 independent events, and by the probability multiplication of each event, acquired results is very little, can ignore the contribution of top event probability; G ₂only has a minimal cut set, G ₂={ X10, X11} calculate by formula (6), obtain P (G ₂)=0.030 × 0.011=0.00033.

P (T)=0.1699+0.00033=0.17023, namely the probability of top event is 0.17023.Known with reference to underground construction risk probability classification standard, such event belongs to sporadic accident.

3.4 sensitivity analysis

Calculate the probability of top event according to accident tree, can determine that the probability of unsticking accident may occur whole Bolt System on the one hand, can sensitivity analysis be passed through on the other hand, disclose the percentage contribution of elementary event for top event.

Elementary event sensitivity coefficient:

$C{I}_g\left(i\right)=\frac{\frac{\∂Q}{\∂q_i}}{\frac{Q}{q_i}}=\frac{\∂Q}{\∂q_i}\·\frac{q_i}{Q}---\left(8\right)$

Wherein, Q is probability of happening and P (T), the q of top event _iit is the probability of happening of i-th bottom event.

The each elementary event sensitiveness sequence of table 6

Sequence number	Elementary event	Sensitivity coefficient
			1	X 8	0.194
2	X 2	0.159
			3	X 4	0.144
4	X 7	0.133
			4	X 6	0.133
5	X 9	0.124
			6	X 17	0.092
6	X 1	0.092
			7	X 3	0.010
8	X 5	0.008
			9	X 10	0.0018
9	X 11	0.0018
			10	X 12	0.0006
10	X 13	0.0006
			11	X 14	0.0002
11	X 15	0.0002
			11	X 16	0.0002

The order of magnitude of sensitivity coefficient is nonsensical, and its sequence is more meaningful, is conducive to finding in accident tree, to the accident of top event, the most influential bottom event occurs, and table 6 is the sequencing tables calculated with sensitivity coefficient.This ranking results, decides the influence degree of each elementary event to top event and foundation pit anchor unsticking accident, has important directive significance to the establishment of safety evaluation report.

Analysis according to elementary event sensitiveness can be found out, soil bolt unsticking lost efficacy the most responsive to anchoring depth; In the reason causing soil bolt unsticking to lose efficacy, several factor such as " anchoring depth design is not enough ", " prestress application is excessive too early ", " cement mortar ratio is unreasonable ", " grouting way is unreasonable ", " slurry compactness is not enough ", " anchoring body surface area is too small ", " load is excessive " accounts for first six digits, and the sensitivity coefficient of these six events is obviously much bigger than other events, in the design and construction process of soil bolt, must draw attention.

And find the elementary event x relating to water damage ₁₂the 10th is sorted in 17 events, analyze reason, that event owing to relating to water damage is all only in " with door " structure, and be in " with door " structural event and can not appear at separately in a minimal cut set, the impact being in same minimal cut set event can be subject to when sensitivity analysis.The safety evaluation report reply sensitivity coefficient forward event that sorts is evaluated, and should consider to relate to be in sensitivity coefficient in " with door " structural event and to sort the most front several events simultaneously, and points out corresponding Safety Measures and suggestion.

Contrast table 5,6, can find out that sensitivity coefficient sequence is relevant with the probability size of bottom event, bottom event probability is larger, and the sequence of its sensitivity coefficient is more forward, and the probability of bottom event then depends on that people is to the degree of awareness of each event and investigation result.Therefore, the determination of bottom event probability is of crucial importance and complicated, bottom event method of determining probability in this paper, is to be based upon on the basis of expert investigation analysis.For Foundation Pit of Bolt Support engineering, still need a large amount of investigation statisticses to improve this work, with the bottom event probability of given accident tree more accurately.

The above; be only the present invention's preferably detailed description of the invention; protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses, the simple change of the technical scheme that can obtain apparently or equivalence are replaced and are all fallen within the scope of protection of the present invention.

Claims (1)

1. a foundation pit anchor unsticking safe evaluation method, is characterized in that, comprises the following steps:

(1) structure of foundation pit anchor unsticking accident tree

Extensive analysis causes the relation between the intermediate event of top event cause and elementary event, and arranged, then from top event, according to the method for Deductive method, layer by layer deeply, by the refinement gradually of each influence factor, until all factors are the elementary event being difficult to refinement again, and according to the logical relation that each factor is determined between them to top event generation role, form accident tree; Accident tree top event is foundation pit anchor unsticking accident, and intermediate event has two: the body of rod and grouting body interface unsticking and be in the milk body and soil layer interface unsticking;

(2) determination of minimal cut set

Minimal cut set adopt descending method try to achieve, the method is down carried out step by step along accident tree from top event, if run into and door, then with door below all incoming events all arrange on a same row; If run into or door, then or door below all incoming events all come on same row, by that analogy, step by step down, until till being all elementary event, the set of elementary event obtained like this is collectively referred to as boolean and shows cut set, after the absorption Merging of Boolean algebra, just can obtain minimal cut set, and the elementary event comprised in minimal cut set is called the basic reason event of accident;

(3) determination of elementary event probability

Elementary event probability of happening is determined by expert survey, and the determination of elementary event probability of happening adopts following formula:

$P_i=\left(\underset{k=1}{\overset{20}{\Σ}}{W}_k{Q}_{ki}\right)/\underset{k=1}{\overset{20}{\Σ}}{W}_k---\left(5\right)$

In formula: P _irepresent the final expert evaluation value of i-th elementary event probability of happening, Q _kifor kth position expert is to the assessed value of i-th elementary event probability of happening, W _kfor the scoring weight of kth position expert;

(4) quantitative analysis

Mainly comprise calculating two aspects of top event probability and each elementary event sensitivity coefficient:

A top event probability of happening utilizes minimal cut set to calculate;

If each other without the elementary event repeated in each minimal cut set, the probability of happening of top event is:

In formula, r is minimal cut set ordinal number; I is elementary event ordinal number; q _iit is the probability of i-th elementary event; N _gfor least partition assembly count in system; G _rbe r minimal cut set;

If minimal cut set has repeated events each other, when namely minimal cut set intersects, adopt method---the recursion method intersecting and turn to disjoint products will occurred in minimal cut set:

$T=F\left(1\right)+F\left(2\right)+\mathrm{......}+F\left(N_K\right)=\underset{i=1}{\overset{N_K}{\Σ}}F\left(I\right)$

Wherein

F(I)＝C(I)K(I)，

K (I)=K _i, wherein, for K _isupplementary set,

N _kfor the sum of accident tree minimal cut set.

B elementary event sensitiveness sorts

Elementary event sensitivity coefficient: wherein, Q is probability of happening and P (T), the q of top event _ibe the probability of happening of i-th elementary event, sorted by elementary event sensitivity coefficient, the percentage contribution of elementary event for top event can be disclosed;

(5) preventive damage control is formulated

On the basis of qualitative or quantitative analysis, the preventible complexity of the minimal cut set that accident may be caused to occur according to each or the combination of minimum path sets elementary event and importance degree, in conjunction with practical capacity, draw up concrete, practicable preventive action, and be put to carry out.