I am not to be blamed
Many accidents were blamed on the snow
be to blame
If a ship sinks, the captain is to blame
The increase in crime is a sad reflection on our society
The increase in crime is, sadly, to be blamed on our society
I am wondering about how is the function of applying the verb blame, that is, I cannot differentiate when to use it as an intransitive, or passive verb.
Furthermore, I am wonder if the bold parts might mean the same thing or not.
The word blame is used to reflect responsibility for something.
To answer your question about the bolded sentences: "The increase in crime is a sad reflection on our society," holds a nuance that suggests the crime is increasing because society is lacking in morals. There is no implied 'call to action' in that sentence.
In the second case: The increase in crime is, sadly, to be blamed on our society, the sentence uses the word blame which implies a sense of responsibility. Society is responsible for the crime, and it then follows that society is responsible to do something about the crime. This sentence creates a feeling of requiring action.
The word blame is always used transitively like the word "hit". You have to blame someone/something. Blame is used passively in writing, such as the examples that you mentioned. In modern American English, it is rarely used passively ("be to blame") in speech. It would be used with be ~ing instead:
"What happened?"
"They're blaming the captain because the ship sank."
"Oh! I thought they were blaming the ship company instead."
It is also possible to use blame actively, but it's quite rare. In fact, I can only think of it being used in a very direct way. ie. "I blame you/him/her." To which it would (typically) be unnatural to reply, "Why do you blame me/him/her?" You would have to respond, "Why are you blaming me/him/her?"
As a learner I always had the problem with this kind of sentences, but never got the proper answer.
Let's consider the following two sentences -
The film is expected to be released on coming Friday.
The film is expected to release on coming Friday.
I have seen both sentences, but my logic said that the passive form is only possible as the film can't release itself. It has to be someone who will release the film.
But I was wrong. Both of the sentences are possible and correct. Of course the film can't release itself, but it needs someone to release the film. But to understand these two sentences we need to think of them from a different point of view.
In both the sentences the subject of the infinitive clause is not explicitly mentioned. We imagine the superordinate subject to be the subject of the infinite clause. But that is not always the case; if we imagine the subject of the infinitive clause, we can even think of an indefinite subject also. So here lies the secret.
The film is expected to be released on coming Friday.
Here the implied subject of the infinitive clause is a superordinate subject. So we can re-write the sentence as the following, explicitly mentioning the superordinate subject as the subject of the infinitive clause -
The film is expected for it (the film) to be released on coming Friday.
Now consider the other sentence -
The film is expected to release on coming Friday.
Here the implied subject of the infinitive clause is not the superordinate subject, rather the implied subject of the infinitive clause is an indefinite subject. So we can re-write the sentence as the following, explicitly mentioning the indefinite subject as the subject of the infinitive clause -
The film is expected for others to release on coming Friday.
Now coming to your sentences with blame.
The captain is to be blamed.
The captain is to blame.
Both of the sentences are correct. In the first sentence the implied subject of the infinitive clause is the superordinate subject (he), and in the second sentence the implied subject of the infinitive clause is the indefinite subject (other). Now re-writing both the sentences explicitly mentioning the subject of the infinitive clause -
The captain is for the captain to be blamed.
The captain is for others to blame.
Let's explain this aspect of grammar in details.
The structure noun + infinitive can express the idea of obligation.Active and passive infinitives are both possible.
I have got letters to write.
The carpets to be cleaned are in the garage.
If the subject of the clause is the person who has to do the action, active infinitives are used.
I have got work to do (NOT I have got work to be done)
If the subject of the clause is the person or the thing that the action is done to, passive infinitives are normally used after be.
These sheets are to be washed. (NOT These sheets are to wash)
The form is to be filled in with blue ink. (NOT This form is to fill in with blue ink)
The cleaning is to be finished by midday (NOT *...is to finish...)
Active infinitives are possible in a structure with for (explicitly mentioning the subject of the infinitive clause using for)
This form is for you to fill in.
In other cases, active and passive infinitives are often both possible with the same meaning. (similar to your example sentences in your question)
There is a lot of work to do/to be done [when the implied subject of the infinitive clause is work, only to be done is correct. When the implied subject of the infinitive clause is e.g. others, to do is only possible.]
There are six letters to post/to be posted.
Give me the names of the people to contact/to be contacted.
The people to interview/to be interviewed are in the next room.
Consider the following sentence -
She write quickly enough to finish the paper on time.
The infinitive clause - to finish the paper on time - doesn't have a explicit subject, though it's understandable. We can re-write this sentence with a clear subject of the infinitive clause.
She write quickly enough for her to finish the paper on time.
So the subject of the infinitive clause can be omitted or retained if t substitute for the superordinate subject. When there is no subject in the infinitive clause, it's identified with superordinate subject or with an indefinite subject.
There are cases when ambiguity arises as to which subject is implied. Whether the superordinate subject or an indefinite subject is implied is not clear.
She is to young to date.[...for her to date others? or ...for others to date her...?]
When the subject of the superordinate clause is agentive, it may be redundantly repeated.
The knife is sharp enough for it (the knife) to carve the turkey.
Sometimes this optional redundancy is retained for emphasis purpose.
What is an Indefinite Subject?
Consider the following sentence -
We me you leaving the room.
If we hear this sentence, we keep guessing who is leaving the room - you? we? or you and us both?
We met you (when you? we? were) leaving the room.
With infinitive clause, a corresponding finite clause also enables one to identify an understood subject.
I asked to go ~ I asked if I could go.
I asked him to go ~ I asked if he would go.
When no referential link with the nominal can be discovered in the linguistic context, an indefinite subject may be inferred, or else the 'I' of the speaker:
The prospects are not very good, to be candid [...if I am to be candid']
In the above example the subject - I - is inferred, and so it's indefinite subject.
What is a Superordinate Subject?
The subject of a superordinate clause is called a superordinate subject.
A Superordinate clause in grammatical analysis is a term for a clause that contains another clause.
It was raining when I left home.
The clause - It was raining - contains another clause - when I left home. So the clause - It was raining - is the superordinate clause of the subordinate - when I left home.
The subject of the superordinate clause is it, and so it is called superordinate subject.
Agentive role -
Margaret is mowing the grass.
In this sentence Margaret is the subject, mowing is the verb and grass is the direct object of the verb.
The most typical semantic role of a subject in a clause that has a direct object is that of the Agentive participant: that is, the animate being instigating or causing the happening denoted by the verb.
I will only try to answer your last question: No, the two bolded sentences are not equivalent. To say that something "is a sad reflection on" means only that a society in which such crimes happen is not to be admired. It does not say that the society itself was the cause of those crimes. The two sentences aim the same direction, but one goes much further in actually accusing society of causing increased crime.
To begin with, we must remember that the word "blame", apart from being a noun, is only a transitive verb. I don't think it's necessary to explain as to how to form the active and passive voice with this transitive verb as I feel the OP has a good knowledge of Engish. I am sure his confusion is only because he thinks that "blame" is also an intransitive verb.
As a matter of fact, "be to blame" is an idiom, in which the word "blame" has been used as a noun. You use this idiom when you say that someone/something is responsible for something bad or is at fault, for example, which driver was to blame for the accident. Hence, "be to blame" is more idiomatic than "to be blamed".
Please look up the word the idiom "be to blame" in The Free Dictionary, which uses blame in the idiom as a noun.http://www.thefreedictionary.com/blame
As for two sentences about society, they convey the sense in different words.
